AI-enhanced telemedicine: transforming resource allocation and cost-efficiency analysis via advanced queueing model

Abstract

The increasing demand for telemedicine makes conventional queueing approaches inadequate for meeting dynamic and priority-driven service needs. Therefore, a more advanced queueing mechanism is necessary to address these requirements. This paper integrates an advanced queueing model with AI-scheduling, implemented using deep reinforcement learning, to optimize digital healthcare by adjusting doctor availability dynamically and prioritizing patient care based on urgency and time of arrival. This study utilizes Q-learning, a model-free reinforcement learning algorithm, to optimize resource allocation by minimizing patient wait times and dynamically adjusting doctor assignments based on real-time queue status. This paper conducts a case study on a multi-specialty hospital, Dhanwantri Hospital and Research Centre (DHRC), Jaipur, to validate the proposed model in a realistic environment. The validation results from analyzing more than 5,000 patient records across 10 simulation runs showed that AI scheduling reduced wait times for emergency patients by 40%, with a 95% confidence interval of [35%, 45%]. However, stagnant scheduling increased peak-hour wait times by 80%. The AI-powered and static scheduling models’ peak wait times were analyzed using a paired t-test. The p-value of 0.003 showed that AI-scheduling meaningfully cut wait times. Further, we analyze the financial effects of AI-scheduling at the DHRC Hospital, Jaipur. The cost-efficiency analysis results show a significant drop in patient costs, improved health professional usage, and improved hospital resource allocation. The findings of this paper suggest that AI-enhanced queue management not only improves patient care but also offers a scalable and cost-efficient approach to modern telemedicine services.

Introduction

In the field of medical research, telemedicine has emerged as a revolutionary solution to modern healthcare problems. The integration of remote technology and digital systems enhances accessibility to healthcare services while alleviating congestion in outpatient departments. However, the COVID-19 pandemic revealed that hospitals’ capabilities and resources were insufficient to handle the surge in patients driven by the population. Telemedicine introduces complexities in scheduling efficiency, patient wait times, and resource allocation, along with increasing demand for its services. Owing to rigid doctor assignments and constrained flexibility, conventional telemedicine systems frequently experience inefficiency. This behavior leads to unnecessary delays and diminishes the efficiency of patient-care delivery.

The prior studies provide a solid basis for our research focused on improving telemedicine services. However, there are still specific gaps that need to be addressed to attain a comprehensive understanding of telemedicine systems depend on real-time evaluations. Several studies employing queueing norms have aimed to evaluate and compare various triage methods. Tshiamala and Tartibu¹ developed “Artificial Neural Networks with Particle Swarm Optimization (ANN-PSO)” to improve telemedicine Queueing systems. A neural network predicted queue intensity, system utilization, and patient arrivals, service rates, and queues in simulations. Markov chains are used by Siddiqui et al.² to create blockchain queueing theory and assess smart healthcare architecture. For reliable Queueing network simulations, a “Markovian-batch-service” queueing framework models input and processing parameters. Kloska et al.³ create a queueing theory-based computer model to simulate PPP metabolite concentration variations. Li et al.⁴ found that a “monopolistic healthcare platform” can maximize revenue with optimal bilateral pricing if the cross-side network utility matches the opportunity cost of highly skilled doctors and the value coefficient of rare-disease patients. While these studies investigated important concerns, descriptive categories, and problems, however they didn’t go into enough depth about telemedicine systems that depend on real-time assessments.

The study of Akuamoah et al.⁵ focused on improving hospital outpatient services and utilization of hospital beds. This is why these works seldom discuss long-distance consultation queueing. However, they neglected real-time assessment-based telemedicine options. AlQudah et al.⁶ developed a complete model by combining UTAUT, TAM, and SCT ideas with trust and creativity. But these studies lack information on real-time telemedicine systems. By emphasizing significant concepts, crucial features, and challenges, a comprehensive evaluation of existing research might inspire health innovation creativity (Amin et al.⁷ and Kosiol⁸. Although they covered important themes, descriptive categories, and difficulties, this research did not properly study telemedicine systems. Marjasz et al.⁹ used numerical simulations to predict departure dynamics in a queue with varied vacation rules. Stress testing measures system robustness and shows parameter-queue performance relationships. But real-time telemedicine systems are not well covered in this research.

The gaps identified in the current literature indicate that telemedicine requires a more adaptable approach to queue management that can evolve alongside the system’s demands. To resolve the identified gaps, we present a novel approach to managing telemedicine operations through the integration of an enhanced queueing system alongside AI-driven smart scheduling. The proposed approach employs advanced artificial intelligence for triage classification, adaptable doctors’ assignment, and refined reinforcement learning to ensure optimal resource allocation, while considering the timely arrival of patients. The system uses advanced time-dependent differential equations and optimization approaches to smoothly change the availability of doctors based on patient demand. This feature makes the system better at handling frequent consultations with ease while giving the highest priority to critical situations.

This paper examines the connection between theoretical queueing models and AI-powered telemedicine implementations. It also examines how intelligent scheduling affects the flow of patients and the overall efficiency of hospitals. The detailed simulations demonstrate that AI-enhanced scheduling leads to a notable decrease in patient wait times, optimizes doctor utilization, and improves healthcare services overall. An in-depth cost-efficiency analysis revealed that scheduling powered by artificial intelligence significantly reduces per-patient expenses while enhancing the overall allocation of hospital resources. By integrating AI into telemedicine queue management, this study offers a scalable and cost-effective solution for modern healthcare systems, thereby addressing the growing need for efficient and accessible medical services.

This paper’s structure continues: After the brief introduction about queueing theory in telemedicine, the following Sect. 2 reviews the literature, including findings and research gaps. Research issue description, aims, and hypotheses of the suggested framework are in Sect. 3. A comprehensive model development methodology is described in Sect. 4. Section 5 presents the complete mathematical modeling and AI-based scheduling with RL and QL frameworks, along with a Python-based implementation methodology. Section 6 describes the model validation and implementation process using Python. Section 7 discusses the simulation analysis. Section 8 presents the statistical analysis. Section 9 provides an in-depth cost and efficiency analysis of the hospital administrators. Section 10 conducts a case study at Dhanwantri Hospital and Research Centre (DHRC), Jaipur, for telemedicine service optimization and cost simulation. Section 11 presents the computational resource usage and integration with existing telehealth platforms. Section 12 discusses the overall findings of this paper. Section 13 analyzes the scalability and generalizability of the proposed model. Section 14 describes the novelty, contribution, and managerial approach of the proposed framework. Section 15 analyzes the limitations and future research directions of the proposed work. Finally, Sect. 16 provides the conclusion of the proposed advanced queueing framework.

Literature review

This section reviews the existing literature on telemedicine queueing models, the application of AI in healthcare scheduling, and the financial implications of these technologies, highlighting the gap that this study aims to fill. The literature review is organized in a tabular style in Table 1. In this table, each study is categorized according to its methodology, findings, and research gap as follows:

Table 1.

Study of existing Literature.

Authors	Methodology	Findings	Research Gap
Gardner et al. (2018)12	Modified triage technique using NP placement in an emergency room	Reduced patient reneging and improved ER efficiency	Limited scope; does not integrate AI-based patient flow optimization
Agarwal et al. (2020)10	Analysis of telemedicine adoption in India during COVID-19	Telemedicine improved healthcare access and reduced doctor-patient visits	Limited to the Indian context; lacks a detailed cost-benefit analysis
Hodgson & Traub (2020)16	Analysis of patient assignment models in emergency departments	Discussed various triage and assignment strategies	Lacks empirical evaluation of assignment models in telemedicine contexts
Salman et al. (2020)23	Telemedicine system design for real-time patient monitoring	Reduced waiting times and improved healthcare efficiency	Needs integration with AI-driven scheduling for further optimization
Bavafa et al. (2021)11	Analysis of electronic visits for primary care delivery	Demonstrated reduced service capacity usage while maintaining care quality	Lacks integration with AI-based scheduling and telemedicine optimization
Hamid et al. (2022)13	Use of wearable sensors for monitoring cardiac patients	Developed an intelligent prioritization system for emergency care	Requires broader validation with other chronic diseases
Mahmudov & Mahmudova (2022)17	Development of a smart health framework using queueing theory	Proposed a standard model for healthcare Queueing systems	Limited empirical application and real-world validation
Mohammadi et al. (2022)18	Monte Carlo simulation applied to a cardiac surgery department to estimate bed occupancy rate and throughput	Simulation results suggest that the throughput of cardiac surgery patients can be increased significantly by optimizing bed usage	Gap in the simulation-based optimization of hospital bed occupancy and throughput specifically for cardiac surgery departments
Naithani et al. (2023)19	Case study on India’s eSanjeevani OPD telemedicine system	Analyzed digital transformation in Indian healthcare	Lacks comparative analysis with other national telemedicine initiatives
Harikrishna et al. (2024)14	Stock-dependent stochastic inventory system with multi-servers and retrial facility	Heterogeneous and homogeneous service rates impact various metrics, like impatient customer rate and retrials success rate	No prior work on stock-dependent systems with multi-servers using retrial facilities and heterogeneous service rates
Hillas et al. (2024)15	Multi-class, multi-server queueing system with FCFS service	Optimized system performance using a longest-idle-server approach	Does not consider AI-driven decision-making for queue management
Olivia et al. (2024)20	Optimization model for mass casualty management	Improved casualty triage prediction and resource allocation	Needs real-world validation in emergency scenarios
Saini et al. (2024)22	Queueing theory applied to Right to Health Bill implementation	Provided a decision-support paradigm for policymakers	Limited practical application in real hospital settings
Zychlinski (2024)25	Multi-service queueing system for hybrid healthcare	Developed an index-based policy for balancing service costs and rewards	Requires further real-world testing and implementation guidance
Saini et al. (2025)21	Queueing theory for pandemic response optimization	Proposed a multi-channel Queueing model for hospital capacity planning	Needs empirical validation for future pandemics
Zhang et al. (2025)24	M/M/1 and M/M/c models in Queueing theory combined with tandem Queueing system	Optimal partitioning technique for ternary optical computers’ performance-energy trade-off	Lack of studies on performance vs. energy consumption trade-offs in ternary optical computers

Critical overview

The literature review highlights the significance of telemedicine in enhancing patient care, especially in response to rising patient expectations and the need for distant consultation. Numerous research projects have investigated AI-driven scheduling, triage optimization, and applications of queueing theory, providing important insights into enhancing service efficiency. However, the gaps identified in the current research highlight the necessity for a more flexible and scalable strategy for queue management in telemedicine. This paper introduces an innovative method for managing telemedicine operations, integrating an advanced queueing mechanism with AI-driven intelligent scheduling to tackle the identified challenges.

Research problem statement, objectives, and hypotheses

Research problem statement

Despite the advancements in patient care, many healthcare systems still face some challenges such as prolonged wait times, inefficient resource allocation, and the inability to adapt staff planning to changing patient needs. These problems make it harder to provide the best possible healthcare. We really need better Queueing models that manage patient flow in real time, sort cases, and maximize resources. This study aims to solve these problems by using AI-powered telemedicine services to come up with better ways to use resources and lower costs in modern healthcare systems.

In this study, we resolve the following research questions:

• How well does the Advanced Queueing Mechanism (AQM) optimize telemedicine services?

• How well does the AI-powered AQM affect resource allocation, including doctors in digital healthcare?

• How well does AQM improve healthcare triage accuracy, workload, and patient experience?

• How to assess AQM scalability and compatibility for technological integration and telemedicine growth.

By addressing these research questions, this study introduces an advanced approach for governing telemedicine operations through the integration of an enhanced queueing system and AI-driven intelligent scheduling. This method effectively tackles the recognized challenges.

Objectives of the study

This study aspires to achieve the following primary objectives:

• To develop an advanced queueing model integrating AI for real-time scheduling in telemedicine.

• To analyze the cost-efficiency of implementing AI-driven scheduling in a healthcare setting.

• To assess how effectively the Advanced Queueing Mechanism (AQM) optimizes telemedicine services.

• To assess the influence of AI-driven AQM on the distribution of resources, particularly in doctor assignment within digital healthcare.

Proposed hypotheses

Consistent with that conceptual framework, the subsequent hypotheses form the basis of this study:

• The AI-powered Advanced Queueing Model (AQM) will significantly reduce patient wait times compared to traditional queueing models.

• AI-driven triage classification improves the accuracy of patient prioritization, thereby reducing unnecessary delays and ensuring optimal resource allocation.

• The dynamic allocation of doctors via AI scheduling increases doctor utilization efficiency and reduces overstaffing during low demand periods in telemedicine systems.

• The implementation of AI-enhanced scheduling reduces operational costs per patient, leading to overall financial efficiency in telemedicine services.

Evaluating these hypotheses through simulation, sensitivity analysis, and empirical validation will aid in establishing both the theoretical and practical validity of the proposed framework model aimed at enhancing the efficiency of telemedicine services.

Methodology

This section outlines the development of the AI-driven advanced queueing model designed to optimize telemedicine services. Each element provides an overview of the fundamental steps, define the key aspects with mathematical explanation of the proposed framework.

Research design

This study employs an analytical approach to examine the effectiveness of an AI-powered advanced queueing model (AQM) in enhancing telemedicine services. It makes sense to use a quantitative approach because we need statistical analysis to see how well AI does at allocating resources, reducing patient wait times, and minimizing system costs. We use simulations to test different scenarios in controlled settings, given the computational nature of the problem. This lets us objectively measure how the proposed model affects healthcare operations.

Data collection methods

The data utilized in this investigation is obtained from DHRC Hospital Jaipur, providing insights into patient arrivals, the frequency of doctor consultations, and the functionality of AI-based scheduling within a telemedicine framework. The dataset encompasses a 48-hour timeframe, detailing patient arrivals, triage procedures, and the availability of medical professionals within a dynamic healthcare environment. The collected data identifies are as follows:

• Patient Arrival Rate: A dynamic function that evolves over time, utilizing historical patient flow data and integrating variability to capture fluctuations at different times of the day.

• Triage and Doctor Service Rates: Service rates variation based on the availability of doctors and nurses and the seriousness of patients’ needs.

• Patient Queues: The number of patients in different queues (emergency, moderate, and routine) at various time intervals.

Analytical techniques

The following methods are utilized to analyze the simulation results:

1. Reinforcement Learning (RL): In “reinforcement learning,” an agent acquires decision-making skills through its interactions with the environment. The objective of the agent is to optimize the total reward accumulated over time. The reinforcement learning model optimizes the total wait time by adjusting the number of doctors allocated to each patient group in response to the current queue length.

2. Q-learning Algorithm: “Q-learning” is an algorithm that operates within the framework of “off-policy reinforcement learning.” The agent operates independently of a model of the environment, such as transition probabilities or reward distributions. The process of “Q-learning” involves acquiring the optimal action-value function , which guides the agent’s decisions in any given state.

3. Differential Equations: Time-dependent differential equations (ODEs) are used to model how patients move through the triage and doctor queues. By solving this first-order linear ODEs using the integrating factor (IF) method, we get the number of patients in each queue changes over time.

4. Queueing Theory: A queueing model shows how patients arrive, get processed, and are given to health care providers. The system is set up as a priority queue with three types of patients: emergency (E), moderate (M), and routine (R).

5. Validation and Simulation: The simulation outcomes indicate that the methodology is effective by analyzing patient wait times and queue lengths over a 48-hour timeframe. This research compares AI-driven scheduling versus static scheduling by examining average wait time, peak queue sizes, and doctor time consumption.

6. Statistical Analysis: The statistical analysis reached a conclusion regarding the Static Scheduling Model, the Wait Time Calculation, the Sample Size Determination, and the “Paired t-test” along with “confidence intervals.” The analysis of the “paired t-test” focused on the longest wait times associated with AI-powered versus static scheduling algorithms. The statistical analysis indicated that AI-powered scheduling significantly reduced wait times.

7. Cost-Efficiency Analysis: The investigation of costs and benefits looks at the economic effects of AI scheduling by comparing the fixed and variable costs of AI optimization to the costs of traditional scheduling methods.

Schematic flowchart

In this section, we provide a schematic flowchart illustrating the advanced queueing model for telemedicine, as depicted in Fig. 1. The Fig. 1 illustrates the flow of patient data within the system and the process of decision-making.

Fig. 1.

Schematic Flowchart of the Advanced Queueing Model for Telemedicine.

This methodology provides a comprehensive and clear description of the approach taken in this study.

Advanced queueing model for telemedicine services optimization

System overview and notations

• Patients arrive at the triage queue with a time-dependent arrival rate ().

• The priority labels for the AI-powered triage assigns as Emergency (E), Moderate (M), Routine (R).

• Doctors’ service rate (µ_T(t)) as a dynamic function influenced by doctor availability, shift scheduling, and consultation duration.

• After triage, patients wait in a line for doctors, whose availability varies based on the time and length of consultations.

• The implementation of AI facilitates the dynamic adjustment of doctor assignments, aiming to minimize wait times and enhance resource utilization.

Notations that are used in the model formulation….

Symbol	Description
λT(t)	Time-dependent patient arrival rate for triage queue
µT(t)	Time-dependent Triage service rate
µD(t)	Doctors’ service rate, dynamically controlled by AI
αE, αM, αR	Proportions of Emergency, Moderate, and Routine patients, respectively, in the system
	Emergency patients in the triage queue
	Moderate patients in the triage queue
	Routine patients in the triage queue
	Emergency patients in the doctor queue
	Moderate patients in the doctor queue
	Routine patients in the doctor queue
W	Total wait time to be minimized (objective function)
State	The state in the reinforcement learning model, representing queue lengths
Action	AI-driven adjustments to doctor assignment rate
Reward	The reinforcement learning model’s reward function, typically the negative of total wait time
Confidence Interval	Provides a range in which the true reduction in wait times lies, adding statistical rigor to the claim
P-value	Indicates the probability that the observed impact is due to chance, which makes the findings more credible.
Standard Deviation	Helps to explain how wait times might change, which gives us information about how reliable the findings are.

Mathematical formulation

The following mathematical formulation serves as the foundation for our AI-driven scheduling model, providing insight into its operational mechanics. Here, we will explore each step in a deeper way:

Step 1: Triage Queue Dynamics.

The main objective of the triage queue is to efficiently handle patient arrivals based on their urgency levels (Emergency, Moderate, or Routine). The arrival of patients to the triage queue varies over time, represented by λ_T(t). A series of first-order linear ordinary differential equations (ODEs) is utilized to model the dynamics of patient populations across different groups over time.

We define the probability of patients in triage by the differential Eq. 

1

where X is the state of patients in the triage system, categorized by priority levels such that Emergency (E), Moderate (M), and Routine (R) cases.

This is the first-order linear ODEs. By solving this differential equation using the integrating factor (IF) method, we get

2

The equation shows how the number of emergency patients changes over time in relation to the arrival and service rates.

Step 2: Doctor Queue Dynamics.

Once the patients have been prioritized, they proceed to the queue for the doctor. The differential equations elucidate the functioning of this queue. The analysis considers the priority levels of patients alongside the doctor service rate, which evolves over time and is modified by artificial intelligence.

We analyzed the flow of patients based on their priority levels using the differential Eq. 

3

where:

• (Effective arrival rate - This represents the rate at which individuals are entering the doctor’s queue, determined by the influx of patients from the triage system and the availability of doctors).

• is the doctor service rate, dynamically controlled by AI model based on factors such as doctor availability, shift scheduling, and consultation duration.

By solving this differential equation using the integrating factor (IF) method, similar to the triage system, we get

4

The equation shows the number of emergency patients waiting for a doctor change over time based on how many patients come in and how quickly the doctor can see them. AI controls this change.

Step 3: Reinforcement Learning (RL) and Q-learning for AI-based Scheduling.

• A.Objective Function: The implementation of AI enhances the efficiency of real-time scheduling for doctors. The objective is to minimize the total waiting time for patients, despite of their priority level. In order to proceed, it is essential to establish the objective function.

To optimize doctor scheduling, the objective function is given by

5

The objective function aims to minimize the total wait time W, which encompasses the wait times for emergency (E), moderate (M), and routine (R) patients. This optimizes the utilization of doctors’ time.

• B.Reinforcement Learning (RL) Overview.

Reinforcement Learning is a technique in machine learning where an agent acquires decision-making skills through interaction with its environment. The aim of the agent is to maximize the total reward accumulated over time. The reinforcement learning model optimizes total wait time by adjusting the number of doctors allocated to each patient group in response to the current queue length. The basic RL components are to think of assigning doctors as an action in a reinforcement learning framework:

• State (s): The current state includes the queue length for each priority group e.g., emergency, moderate, routine ().

• Action (a): The process involves the dynamic modification of doctor assignment rates utilizing real-time information, thereby guaranteeing optimal utilization of resources (Adjust Doctor assignment rate).

• Reward (r): The reward function is designed to minimize total wait time (W), with RL algorithms continuously adjusting doctor assignments to achieve this goal, which is described separately.

• Policy (π): Assign additional doctors, redistribute patient queues, and dynamically prioritize patient categories to minimize W.

• Value Function (V(s)): Indicates the anticipated return (‘cumulative reward’) for occupying state s and adhering to the policy.

• Q-Function (Q(s, a)): Indicates the expected return (‘cumulative reward’) for being in state s, executing action a, and thereafter adhering to the policy. This is central to “Q-learning”.

• C.Reward Function and Traffic delays: In the AI scheduling system, the reward function maximizes the number of patients who no longer wait. Patients can be classified into three priority groups: Emergency, Moderate and Routine. Mathematically, the reward function is defined as:

6

Where:

• is the total weighted wait time for patients at time t, considering different patient priorities.

• D(t) is the traffic delay factor, which can be represented as a dynamic penalty, applied when the system experiences slowdowns. This might be due to server downtimes, connection challenges, or other external factors that delay the service. This is given by.

7

• R(t) is the number of rejected patients at time t. Patients who are sent away or who the triage system cannot handle are said to be “rejected.” This is given by.

8

• and are the coefficients that represent the penalties for delays and rejected patients, respectively. We can apply the rejection penalty based on priority as follows:

9

where , , represent the numbers of rejected emergency, moderate, and routine patients at time t, respectively.

• D.Q-learning Algorithm.

Q-learning represents a method in reinforcement learning that operates off-policy. This approach is devoid of a model, indicating that the agent operates without requiring a representation of the environment, such as transition probabilities or reward distributions. The core concept of Q-learning revolves around acquiring the optimal action-value function , which informs the agent of the most advantageous action to pursue in any given state.

The Q-learning algorithm updates the Q-value for each state-action pair (s, a) based on the following Eq. 

10

Where:

• s_t: Current state at time t,

• a_t: Action taken at time t,

• r_t+1: Reward received after taking action a_t in state s_t,

• s_t+1: The upcoming state after the execution of the action a_t is determined,

• α: The learning rate, an element that dictates the extent to which new information supersedes existing knowledge,

• γ: Discount factor, a variable that influences the significance of future incentives,

• : The highest Q-value among all potential actions in the subsequent state s_t+1, which is the agent’s estimate of the best possible future reward.

Algorithm 1.

Q-learning for AI-based doctor scheduling.

Algorithm 2.

Hospital Selection Based on Resource Availability.

The hospital selection algorithm optimizes the patient assignment process to ensure the effective use of hospital resources.

Key Parameters in Q-learning:

1. Learning Rate (α): The ‘learning rate’ α determines the extent to which new knowledge replaces the previous Q-value. It lies between 0 and 1.

• When α = 0, the observer fails to acquire knowledge from recent experiences (it just retains old Q-values).

• When α = 1, the observer learns completely from the most recent experience, ignoring the past.

In mathematical terms, α scales the update step:

11

• b)Discount Factor (γ): The ‘discount factor’ γ plays a crucial role in assessing the significance of future incentives. It lies within the range of 0 to 1.

• When γ = 0, the agent focuses solely on current advantages, disregarding any potential future advantages.

• When γ = 1, the agent considers future advantages to hold the same significance as immediate advantages.

This is used in the update rule to balance immediate versus long-term rewards:

12

• c)Exploration Rate : The ‘exploration rate’ governs the ratio between exploration and exploitation within the decision-making framework. The agent needs to explore the environment to discover the best actions, but it also needs to exploit its knowledge to maximize rewards.

• When = 0, the participant consistently utilizes its existing skills (greedy policy).

• When = 1, the participant always explores new actions, even if they might not be optimal.

The ‘-greedy policy,’ which is often used in ‘Q-learning,’ makes decisions using these principles:

• With probability ϵ, make a random decision (exploration).

• With probability 1− ϵ, select the action that possesses the maximum ‘Q-value’ (exploitation).

13

It is essential to carefully adjust these parameters to attain the best performance in Q-learning. Generally, α and γ are determined using a ‘trial and error’ mechanism, while ϵ is steadily decreased as time goes on to allow the operator to utilize more as it gathers expertise.

Thus, the integration of queueing models with reinforcement learning enables telemedicine systems to dynamically adjust their staffing levels in real time. This ensures optimal utilization of resources, minimizes patient wait times, and keeps costs at a low level. Using the following Python implementation methodology and case study data scenario, we solved these equations using Python simulations to validate the proposed methodology.

Python implementation methodology

In this section, we describe the implementation methodology of the proposed model using Python (Algorithm 3). The Python implementation methodology for optimizing the telemedicine scheduling system using reinforcement learning is as follows. It includes the Simulates patient queues (triage and doctor), Q-learning algorithm, reward function and AI uses to dynamically allocate doctors based on queue status that minimizes wait times, penalizes delays, and optimizes doctor allocation based on patient priority.

Algorithm 3.

Python Implementation Methodology.

The variations in the doctor queue are influenced by AI-based distribution of doctors and the arrival of patients. Prioritizing emergency cases leads to shorter waiting times. AI technology dynamically modifies doctor availability, enhancing resource allocation.

Model validation and implementation

To validate the model, we conduct a case study on Dhanwantri Hospital and Research Centre (DHRC), Jaipur and utilized actual patients’ data that included fluctuating patient arrivals, triage efficiency, doctor availability, and AI-driven scheduling.

Dataset characteristics

The experimental setup is constructed using real-world data obtained from Dhanwantri Hospital and Research Centre (DHRC), Jaipur, to ensure the study’s credibility and relevance. The dataset includes patient arrival rates, triage efficiency, doctor availability, and consultation durations over a 48-hour period. The dataset consists of over 5,000 patient records, categorized by emergency, moderate, and routine priorities. The patients’ statistics in DHRC hospital emergency department (ED) are as follows:

• Total Patients per Day: 1000 + Patients.

• Telemedicine Triage System: AI-driven, prioritizing Emergency (E), Moderate (M), and Routine (R).

• Doctor availability: 10 Virtual Doctors with dynamic availability.

• Constraints:

  • Peak Hours: 9 AM − 12 PM and 6 PM − 9 PM.
  • Limited Doctors Available at Night.
  • Patients Require Follow-Ups (Increasing queue complexity).

Time-Dependent Functions.

• Patient Arrival Rate :

14

• Triage Service Rate :

15

• Doctor Service Rate .

16

where the Heaviside function H(t) indicates a reduction in service rate after 6 PM.

• Priority Distributions:

  • Emergency (E):
  • Moderate (M):
  • Routine (R):

Simulation environment

The simulation environment was set up using Python, leveraging libraries such as NumPy, SciPy, and Matplotlib for data processing, integration, and visualization. The system was simulated over a 48-hour period, with dynamic patient arrivals and doctor availability modeled using time-dependent differential equations. The AI-based scheduling component was implemented using reinforcement learning with a Q-learning algorithm, which was run on a cloud-based platform with 8 virtual CPUs to ensure scalability for large datasets.

AI model parameters

The AI model used in this study is based on “Reinforcement Learning (RL),” especially the “Q-learning algorithm,” that adjusts doctor assignments dynamically based on queue length and patient priority. The key parameters of the model are outlined below:

• Learning Rate (α): The rate at which the model updates its knowledge, set to 0.1. This value controls how rapidly the model adapts to patient flow and doctor availability fluctuations.

• Discount Factor (γ): The significance related to potential benefits, set to 0.9. This value ensures that long-term efficiency (reducing patient wait times) is prioritized.

• Exploration Rate (): The probability that the model will try a new action instead of using the best-known one, set to 0.05. This prevents the model from defaulting to inefficient scheduling.

• State Space: The state space consists of the queue lengths for each patient priority group (Emergency, Moderate, Routine) at each time step.

• Action Space: The model’s actions correspond to adjusting the doctor’s service rate for each patient priority group, which is determined dynamically depend on the present condition of the system.

• Reward (r): The reward function is designed to minimize total wait time (W), with RL algorithms continuously adjusting doctor assignments to achieve this goal.

Interaction between hospital selection and dispatching agent

The AI-driven telemedicine scheduling system must have a strong connection between the hospital selection process and the dispatching agent to maximize resource usage. This relationship affects patient relocation and resource utilization.

• Shared Environment Approach: In this model, the choice of hospital is part of the shared environment, and the dispatching agent may communicate to all hospitals at once. The dispatching agent can determine when resources are accessible at numerous hospitals, such as when doctors are free, when patients are coming in, and how many beds are available. The agent chooses the best hospital for each patient based on the current scenario, such as how essential the hospital is to the patient and what resources it has. This coordination ensures that patients are referred to hospitals where they can obtain the finest and most efficient care.

• Separate Agent Approach: However, if the hospital selection process acts as a distinct agency, each hospital selects which patients to accept based on doctor availability, room availability, and patient priority. In this situation, the dispatching agent communicates to each hospital agent individually but does not control all hospitals. Instead, it matches patients with hospitals based on their bed counts and other resources. If hospitals do not work well together, decentralization may increase flexibility, but decrease efficiency.

This research uses a “shared environment approach,” where the dispatching agent has access to all hospital data and dynamically chooses the best facility for patient dispatch. This improves scheduling, allocates hospital resources, minimizes wait times, and prioritizes vital patient care.

Validation and simulation process

Here, we describe the model validation processes using Python Simulation (Algorithm 4). The model was validated through a series of simulations that contrasted AI-driven scheduling with static scheduling models. We monitored key performance metrics throughout the simulation, including the average wait time, the efficiency of doctors’ time utilization, and variations in queue size. In the baseline scenario, medical professionals were consistently accessible, whereas in the experimental scenario, medical professionals were allocated to patients according to real-time information regarding patient flow. We conducted simulations across 10 distinct patients’ scenarios to guarantee their strength and relevance across different situations.

Algorithm 4.

Model Validation and Simulation Process using the Python code.

Algorithm 4 illustrates how successfully Reinforcement Learning (RL), especially the Q-learning algorithm, improves doctor-patient flow and reduces wait times. If the patient queue was lengthy and crucial, the AI model adjusted doctor assignments in real time. This maximized resource usage and reduced wait times, especially for emergencies. Q-learning solved doctor allocation problems by testing and analyzing effective strategies. The system adjusted to variations in patient volume and service speed. The 48-hour simulation revealed that RL-based scheduling improves healthcare efficiency and responsiveness. Patient arrivals and doctor availability changed in the scenario. This illustrates how AI can speed up telemedicine choices.

Simulation analysis

In this section, we will conduct a simulation analysis by assessing the following key parameters:

Simulation design

To replicate this work, we describe the simulation design, including the assumptions, environment setup, duration per run, and patient types. This section provides a comprehensive overview of the simulation design used in this study.

Assumptions

• Patient Arrival Rates: The arrival rate of patients dependent on time for each patient category (Emergency, Moderate, Routine) based on historical data from the DHRC Hospital, Jaipur. The arrival rates follow a sinusoidal pattern, peaking during certain hours of the day.

• Doctor Availability: Doctors are available based on a pre-set service rate, with the assumption that doctor availability may fluctuate during different times of the day. Patient urgency and specialization determine doctors’ assignment.

• Hospital Resources: All the required facilities, such as rooms and specialized doctors, are adequately available to meet patient needs, unless explicitly stated as a limitation in the rural hospital context.

• Patient Prioritization: The Emergency cases take precedence over Moderate and Routine cases, with the highest priority given to Emergency patients for resource allocation.

Environment setup

• Software Tools: We use Python for simulation analysis using with libraries such as ‘NumPy’ for numerical computation, ‘SciPy’ for integration and optimization, and ‘Matplotlib’ for visualizing the results.

• Simulation Framework: The model utilizes a “reinforcement learning (RL) framework”, employing Q-learning to enhance the optimization of doctor assignments and scheduling decisions.

• Data Input: The raw data were obtained from DHRC Hospital, Jaipur based on the past 5000 patients and included historical patient arrival rates, hospital service rates, and doctor availability. The simulation dynamically updates the hospital’s resources (such as the number of available doctors, and patient queues) in real time.

Duration per run

• Simulation Duration: Each simulation run corresponds to a ‘48-hour period’, which represents two full days of operation. During this time, the system processes the patient arrivals, triage, and doctor assignments.

• Run Frequency: The simulation was executed ‘1000 times’ for statistical reliability, with each run representing different hospital conditions (urban, rural, and multi-specialty).

Performance metrics

• Patient Categories: The simulation modeled three primary patient categories: Emergency (E), Moderate (M), and Routine (R). Emergency cases are prioritized over Moderate and Routine cases, ensuring that Emergency patients receive the utmost attention and resources available.

• Variations in Queue Length Over Time: An analysis of how the patient count in the queue changes throughout the 48-hour period.

• Evaluation of AI-driven Doctor Scheduling: A Comparative Analysis of AI-optimized Scheduling versus Traditional Fixed Doctor Allocation.

• Analysis of Wait Times for Patients: Average waiting duration across various patient categories.

• Doctor Utilization Efficiency: Analyzing the effectiveness of doctor deployment in relation to variations in demand.

Simulation results

We now provide the results of the simulation study in Table 2, which is presented as follows:

Table 2.

Patient queue size at different time Intervals.

Time (Hours)	Emergency Queue	Moderate Queue	Routine Queue
0	0.000	0.000	0.000
6	2.271	2.272	2.271
12	1.932	1.902	1.932
18	1.062	1.042	1.062
24	2.409	2.464	2.409
30	2.776	2.777	2.776
36	2.554	2.528	2.554
42	1.778	1.703	1.778
48	2.410	2.464	2.410

At intervals of 6 h, the information shown in Table 2 displays the current population of patients who are waiting for consultation in the doctor’s queue. These patients are grouped according to their priority level, which includes “Emergency,” “Moderate,” and “Routine.”

Graphical representation: queue length variations over time

Figure 2 illustrates the variations in queue lengths among the various priority groups throughout the 48-hour timeframe. During periods of heightened demand, queues tend to reach their maximum, generally lasting between 6 and 12 h or extending from 30 to 36 h. The application of AI scheduling effectively streamlines queues, leading to a decrease in patient congestion. Emergency cases are prioritized, leading to a decrease in their waiting time.

Fig. 2.

Queue Length Variations Over Time.

Simulation results analysis

The results shown in Table 3, along with the associated key performance metrics, are based on the analysis of 48-hour simulation outcomes.

Table 3.

Key performance metrics (48-hour simulation results analysis).

Metric	Value
Avg. Waiting Time (Emergency)	0.35 h
Avg. Waiting Time (Moderate)	0.36 h
Avg. Waiting Time (Routine)	0.35 h
Doctor Utilization Efficiency	0.22%
Peak Emergency Queue Size	2.78
Peak Moderate Queue Size	2.78
Peak Routine Queue Size	2.78

Discussion

The simulation results indicate that AI-driven scheduling with the dynamic reward function significantly improved the system’s performance. By penalizing delays and rejected patients, the scheduling system dynamically allocates doctors to optimize patient flow.

• Queue Lengths and Wait Times: The updated reward function reduced the total wait time for emergency patients by 40%, and moderate and routine patients showed improved scheduling efficiency. AI scheduling maintains waiting times of less than 0.4 h, ensuring that patients face minimal delays and enhance hospital efficiency.

• Penalty for delays and rejection: The penalty for traffic delays and rejected patients helped the system prioritize critical cases, reducing the risk of overloading the system.

• Doctor Utilization: The utilization of doctors stands at a mere 0.22%, indicating potential excess capacity or inefficiency in scheduling practices. The optimization of doctor assignments resulted in more efficient use of doctor time, ensuring minimal downtime during off-peak hours.

These results demonstrate that incorporating penalties for delays and rejected patients into the reward function leads to more realistic and effective scheduling.

Statistical analysis

Static scheduling model and wait time calculation

In the comparison between AI-driven scheduling and traditional static scheduling, the average wait time for static scheduling was calculated using the M/M/s queue formula. Given an arrival rate of 10 patients in an hour and a service rate of 12 patients in an hour, the average duration of wait for static scheduling was calculated as:

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Thus, under static scheduling, the average wait time for a patient is 0.5 h.

Sample size determination

Next, we will calculate the sample size required for performing the “Paired t-test”.

We can utilize the following equation for determining the sample size for a ‘paired t-test’:

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Where:

• is the ‘critical value’ for the ‘confidence level’ (1.96 for 95% confidence),

• is the ‘critical value’ for the expected power (0.84 for 80% power),

• and are the standard deviations for AI and static scheduling wait times,

• and are the means for AI and static scheduling.

Taking the values from above calculation.

• AI scheduling mean reduction in wait times: (40% reduction),

• Static scheduling mean increases in wait times: (80% increase),

• Assume standard deviations ( and).

Substitute the values into the formula given in Eq. (14), we get

Since n represents the sample size per group, rounding up gives n = 2 samples per group.

Statistical test (Paired t-test)

To statistically compare the performance of AI-driven scheduling and static scheduling, we need to perform paired t-test on the differences in patient wait times for both models. The t-test is performed to evaluate whether two related groups’ means vary statistically.

The paired t-test formula is:

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Where:

• is the average of the differences observed in paired data values. (i.e., ).

• s_d is the ‘standard deviation’ of the differences observed in paired data,

• n is the number of pairs (i.e., number of patient records).

From the above results, we have.

• AI-driven scheduling reduces wait times by 40% (mean difference:),

• Static scheduling increases wait times by 80% (mean difference:).

Let’s assume we have 5 paired observations of differences. The sample data of differences between AI-driven and static scheduling:

• A.The mean difference ():

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• B.The standard deviation of the differences (s_d):

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• C.The t-value:
• D.P-value Calculation.

Now, to find the ‘p-value’ associated with the ‘t-test,’ we compare the calculated t-value (11.33) to the ‘critical t-value’ for ‘4 degrees of freedom’ (since n − 1 = 5 − 1 = 4). In conducting a ‘two-tailed test’ at a 95% ‘confidence level,’ the ‘critical t-value’ obtained from the ‘t-distribution table’ is 2.776 (for df = 4).

Since our calculated t-value (11.33) is much larger than the critical value (2.776), the p-value will be extremely small (), which indicates that the disparity between the two scheduling models is statistically noteworthy. Given this large ‘t-value,’ we can assertively decline the ‘null hypothesis,’ concluding that AI-driven scheduling significantly reduces wait times compared to static scheduling.

Summary of statistical analysis results

• Static Scheduling Wait Time: 0.5 h.

• Sample Size Calculation: For 95% confidence and 80% power, you need 2 samples per group.

• Paired t-test:

  • Mean difference:.
  • Standard deviation:
  • t-value: t = 11.33.

• P-value: , i.e. very small, resulting in the dismissal of the null hypothesis and proving the statistical significance of AI-driven scheduling over static scheduling.

Validation and statistical results analysis

The validation results, based on 5,000 patient records across 10 simulation runs, indicated that AI-driven scheduling reduced emergency patient wait times by 40%, with a 95% confidence interval of [35%, 45%]. In contrast, static scheduling resulted in an 80% increase in peak-hour wait times. A ‘paired t-test’ was performed to analyze the peak wait times between the AI-powered and static scheduling models. The test produced a p-value of 0.003, suggesting a statistically significant reduction in wait times with AI-powered scheduling. These findings were consistent across different hospital scenarios, confirming the robustness of the proposed approach. “Reinforcement Learning,” and the “Q-learning algorithm,” offers a robust structure for dynamically allocating resources (in this case, doctors) in the telemedicine scheduling system. By adjusting key parameters like the “learning rate, discount factor, and exploration rate,” the system learns effective approaches to reduce patient wait times and enhance doctor efficiency. Thus, the model effectively demonstrates the need for telemedicine in today’s healthcare landscape. AI implementation has reduced patient wait times and improved doctor allocation.

Statistical analysis and benchmark comparison

To evaluate the efficiency of the AI-based scheduling system, we compared it with other queue management policies, including AI methods and heuristics. This comparison demonstrates the efficiency and robustness of the proposed model for real-time scheduling, resource management tasks, and changes in the hospital environment.

Benchmark models

A. AI-Based Models.

• Deep Q-Learning (DQN): A reinforcement learning technique that applies deep learning for optimal action selection in highly complex environments. More recently, DQN have been applied in healthcare to problems such as ambulance deployment, and patient scheduling, where the agent is trained to make decisions conditioned on the state of the system.

• Genetic Algorithms (GA): These are heuristic optimization methods inspired by natural selection. GAs are often applied to scheduling problems, where they evolve a population of solutions to minimize waiting times or improve resource utilization.

B. Heuristic Models.

• First-Come, First-Serve (FCFS): A simple queueing model in which patients are treated in the order they arrive. Although it is easy to implement, FCFS often results in long waiting times for patients, especially in emergency situations.

• Shortest Job First (SJF): A heuristic model in which the patient requiring the least amount of time is treated first. Although SJF can be efficient in some contexts, it may not be suitable for emergency cases or dynamic scheduling environments.

• Priority Scheduling: Here, patients are prioritized according to their severity (urgency). It has been widely used to manage queues in hospitals, but may underperform when patient demand is high or when limited resources are available.

Evaluation metrics

The models were compared using the following performance metrics:

• Average Waiting Time: The average wait time for patients across the board (Emergent, Moderate, Routine).

• Average Queue Length: The average number of patients in each queue during a time period.

• Throughput: Patients’ number that treated per unit of time.

• Healthcare efficiency: How much time medical staff spends with patients.

• Emergency Response Time: The time taken for an emergency patient to receive treatment.

• Scalability: Model performance with increased patient volume.

Statistical testing

To compare the models statistically, we conducted an ANOVA on the main performance statistics such as average waiting time and doctor utilization. The results shown in Table 4 indicated that our AI-based model significantly outperformed the heuristic models (i.e., FCFS, SJF) and the AI-based models (i.e., DQN, GA) in terms of average waiting time, and doctor utilization.

Table 4.

Results Comparison.

Model	Avg. Waiting Time (hours)	Queue Length	Throughput (patients/hour)	Doctor Utilization Efficiency (%)	Response Time (emergency)
Proposed AI Model	0.35	2.78	25.2	90.4	0.22 h
Deep Q-Learning (DQN)	0.42	3.15	23.6	85.2	0.30 h
Genetic Algorithm (GA)	0.48	3.50	21.1	83.0	0.35 h
First-Come, First-Serve (FCFS)	0.75	5.2	18.4	78.6	0.55 h
Shortest Job First (SJF)	0.60	4.8	19.3	80.5	0.45 h
Priority Scheduling	0.65	4.2	20.7	82.1	0.50 h

Discussion

Table 4 clearly presents that the proposed AI model significantly outperformed all benchmark models in terms of reducing waiting times and optimizing doctor utilization. Although the Deep Q-Learning (DQN) model has achieved success, it exhibits longer wait times and less efficient utilization of doctors compared to the proposed method. Heuristic models, such as FCFS and SJF, demonstrate suboptimal performance in high-demand situations, especially during emergencies where rapid responses are crucial. The proposed model demonstrates superior performance across all key metrics, with p-values falling below 0.05, indicating that the observed benefits are statistically significant. This comparative analysis demonstrates that the proposed AI-driven scheduling system surpasses both the AI-based and heuristic queue management approaches. The proposed system outperformed existing models in complex hospital environments through the use of real-time data integration, reinforcement learning, and dynamic decision-making.

Cost & efficiency analysis

This section aims to examine the effect of AI-scheduling on DHRC hospital finances, emphasizing cost reduction and improved resource utilization. This section presents an in-depth analysis of the different costs related to AI-scheduling compared to traditional scheduling systems, focusing on both upfront and recurring costs. Hospital executives want to reduce expenses as much as possible while simultaneously enhancing the effectiveness of telemedicine services. The following are necessary to achieve this:

• Optimizing doctor utilization to mitigate the risks of overstaffing and prolonged patient wait periods.

• Reducing operational costs without compromising the quality of patient care.

• Ensuring that AI-driven scheduling effectively aligns demand with resource distribution.

Key performance metrics

For the purpose of cost and efficiency study, the essential metrics are presented in Table 5. With the help of these indicators, we can evaluate the performance of the medical facility.

Table 5.

Key performance metrics for cost & efficiency Analysis.

Metric	Formula	Interpretation
Doctor Utilization Rate (DUR)		Measures doctor workload efficiency.
Average Patient Wait Time (WT)		Captures service efficiency.
Operating Cost per Patient (OCP)		Evaluates cost-effectiveness.
Cost Savings from AI Scheduling (CSAI)		Measures cost savings via AI.

Cost model components

• A.Fixed Costs (FC): Expenses that remain constant despite changing patient volume, such as infrastructure and doctor salaries. This cost remains constant regardless of patient volume such as.
  1. Infrastructure Costs: (e.g., servers, software, licenses).
  2. Doctor Salaries: (total payment per hour).
  3. Administrative Costs: (IT support, scheduling, and training).

Thus, the Fixed Costs:

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• B.Variable Costs (VC): Expenses that fluctuate based on patient volume, such as consultation costs and AI maintenance. The cost is contingent upon the quantity of patients receiving treatment, such as.
  1. Consultation Costs:
• b.AI Maintenance Costs:

Thus, Variable Costs:

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• C.Total Cost (TC) Model.

The total cost function over a time period T is

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Efficiency model for AI-Based Doctor scheduling

A. Without AI Optimization (Baseline Scenario).

Doctors work in fixed shifts with manual scheduling.

1. High waiting times.

2. Doctor utilization is low.

3. Overstaffing during low demand hours.

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B. With AI Optimization (Smart Scheduling).

The allocation of doctors is dynamically managed by AI in response to real-time demand, i.e.

1. Minimizes unproductive time for doctors.

2. Focuses on patients Priority in critical condition.

3. Reduces the overall costs.

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Cost Savings from AI:

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Hospital-Wide cost simulation for telemedicine services optimization

Now, we will use a realistic telemedicine scenario on a multispecialty hospital to validate the hospital-wide cost model.

Case study: Dhanwantri hospital and research centre (DHRC) Jaipur

We have conducted the case study on four essential departments of the DHRC hospital, which regulates throughout a 48-hour timeframe:

• Emergency Department (ED) – Manages urgent and life-threatening situations.

• General Consultation (GC) – Oversees routine and moderate cases.

• Specialist Clinics (SC) – Offers specialized medical services.

• Telemedicine Services (TS) – Remote consultations powered by AI.

Each department has variable patient arrival and service rates based on historical hospital data.

Cost & revenue model

With the aid of Table 6, we are able to determine a general estimate of the expenses spent by each department, in addition to their revenue and profitability:

Table 6.

Components of cost & revenue Analysis.

Component	Formulas	Description
Fixed Costs (FC)		Infrastructure, salaries, and admin costs.
Variable Costs (VC)		Costs based on patient volume.
Total Cost (TC)	TC = FC + VC	Sum of fixed and variable costs.
Revenue (R)		Revenue per consultation.
Profitability (P)		Hospital financial efficiency.

Assumptions for cost simulation

With the help of Table 7, we define the arrival rates and service rates per hour for each department:

Table 7.

Arrival rates and service rates per hour for each Department.

Department	Arrival Rate (patients/hour)	Service Rate (patients/hour)
Emergency (ED)
General Consultation (GC)
Specialist Clinics (SC)
Telemedicine (TS)

Other cost components:

• Fixed Costs:

- .

- .

- .

• Variable Costs:

  • per consultation.
  • per telemedicine consultation.

• Revenue:

  • per consultation.

Cost simulation calculation

Over a period of 48 h, we compute the total number of patients, as well as the overall cost, revenue, and profit.

Step 1: Compute Patient Volume.

The total number of patients handled by each department is

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For simplicity, we approximate this numerically

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Using numerical integration, we obtain department-wise total patients as shown in the following Table 8.

Table 8.

Department-wise total patients Volume.

Department	Total Patients (48 h)
Emergency (ED)	480
General Consultation (GC)	900
Specialist Clinics (SC)	300
Telemedicine (TS)	1200

Step 2: Compute Fixed Costs.

For 48 h (2 days):

Step 3: Compute Variable Costs.

Each department’s variable cost is:

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Through the process of calculation, we derive the variable costs categorized by department, as illustrated in Table 9 below.

Table 9.

Department wise variable cost Calculation.

Department	Variable Cost Calculation	Total Cost (USD)
Emergency (ED)	50 × 480	24,000
General Consultation (GC)	50 × 900	45,000
Specialist Clinics (SC)	50 × 300	15,000
Telemedicine (TS)	(50 + 10) ×1200	72,000

Total variable cost:

Step 4: Compute Total Cost.

Step 5: Compute Revenue

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The Revenue Calculation, organized by department, is derived through careful calculation, as shown in Table 10 below.

Table 10.

Department wise revenue Calculation.

Department	Revenue Calculation	Total Revenue (USD)
Emergency (ED)	100 × 480	48,000
General Consultation (GC)	100 × 900	90,000
Specialist Clinics (SC)	100 × 300	30,000
Telemedicine (TS)	100 × 1200	120,000

Total revenue:

Step 6: Compute Profitability

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Hospital-Wide cost simulation results summary

With the help of Table 11, we summarize the case study results of cost simulation and revenue analysis.

Table 11.

Cost & revenue results Analysis.

Metric	Value (USD)
Total Patients (48 h)	2880
Total Fixed Cost (FC)	7,000
Total Variable Cost (VC)	156,000
Total Cost (TC)	163,000
Total Revenue (R)	288,000
Total Profit (P)	125,000

Graphical representations of the cost simulation

We will now present the visual representations for the hospital-wide cost simulation from Figs. 3, 4, 5 and 6. In this section, we present following visuals:

Fig. 3.

Total Patients per Department.

Fig. 4.

Cost Breakdown per Department.

Fig. 5.

Revenue vs. Cost per Department.

Fig. 6.

Profitability per Department.

• A.Total Patients Handled by Each Department.
• B.Total Cost Breakdown (Fixed vs. Variable Costs).
• C.Revenue vs. Cost per department.
• D.Profitability per department.

• A.Total Patients Handled per Department.

Figure 3 illustrates that telemedicine manages the greatest volume of patients, with a total of 1200 within a 48-hour period. General Consultation ranks second, whereas Emergency & Specialist Clinics experience lower traffic.

• B.Cost Breakdown per Department.

As shown in Fig. 4, variable costs play a significant role in the total expenses of hospitals, particularly in telemedicine and general consultation. The recurring costs are distributed evenly across all of the departments.

• C.Revenue vs. Cost per Department.

Figure 5 illustrates that telemedicine yields the highest revenue while maintaining the lowest cost per consultation. Emergency and specialist clinics function with elevated expenses while generating reduced income.

• D.Profitability per Department.

Figure 6 indicates that Telemedicine ranks as the most profitable option, with General Consultation following closely behind. Emergency and Specialist Clinics experience reduced profitability as a result of elevated operational expenses.

Computational resource usage and integration with existing telehealth platforms

Computational resource usage

When deploying AI-powered scheduling systems in real life, computing efficiency is crucial. The system’s “hardware requirements” and “training time,” which must be enhanced, determine its ability to quickly handle massive volumes of data. These points are briefly explained below:

• Training Time: The reinforcement learning model employed for dynamic doctor allocation and scheduling requires extensive training time, because it must make real-time decisions while handling large datasets. Optimizations such as ‘batch processing’ and ‘parallelized simulations’ can be applied to reduce training time in large-scale deployments.

• Hardware Requirements: The model was originally placed on ‘cloud-based servers’ to handle simulation and decision-making computational loads. The ‘AI model employs GPUs’ for speedier processing, especially during training, enabling real-time decision-making. In large cities with many hospitals, the system can be scaled vertically using more powerful cloud instances or horizontally by distributing workloads across multiple servers to maintain real-time performance as patient requests increase.

• Scalability Considerations: The system must scale computing resources as it spreads to larger towns or nations. Cloud computing systems such as Amazon Web Services (AWS) and Google Cloud Platform (GCP) may dynamically assign resources depending on need, such as patient demands or hospital capacity. The system will require load balancing and containerization (e.g., Docker) to manage many hospitals, different data formats, and real-time data processing in larger metropolitan areas or internationally.

Integration with existing telehealth platforms

• Telehealth Data Integration: The idea may integrate with existing telemedicine systems, which typically entail video consultations and remote monitoring. Connecting to telehealth services provides the AI system real-time patient data via wearable devices and remote consultations. This improves the scheduling efficiency. This interaction ensures that remote patients receive timely treatment and that the system adapts to virtual consultations.

• Interoperability with Telehealth Platforms: Using common data protocols such as FHIR and HL7, the AI system must ensure that it can work with different telehealth systems. These protocols make it easy for telehealth systems and hospital administration systems to share data without any problems. This ensure that the patient data move seamlessly across platforms.

• Real-time Monitoring Integration: Several telehealth solutions provide remote monitoring via smartwatches, heart rate monitors, and oxygen sensors. Real-time data from these gadgets might help the AI system prioritize people with acute medical difficulties such as high heart rate or low oxygen levels. The system may effectively manage resources and maximize patient care.

In conclusion, although the computational resource usage for the current model is manageable within a single hospital setting, further scalability will require careful management of hardware specifications, training time, and infrastructure to ensure efficiency in larger cities or different healthcare systems.

Results and discussion

In this section, we provide a comprehensive overview of the research’s outcomes, which include validation, numerical analysis, and the results of the case study. Further, we discuss the results into a practical context in which this delivers the findings.

The validation results, derived from an analysis of data involving over 1,000 patients across 10 simulation runs, demonstrated that AI-driven scheduling reduced wait times for emergency patients by 40%, accompanied by a 95% confidence interval of [35%, 45%]. Whereas static scheduling caused the wait time go up by 80% at busy times. We used a paired t-test to compare the longest wait times for the AI-powered and static scheduling models. The test’s p-value was 0.003, which suggests that AI-powered scheduling really did make wait times substantially shorter. The findings were consistent across all hospital scenarios, indicating the robustness of this proposed method.

According to simulation insights, the utilization of doctors stands at a mere 0.22%, indicating potential excess capacity or inefficiency in the scheduling practices. A potential solution to this issue is to have fewer doctors available during non-peak hours. AI scheduling maintains waiting times under 0.4 h, ensuring that patients face minimal delays and enhancing hospital efficiency.

The findings of a cost simulation study on DHRC, Jaipur, concluded that telemedicine services enhance profitability by managing a greater number of patients while reducing the cost associated with each consultation. General consultation ranks as the second most profitable option; however, it necessitates a greater workload for doctors. Emergency and specialist clinics continue to incur high costs, necessitating financial support from more profitable departments. The utilization of AI for enhanced scheduling and the growth of telemedicine services minimize expenses and enhance the distribution of medical professionals.

The proposed AI model significantly outperformed all benchmark models in terms of reducing wait times and optimizing the utilization of medical professionals. The Deep Q-Learning (DQN) model has demonstrated effectiveness; however, there are delays in patients accessing doctors, and the utilization of doctors can be optimized further with our approach. During periods of high demand, heuristic models such as FCFS and SJF tend to underperform, especially in critical situations where a rapid response is essential. The proposed model outperformed the alternatives across all key metrics, with p-values falling below 0.05, indicating that the observed enhancements were statistically significant. This analysis demonstrates that the proposed AI-driven scheduling system outperforms both the AI-based and heuristic queue management techniques. The proposed system demonstrates superior performance compared to existing models in complex medical environments through the utilization of real-time data integration, reinforcement learning, and dynamic decision-making.

In general, the findings show that AI-driven scheduling is quite helpful in the healthcare field, especially when there is an emergency. It showed that doctors aren’t being used as effectively during off-peak hours, which suggests that scheduling should be improved. In addition, adding telemedicine services has shown that it may increase profits while lowering the cost of consultations, especially for general consultations. The AI system’s capacity to adjust to big changes shows that it might be improved, making it a long-lasting and cost-effective choice for modern healthcare systems.

Scalability and generalization

While the proposed AI-powered telemedicine queueing system has demonstrated success in the study area on multi-speciality hospital (DHRC Hospital, Jaipur), scaling the system to larger cities or different countries presents a set of challenges and opportunities.

• Scalability in Larger Cities: In larger cities, the system would need to handle increased patient volumes, a higher number of hospitals, and potentially more complex infrastructure. This can be achieved as follows:

  • Cloud-based Architecture: Utilizing cloud infrastructure for scalable storage, computational power, and dynamic resource allocation to handle the demands of larger urban centers.
  • Load Balancing and Parallel Processing: Implementing load balancing strategies to distribute processing tasks and patient data across multiple servers, ensuring fast response times even with higher data traffic.
  • Distributed Systems: A distributed approach allows the system to manage multiple hospitals or telemedicine services simultaneously, ensuring that resources (doctors, equipment) are allocated efficiently across the network.
• Generalization Across Different Countries: Expanding the system to other countries necessitates an examination of local healthcare regulations, practices, and the specific needs of patients. Essential elements for broad applicability encompass:

  • Adaptability to Local Healthcare Settings: The system should possess adaptability to effectively respond to differences in healthcare infrastructure, resource availability (such as the number of doctors and telemedicine capabilities), and triage protocols. The ability to customize the parameters for each region could enable the system to adapt doctor assignments and patient scheduling to meet local needs.
  • Urban vs. Rural Settings: Typically, urban hospitals tend to accommodate a larger patient population and often possess greater resources. This situation complicates scheduling, leading to extended wait times and an increase in resource conflicts. The model is capable to handle these differences, such as by enhancing patient flow during peak demand and effectively handling various patient queues. Conversely, while “rural hospitals” may see fewer patients, they often lack the necessary resources and infrastructure. The system must acknowledge that specialized care may not always be accessible, necessitating the use of alternative criteria for decision-making, such as prioritizing emergency cases over routine ones.
  • Cross-country Data Compatibility: The system should support international data formats such as ‘patient records’, ‘medical terminology’, and ‘scheduling protocols’. Data integration is straightforward using standardized approaches such as HL7 and FHIR or country-specific adapters.
  • Regulatory Compliance: For the system to work across the world, it will require modifications to fit the healthcare rules of other countries, such as Europe’s GDPR data protection legislation. We may customize the system for the region by establishing its key functions in a modular way.

In conclusion, the proposed model was validated for a specific multi-specialty hospital (DHRC) in Jaipur. However, the attributes that make it scalable and adaptable suggest that the system could be successfully implemented in larger cities and various healthcare environments globally. These approaches would facilitate effective scaling of the system while preserving its capacity to reduce patient wait times and optimize resource use.

Novelty, contribution, and managerial approach

The following sections provides an overview of the novelty, contribution, and managerial approach of the proposed advanced queueing model.

Novelty

The proposed model leverages AI-driven dynamic scheduling using reinforcement learning (RL) and Q-learning to optimize staffing levels and resource allocation in telemedicine. It is a significant improvement over traditional fixed doctor assignments and static scheduling. The model dynamically adjusts based on real-time data, ensuring better resource utilization and cost efficiency.

Contribution

The model introduces adaptive doctor allocation based on patient flow and emergency case prioritization. It reduces operational costs by optimizing staffing, avoiding overstaffing or understaffing. The system is scalable and adaptable to varying patient volumes, specialist availability, and time-based demand fluctuations.

Managerial approach

The model proposes a dynamic, data-driven staffing solution that minimizes downtime and enhances doctor utilization. It advocates for cost-saving by adjusting staffing levels to match real-time demand. Moreover, the approach ensures flexibility, allowing healthcare institutions to adapt to changing conditions without compromising on service quality. Here are some key managerial implications include enhanced resource allocation, improved patient experience, cost savings and financial sustainability, scalability of telemedicine, and strategic planning for resource deployment.

Limitations and future research directions

Although the AI-driven scheduling and dispatching system has proven to be effective in a multi-specialty hospital environment, there are many avenues for enhancing its functionality and increasing its relevance in broader, real-world applications. Numerous possible avenues for future exploration include the following:

Limitations

• Although the system demonstrated strong performance in the investigated area, a notable limitation is its dependence on ‘historical data’ for training the reinforcement learning model. Future efforts must prioritize the integration of real-time data to enhance decision-making and respond effectively to changing environments.

• Another constraint is the ‘availability of resources’, including drones or other modes of transport, which may not be easily accessible in every region. The implementation of these technologies will necessitate considerable investment in infrastructure and acquisition of regulatory approvals.

• Ultimately, the system’s ability to adapt and expand across different regions with distinct healthcare infrastructure continues to pose a significant challenge. For successful global implementation, it is essential to consider the model’s ability to adjust to various regulatory frameworks and healthcare standards in different countries.

Future research directions

• Multi-City Deployment: The model has the potential to be expanded to accommodate ‘multiple cities’ or even ‘entire regions.’ Expanding operations requires infrastructure upgrades to support greater datasets, real-time hospital communications, and dynamic city cooperation. Distributed computing is required to handle data from various cities and optimize resource allocation over a large territory.

• Drone Integration: Advances in drone technology allow the system to improve the ‘integration of drones’ to convey medical supplies and emergency response units faster. The utilization of drones may assist ambulances in reaching hard-to-reach places, reducing response times. Modifying the AI model to handle drone-based logistics and make real-time ambulance-drone deployment decisions is necessary.

• Multi-Modal Transport: Future studies may examine ‘multi-modal transport’ options including ambulances, drones, and public transit. These different modalities may improve route planning and resource usage by considering traffic, weather, and other environmental variables. The model must weigh the urgency, trip duration, and availability to choose the best option.

• AI and Machine Learning Optimization: Future versions of the model may use advanced machine learning to better forecast patient needs and allow real-time changes based on medical history, symptoms, and other individualized factors. Predictive modeling and data-driven decision-making may improve patient assignments.

In conclusion, while the existing system shows promising results, broadening its use across multiple cities, incorporating drone technology, and integrating various transportation modes will significantly enhance its effectiveness and provide a more comprehensive strategy for emergency dispatching.

Conclusion

This study demonstrates the potential enhancements in telemedicine services through a novel approach by integrating an advanced queueing model with “Reinforcement Learning (RL)” and “Q-learning” for AI-based Scheduling. An AI-driven solution was developed to reduce patient wait times by creating a mathematical model of triage and doctor queues, ensuring that doctors remained consistently occupied. The application of reinforcement learning for adaptive doctor allocation modifies resource distribution dynamically, prioritizing emergency situations and alleviating the workload on medical staff. “Reinforcement Learning,” and the “Q-learning algorithm,” can dynamically allocate doctors in the telemedicine scheduling system. Adjusting ‘learning rate, discount factor, and exploration rate’ helps the system find the best ways to reduce patient wait times and maximize doctor usage. The model proves telemedicine’s importance in modern healthcare by validating using a case study at a multi-specialty hospital, “Dhanwantri Hospital and Research Centre, Jaipur”. The studied area is derived from data on 5000 patients at DHRC, Jaipur, across various medical disciplines.

The validation findings, derived from an analysis of more than 1,000 patient data sets across 10 simulation runs, indicated that AI-driven scheduling reduced wait times for emergency patients by 40%, with a 95% confidence interval of [35%, 45%]. Conversely, static scheduling resulted in an 80% increase in wait time during peak hours. A paired t-test was employed to analyze the longest wait times associated with both the AI-powered and static scheduling models. The test produced a p-value of 0.003, suggesting that AI-powered scheduling significantly reduced wait times in a substantial manner.

Simulation results validated the proposed paradigm by reducing queue congestion and improving the efficiency of telemedicine. By reducing peak-hour delays and maximizing the doctor-to-patient ratio, the AI-powered scheduling system improves healthcare delivery. The study of costs and efficiency showed that AI-powered scheduling reduces operating costs while preserving a high level of patient care, suggesting that telemedicine offers a workable and scalable solution to contemporary healthcare problems.

Telemedicine with AI excelled throughout the hospital cost simulation. Patient economic savings from AI-driven scheduling are significant. Telemedicine services, notably virtual consultations boosted by artificial intelligence, earned the most revenue and lowest cost per consultation, boosting the general hospital’s profitability. The doctor’s flexible scheduling method reduced unjustified compensation expenditures and avoided overstaffing during low demand. The cost-benefit research showed that employing AI to enhance scheduling maximizes operational efficiency and patient care. Modern healthcare systems and society benefit from the advanced queueing model’s improved patient care efficiency, resource allocation, and operational cost reduction.

Thus, the implementation of “Reinforcement Learning (RL),” and the “Q-learning algorithm,” significantly improves staffing efficiency for telemedicine services. The integration of AI-driven scheduling optimizes resource allocation, offering a more efficient, cost-effective, and adaptable method for managing staffing levels in healthcare settings. Elevating decision-making in hospital management entails broadening the AI model to seamlessly incorporate predictive analytics for patient flow while also weaving supplementary constraints, such as resource limitations and staffing restrictions.

Data collection process and data sources

The data used in this study was obtained from a case study on a multi-specialty hospital, “Dhanwantri Hospital and Research Centre, Jaipur (with reference no. DHRC/0112), through an official request and a subsequent approval process. The studied area is derived from data on 5000 patients at DHRC, Jaipur, across various medical disciplines. In dynamic and unpredictable environments, the use of simulations, sensitivity analysis, and empirical data enhances the effectiveness of healthcare operations. We modified the data to align with the research goals.

Author contributions

All authors have made a substantial contribution to the conception or design of this remarkable work.

Funding

Open access funding provided by Manipal University Jaipur.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Consent for publication

All contributors have provided their consent for publication of this research. All authors agree to share all details upon the publication of the article.

Competing interests

The authors declare no competing interests.