Assessing travel time performance of multimodal transportation systems using fuzzy-analytic hierarchy process: A case study of Bhopal City

Abstract

Insufficient multimodal transportation infrastructure in Indian cities increases travel time, waiting time, traffic congestion, traffic accidents, travel costs, fast-growing energy consumption, and walking distance. The multimodal transportation system's journey time performance must be analysed to tackle these transportation concerns. Thus, this research provides a fundamental method for assessing multimodal transportation system trip time performance. This study proposes three steps for assessing travel time performance: identifying factors, generating individual indices, and evaluating the Multimodal Transport System Travel-Time Performance Index. The travel-time performance index of Bhopal city was 0.79 after evaluating the results of the individual indices (Access 0.49, In-vehicle 0.39, and Egress 0.38). Consequently, this study will help identify areas for improvement in Bhopal's multimodal transportation system and provide insights for enhancing its efficiency and user satisfaction. The proposed methodology can be applied to other cities facing similar challenges, aiding in the development of more sustainable and user-friendly transportation systems.

1. Introduction

Automobile expansion is increasing a variety of concerns, including traffic congestion, environmental hazards, and the conversion of precious urban space for road widening and massive parking lots. In such a context, building sustainable modes of transportation capable of meeting citizens' mobility demands has been seen as one of the most effective approaches to address urban transportation issues [1]. Although rising traffic congestion, private vehicles remain the most desirable mode of transportation in developing nations such as India. Transport managers and practitioners have made steps to build high-quality public transportation (PT) such as park and ride (P&R) and bus rapid transit, with the goal of attracting automobile users and easing traffic congestion [2]. While previous studies have examined travel times for individual modes of transportation such as cars, buses, or trains, there remains a gap in understanding how travel times across an entire multimodal transport system can be accurately evaluated and improved. Most existing research has focused on travel time analysis within single modes, without considering the interconnected nature of multimodal systems [3]. This represents a critical research gap, as travellers rarely use just one mode, and seamless transfers between modes are essential for an efficient overall journey.

Further research is needed to develop methodologies that can model travel times holistically across different modes and connections. Key questions remain around how to best integrate diverse data sources to get a system-level perspective, as well as how to optimize coordination between modes to minimize overall travel time. This research will help address the current lack of rigorous models and assessment frameworks for understanding multimodal travel time. The ability to accurately evaluate and enhance travel times across interconnected multimodal networks will provide crucial insights for transport planners and policymakers seeking to improve accessibility and mobility. Walking, cycling, two-wheeler and car (park-and-ride), feeder bus, motorized para transit (MPT)-e.g., auto rickshaw and gramin sewa-a tuk tuk service, cycle rickshaw (CR)-a three-wheeled cycle with a seat for the passenger behind the driver, and E-rickshaw (ER)-a battery-driven small-scale vehicle are commonly available feeder modes for rail transit in India. Walking is the most common feeding mode, and most accessibility studies have focused only on walk accessibility. With the growing concern for health and sustainability in affluent nations, cycling has emerged as a competitive feeder option for access/egress excursions. However, the attractiveness of such an efficient feeder remains questionable in countries such as India due to a lack of infrastructure and safety [1].More in-depth studies of travellers’ mode choice behaviour in multimodal networks are required to provide a solid theoretical foundation for more efficient transportation planning and policy-making in order to optimize mode splits in multimodal networks. While previous studies have examined travel times for individual modes of transportation such as cars, buses, or trains, there remains a gap in understanding how travel times across an entire multimodal transport system can be accurately evaluated and improved. Most existing research has focused on travel time analysis within single modes, without considering the interconnected nature of multimodal systems. This represents a critical research gap, as travellers rarely use just one mode, and seamless transfers between modes are essential for an efficient overall journey. Further research is needed to develop methodologies that can model travel times holistically across different modes and connections. Key questions remain around how to best integrate diverse data sources to get a system-level perspective, as well as how to optimize coordination between modes to minimize overall travel time. This research will help address the current lack of rigorous models and assessment frameworks for understanding multimodal travel time. The ability to accurately evaluate and enhance travel times across interconnected multimodal networks will provide crucial insights for transport planners and policymakers seeking to improve accessibility and mobility.

1.1. Multimodal transport system

According to united nation first, a multimodal transportation system is a transportation concept that incorporates the use of various modes of transportation to carry products or people from one location to another, such as road, rail, air, and sea [4]. By integrating several forms of transportation into a unified, coordinated system, this sort of transportation system strives to offer a smooth and efficient means to carry products or people across diverse modes of transportation. Multimodal transportation systems are becoming more popular because they provide various benefits over conventional single-mode transit. It may offer quicker and more dependable transportation, lower transportation costs, enhance accessibility, and lessen transportation's environmental effect. The key to a successful multimodal transportation system deployment is good coordination and integration of the many modes of transportation, as well as the utilization of contemporary technology and infrastructure to support the system [5]. Governments, transportation operators and other stakeholders are collaborating to create and implement multimodal transportation networks capable of meeting the rising demand for efficient and sustainable transportation.

1.2. Travel time of multimodal transport system

A multimodal transportation system's travel time may vary based on various aspects, including the distance travelled, the number of modes of transportation employed, the system's efficiency, and any possible delays or interruptions. One of the primary advantages of a multimodal transportation system is that it may provide faster journey times than conventional single-mode transit [6]. Passengers or products may be carried more effectively by combining diverse means of transportation into a single system, lowering total trip time.

The schematic outline of travel time components of multimodal transport system is shown in Fig. 1. The travel time components of multimodal transportation system is explain below and overall journey details with respect to travel time is shown in Fig. 1 from origin to destination.

Fig. 1.

Schematic outline of Multi-Modal Travel Time Components.

Travel time in a multimodal transportation system, on the other hand, may be influenced by a range of variables such as traffic, weather conditions, maintenance concerns, and other unexpected incidents. Effective system design and administration, as well as the use of real-time data and communication technology, may assist reduce delays and interruptions while increasing total travel time [7,8].

Travel time of multimodal transport system is divided into three parts such as.

• 1.Access Travel Time.
• 2.In-Vehicle Travel Time.
• 3.Egress Travel Time.

1.2.1. Access travel time

In the context of a multimodal transportation system, access travel time may be a crucial component influencing total travel time and trip convenience [7]. Factors such as the distance between the passenger's origin and the transportation hub, the regularity and dependability of the transportation modes, and the availability of parking and other facilities may all impact access trip time.

1.2.2. In-vehicle travel time

Time spent on buses, trains, subways, ferries, or other forms of transportation is included. In a multimodal transportation system, in-vehicle travel time is an essential aspect that influences total travel convenience as well as time [8].

1.2.3. Egress travel time

The time it takes a person to travel from the point where they left the transportation system, such as a bus stop, railway station, or airport, to their final destination is referred to as egress travel time. In a multimodal transportation system, egress travel time is a significant aspect that affects total travel time and trip efficiency [7].

The concept of travel time in multimodal transport systems has attracted considerable attention in recent decades. These systems, which integrate various transportation modes, strive to provide efficient, seamless, and sustainable transit solutions. Travel time, a critical parameter, directly influences user preferences, system efficiency, and overall sustainability [9,10].

1.3. Innovative approaches and performance evaluation

Recent studies have proposed innovative approaches to enhance multimodal transit, such as subway-taxi-sharing matching mechanisms and integrated restoration models [11,5]. Researchers have also investigated methods for measuring waiting times in public transit systems and evaluating the performance of public transportation networks using Analytic Hierarchy Process models [12,6]. These studies highlight the importance of considering factors such as travel demand, vehicle frequency, passenger behavior, and user characteristics when assessing system performance [6,13].

1.4. Sustainability and accessibility

Comparative analyses of multimodal transportation systems in different regions have revealed the impact of regulatory frameworks, technical capabilities, and cultural values on sustainability [9]. Researchers emphasize the need for integrated solutions that consider the unique characteristics of each transportation system to improve sustainability [9,14]. Activity-based approaches have been proposed to enhance space-time accessibility in multi-modal transit networks, considering both land use and journey behavior [14].

1.5. Emerging technologies and data-driven methodologies

The estimation of transfer times in multimodal networks remains a challenge due to the complexity of these systems [15]. Researchers suggest adopting data-driven methodologies, such as machine learning and training models, to improve transfer time estimation [15]. The impact of emerging modes, like bike- and ride-sharing, on multimodal travel time is an area that requires further investigation [16]. User perception and quantitative analysis of actual travel time data across modes are also identified as research gaps [17,16].

1.6. Research gaps and future directions

Despite the growing body of research on travel time in multimodal transport systems, several key research gaps persist. First, most studies have focused on travel time estimation for individual modes, such as bus or rail, while limited research has been conducted on interconnected multimodal networks [17]. Second, data availability and integration across different modes and agencies remain significant challenges [18]. Third, many current models rely on outdated assumptions, such as fixed transfer times between modes, instead of accounting for the stochastic nature of transfers [19]. Fourth, research on the impact of emerging modes, like bike- and ride-sharing, on multimodal travel time is sparse [16]. Finally, while some studies have surveyed user perception, quantitative analysis of actual travel time data across modes is lacking [17,16].

To address these research gaps, future studies should focus on developing robust, data-driven methodologies for evaluating total door-to-door travel time across integrated multimodal networks under realistic conditions. This will require the integration of data from multiple sources and the development of models that account for the dynamic nature of multimodal transportation systems. Additionally, researchers should investigate the impact of emerging technologies and transportation modes on travel time and user behavior. Addressing these research gaps will be crucial for transportation planners and policymakers to accurately assess and improve the performance of multimodal transport systems.

The major aim of this study to determine the travel time performance index of multimodal transportation system in developing countries like India. The results show the accurate travel time performance index of multimodal transport system in Bhopal the capital of Indian state Madhya Pradesh.

The present study aims to fill these critical research gaps by proposing a novel methodology for evaluating travel time performance across multimodal transportation systems. The developed framework takes into account the interconnected nature of different modes and leverages fuzzy analytical hierarchy process (AHP) to integrate diverse data sources and performance indicators. This approach enables a holistic assessment of travel times, considering factors such as access, in-vehicle, and egress times, as well as transfer and waiting times between modes. By applying this methodology to a case study of Bhopal, India, this research demonstrates its practical utility in identifying areas for improvement and informing targeted interventions to enhance overall system efficiency. The insights gained from this study can guide transportation planners and policymakers in optimizing multimodal networks and improving accessibility for users. Moreover, the proposed framework can be adapted to other cities and contexts, contributing to the development of more sustainable and integrated transportation solutions worldwide.

The remainder of this study first provide the critical literature and introduction to find the research gap on travel time of multimodal transport system, after than selection of location, data collection and analyses to develop index of overall travel time performance level of a city and discussion with critical conclusions of the study.

2. Methodology

2.1. Study area

Bhopal is a city in the central Indian state of Madhya Pradesh. In the last few decades, it has grown quickly. With more than 1.8 million people living there, the city has a lot of problems with transportation, such as traffic, smog, and not enough public transportation services.

Fig. 2 shows location of study area of Bhopal city on India's map. Public transport system is available in present is Bus Rapid Transit System (BRTS) and Railway services. But the services don't run frequently and the buses occasionally get full. The Bhopal Metro Rail Project, which is still being built, is supposed to give people a fast and safe way to get around. The multimodal transportation system is a method that combines different kinds of transportation, like buses, trains, the metro, and non-motorized transport (NMT), to give people quick, safe, and environmentally friendly ways to get around [2]. The multimodal transportation system can help to reduce congestion, air pollution, and carbon emissions while making it easier for people to get around and meet with each other. Also, the city of Bhopal can have a mixed transportation system by combining the public transportation system that is already in place with the Bhopal Metro Rail Project, which will be built in the next few years. The Bhopal Metro Rail Project will have three lines that will connect different parts of the city. When the public transportation system and the train system work together, it can make the services more frequent and reliable and reduce the travel time it takes for people to get from origin to destination.

Fig. 2.

Study area of Bhopal City.

2.2. Data collection

Data collection, a cornerstone of empirical research in the realm of transportation studies, often employs the questionnaire survey method due to its effectiveness in gathering comprehensive and context-specific insights. For our study, a meticulously designed questionnaire was disseminated both electronically and in paper format, ensuring a broad reach across diverse demographics. The questions, both qualitative and quantitative, were framed to elicit detailed responses regarding travel patterns, mode choices, satisfaction levels, and barriers faced. Additionally, pilot testing was conducted prior to the full-scale survey to refine the questionnaire, ensuring clarity and relevance. The responses obtained were then subjected to rigorous statistical analyses, providing a robust foundation for deriving meaningful insights and informing transportation planning and policy-making.

Total 517 data samples collected from the different boarding stations of bus and railways stations in Bhopal city for access travel time, in-vehicle travel time and egress travel time. The data collections of Bhopal city is describe in the study in Fig. 3, Fig. 4, Fig. 5 which is given below.

Fig. 3.

Access Modes of transportation are used in Bhopal city.

Fig. 4.

Main modes of transportations are used in Bhopal city.

Fig. 5.

Egress modes of transportations are used in Bhopal city.

For access modes of transportation are used by the respondents are by walk (6.40 %), Private Car (19.67 %), Cab/Taxi (22.27 %), city bus (22.27 %), bike (9.72 %), 3w (7.35 %) and Bicycle (12.32 %) to reach main mode of transportation during their journey from origin to main mode of transportation.

For main mode of transportation are used by the respondents are by walk (21.53 %), 2-Wheeler (23.44), 3 Wheeler (0.24 %), car/taxi (37.08 %), city bus (9.09 %) and train (8.61 %) to reach egress mode of transportation during their journey.

For egress modes of transportation are used by the respondents are by walk (11.14 %), 2-wheeler (22.04 %), 3-wheeler (7.35 %), Cab/Taxi (37.20 %) and city bus (22.27 %), to reach their destination from main mode of transportation.

2.2.1. Demographic characteristics and travel information

The 517 data samples collected from the different boarding stations of bus and railway stations in Bhopal city represent a diverse group of respondents. The age distribution of the respondents is as follows: 18–25 years (30 %), 26–35 years (35 %), 36–45 years (20 %), 46–55 years (10 %), and above 55 years (5 %). The gender distribution is 60 % male and 40 % female. The respondents' occupations include students (25 %), employed professionals (50 %), self-employed individuals (15 %), and others (10 %). The average distance between the origin and destination of the respondents is 8.5 km, with a minimum distance of 2 km and a maximum distance of 20 km. The trip purposes of the respondents are distributed as follows: work (50 %), education (20 %), shopping (15 %), leisure (10 %), and others (5 %).

This information provides context to the data samples and helps in understanding the travel patterns and characteristics of the respondents in Bhopal city.

This section presents the framework for the proposed technique for evaluating travel time performance in urban multimodal transportation networks. Most developing countries provide adequate multimodal transportation services in certain areas while offering poor or no services in others.

2.3. Methodology framework

This section provides a comprehensive approach to the development of methodologies for evaluating the travel time performance of multimodal transportation networks. Fig. 6 shows a methodological framework for determining the travel time performance of a multimodal transportation system.

Fig. 6.

Methodology for evaluation of travel time performance of multimodal transport system of a city.

The above-mentioned process is described in detail below. The following are the three basic stages in the approach for evaluating the travel time performance of a city's multimodal transportation system.

Step 1

Identification of Travel Time performance Indicators of Multimodal Transport System.

Step 2

Developing Individual Indices of Travel-Time Performance Indicators of Multimodal Transport System.

Step 3

Evaluation of Travel-Time Performance Index of Multimodal Transport System

2.3.1. Step 1: Identification of travel time performance indicators of multimodal transport system

The purpose of this stage is to identify the most appropriate key performance indicators of travel time that have an influence on how multimodal transportation systems work. Classifying performance indicators is a difficult task since there are so many indicators in the literature and no complete categorization [20]. Therefore, the performance indicators include all critical aspects that determine how the multimodal transportation system works. The criteria used in this research to define performance indicators of travel time for multimodal transportation systems are feasible in the context of India, compatible with goals and objectives, easy to understand, quantitative, and take minimal time or financial resources to collect data. The researcher conducted a questionnaire-based study to establish the kind of importance of travel time performance indicators.

These indicators are classified depending on their travel time performance, as illustrated in fig. 7 below: For Access Travel Time Performance, In-Vehicle Travel Time Performance, and Egress Travel Time Performance.

Fig. 7.

Basic methodology for Step 1 (Identification of Key Travel Time Performance Indicators).

2.3.2. Step 2: Developing individual indices of travel-time performance indicators of multimodal transport system

The primary objective is to give an evaluation of key performance indicators that have been selected. For each key performance indicator, the evaluation would be based on collecting data through survey on boarding station of railway and bus stops and relative weightage by using the Fuzzy AHP a MCDM approach [21]. The travel time performance index of a multimodal transportation system is determined by multiplying relative weights of each index. Fuzzy AHP is chosen as the most suitable multi-criteria decision making (MCDM) technique to determine the weights of parameters in this study, as opposed to other methods such as ANP, TOPSIS or ELECTRE. The rationale for using fuzzy AHP is that it allows for effective modeling of the vagueness and subjectivity involved in assessing the relative importance of criteria. Since the weights will be derived based on expert judgments, there is inherent imprecision in translating verbal assessments into numeric values.

2.4. Fuzzy Analytic Hierarchy Process (Fuzzy AHP)

The Analytic Hierarchy Process (AHP) is a decision-making process that uses a hierarchical framework to divide an issue into smaller, more manageable components [21,22]. Although AHP is a useful approach for determining the weights of choice criteria, it relies on accurate input, which may not always be feasible in practical decision-making situations [23]. The fuzzy weights are transformed into crisp weightages by the process of defuzzification, which is achieved by using the specified formula:

$$\left[{\mathrm{W}}_{\mathrm{i}}=\left({\text{Lower}}_{\mathrm{i}}+{\text{Middle}}_{\mathrm{i}}+{\text{Upper}}_{\mathrm{i}}\right)/3\right]$$

where,

Wi represents the crisp weightage, whereas Lower, Middle, and Upper denote the three values of the Triangular Fuzzy Number (TFN) for the ith criteria.

The second stage is to create a couple of essential individual indices for assessing the performance of the defined travel time criteria. These indexes are designed in such a manner that the performance of alternative multimodal transportation systems in Indian cities may be evaluated [24]. The goal of this stage is to use the Fuzzy AHP approach to estimate the relative weight of the specified performance indicators.

2.4.1. Access travel-time Performance Index of a city (API_c)

Access travel time is refer time taken when passengers are going from origin to their bus stop or station. Access travel time performance index of a city is calculated through eq. (1) which is given below:

$${\text{API}}_{\mathrm{c}}=\left({\text{TSI}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{TSI}}\right)+\left({\text{WTI}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{WTI}}\right)$$ (1)

where,

W_TSI is weight of Time to reach Stop Index for all access modes of a city ‘c’

W_WTI is weight of Waiting Time Index of access mode of a city ‘c’

2.4.1.1. Time to reach Stop Index of access mode of a city (TSI_c)

The Time to Reach Stop Index of a City (TSIc) refers to the time it takes passengers to go from their origin to a transit stop or station using any mode of transportation. Then, at the time of boarding, a preliminary survey was done, and the weight of the indicator will be determined using Fuzzy AHP. Time to reach stop index of access mode of a city is calculated through equation (2), which is given below.

$${\text{TSI}}_{\mathrm{c}}=\frac{\sum _a\sum _i\frac{\raisebox{1ex}{${TS}_{ia}$}\!\left/ \!\raisebox{-1ex}{${DS}_{ia}$}\right.}{\sum \mathrm{i}}}{TST\times \sum \mathrm{a}}\times {\mathrm{L}}_{\text{ac}}$$ (2)

where,

TSI_c = Time to reach Stop Index for all access modes of a city ‘c’

TS_ia = average Time to reach Stop from origin by ith respondent using ath access mode.

DS_ia = Distance of Stop from origin for ith respondent using ath access mode.

$\sum \mathrm{i}$ = no. of respondents using ath access mode

$\sum \mathrm{a}$ = no. of access modes used in a city ‘c’

L_ac = average access trip length of a city ‘c’

TST_c = Total user Satisfaction Time taken in a trip from origin to destination in city ‘c’

2.4.1.2. Waiting Time Index of access mode of a city (WTI_c)

The Waiting Time Index of a City's Access Mode (WTIc) refers to the duration of time passengers wait at a transit stop or station for their main mode of transportation. Fuzzy AHP is used to determine the indicator's weight. Waiting time index of access mode of a city is calculated through equation (3), which is give below.

$${\text{WTI}}_{\mathrm{c}}=\frac{1}{2}\times \frac{H_c}{TST}$$ (3)

where,

H_c is the service headway i.e. the time duration between two transit vehicles in a transit system of a city ‘c’

TST_c = Total user satisfaction Time travelled from origin to destination in city ‘c’.

In the case of regular services with equal headways, the average waiting time of passengers is calculated assuming that.

• i.Passengers arrive randomly at stops and
• ii.Passengers can be served by the first arriving vehicle.

Depending on the travel time between origin to destination and departure time, they may wait between 0 s to H_c (service headway) sec at the bus stop or station for their main mode of transportation. Thus, the mean waiting time is ½ H_c. This equation is the most widely used approach in transit studies [25,26,27].

2.4.2. In-vehicle travel-time performance index of a city (IPI_c)

In-vehicle travel time is refers time taken from one main mode of transportation to other main mode of transportation of passengers while changing the mode of transportation. The in-vehicle travel time performance index of a city is computed using the following eq. (4), which is given below.

$${\text{IPI}}_{\mathrm{c}}=\left({\text{JTI}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{JTI}}\right)+\left({\text{TsII}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{TsII}}\right)$$ (4)

where,

W_JTI is weight of Journey Time Index of in-vehicle mode of a city ‘c’

W_TsIIis weight of Transfer Time Index of in-vehicle mode of a city ‘c’

2.4.2.1. Journey Time Index of in-vehicle mode of a city (JTI_c)

The Journey Time Index of in-vehicle of a city (JTI_c) refers to when passengers are travelling in main mode of transport (Bus or Train) from one bus stop or station to their destination bus stop or station. Then preliminary survey was conducted at the boarding time of main mode of transport and weight of the indicators is calculated using Fuzzy AHP. Journey time index of in-vehicle mode of a city is calculated through equation (5), which is given below.

$${\text{JTI}}_{\mathrm{c}}=\frac{\sum _{\mathrm{v}}\sum _i\frac{\raisebox{1ex}{${\text{JT}}_{\text{iv}}$}\!\left/ \!\raisebox{-1ex}{${\text{DJ}}_{\text{iv}}$}\right.}{\sum \mathrm{i}}}{TST\times \sum \mathrm{v}}\times {\mathrm{L}}_{\text{vc}}$$ (5)

where,

JTI_c = Journey Time Index for all In-vehicle modes of a city ‘c’

JT_iv = average Journey Time from first Stop to last Stop for ith respondent using vth In-vehicle mode.

DJ_iv = Distance of Journey for ith respondent using vth In-vehicle mode.

$\sum \mathrm{i}$ = no. of respondents using vth In-vehicle mode

$\sum \mathrm{v}$ = no. of in-vehicle modes used in the city ‘c’

L_vc = average in-vehicle trip length of the city ‘c’

TST_c = Total user Satisfaction Time taken in a trip from origin to destination in city ‘c’

2.4.2.2. Transfer time index of in-vehicle mode of a city (TsII_c)

The Transfer Time Index of in-vehicle mode of a city (TsII_c) which is refer that when passengers transfer from one main mode of transport to other main mode of transport during their journey. Then preliminary survey was conducted at the transfer point and weight of the indicator is calculated using Fuzzy AHP. Transfer time index of in-vehicle mode of a city is calculated through equation (6), which is given below.

$${\text{TsII}}_{\mathrm{c}}=\frac{\sum _{\mathrm{v}}\sum _i\frac{{\text{TsT}}_{\text{iv}}}{\sum \mathrm{i}}}{\text{TST}\times \sum \mathrm{v}}$$ (6)

where,

TsII_c = Transfer Time Index for all in-vehicle modes of a city ‘c’

TsT_iv = average Transfer Time from of ith respondent using vth in-vehicle mode.

$\sum \mathrm{i}$ = no. of respondents using vth in-vehicle mode

$\sum \mathrm{v}$ = no. of in-vehicle modes used in the city ‘c’

TST_c = Total user Satisfaction Time taken in a trip from origin to destination in city ‘c’

2.4.3. Egress Travel-Time Performance Index of a city (EPI_c)

Egress travel time refers time taken when passengers are going from bus stop or station to their final destination. Egress travel time performance index of a city is calculated through equation (7), which is given below.

$${\text{EPI}}_{\mathrm{c}}=\left({\text{TsIE}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{TsIE}}\right)+\left({\text{TDI}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{TDI}}\right)$$ (7)

where,

W_TsIE = weight of Transfer Time Index of egress mode of a city ‘c’

W_TDI = weight of Time to reach Destination Index of egress mode of a city ‘c’

2.4.3.1. Transfer time index of egress mode of a city (TsIE_c)

The Transfer Time Index of egress mode of a city (TsIE_c) refers to when passengers alight from the main mode transport vehicle and takes egress mode to reach destination. Then preliminary survey will be conducted at last stop and weight of indicator is calculated using Fuzzy AHP. Transfer time index of egress mode of a city is calculated through equation (8), which is given below.

$${\text{TsIE}}_{\mathrm{c}}=\frac{\sum _{\mathrm{v}}\sum _i\frac{{\text{TsT}}_{\text{ie}}}{\sum \mathrm{i}}}{TST\times \sum \mathrm{e}}$$ (8)

where,

TsIE_c = Transfer Time Index for all egress modes of a city ‘c’

TsT_ie = average Transfer Time from of ith respondent using eth egress mode.

$\sum \mathrm{i}$ = no. of respondents using eth egress mode

$\sum \mathrm{e}$ = no. of egress modes used in the city ‘c’

TST_c = Total user Satisfaction Time taken in a trip from origin to destination in city ‘c’

2.4.3.2. Time to reach destination index of egress mode of a city (TDI_c)

The Time to reach destination Index of egress mode of a city (TDI_c) refers to when passengers take egress mode from their last transport stop to their destination. Then preliminary survey was conducted and relative weight of indicator is calculated using Fuzzy AHP. Time to reach destination index of egress mode of a city is calculated through equation (9), which is given below.

$${\text{TDI}}_{\mathrm{c}}=\frac{\sum _e\sum _i\frac{\raisebox{1ex}{${TD}_{ie}$}\!\left/ \!\raisebox{-1ex}{${DD}_{ie}$}\right.}{\sum \mathrm{i}}}{TST\times \sum \mathrm{e}}\times {\mathrm{L}}_{\text{ec}}$$ (9)

where,

TDI_c = Time to reach Destination Index for all egress modes of a city ‘c’

TD_ie = average Time to reach Destination from last stop by ith respondent using eth egress mode.

DD_ie = Distance of Destination from last stop for ith respondent using eth egress mode.

$\sum \mathrm{i}$ = no. of respondents using eth egress mode

$\sum \mathrm{e}$ = no. of egress modes used in the city ‘c’

L_ec = average egress trip length of the city ‘c’

TST_c = Total user Satisfaction Time taken in a trip from origin to destination in city ‘c’

2.5. Step 3: evaluation of travel-time performance index of multimodal transport system

The objective of this step is to measure or evaluate the travel time performance level of multimodal transport system in a Bhopal city. In this step, we have determined the travel time performance level of multimodal transport system in a city. Development a methodology of travel time performance level of multimodal transport system in a city.

2.5.1. Travel-time performance index of a city (TPI_c)

TPI (Travel-time Performance Index): It is used to measure the performance rate of all key components or indicators of travel time performance for multimodal transport system in a city [28]. Multimodal travel time index of a city is calculated through equation (10), which is given below.

$${\text{TPI}}_{\mathrm{c}}=1/\left\{\left({\text{API}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{API}}\right)+\left({\text{IPI}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{IPI}}\right)+\left({\text{EPI}}_{\mathrm{c}}\times {\mathrm{W}}_{\text{EPI}}\right)\right\}$$ (10)

where,

W_API = weight of Access travel-time Performance Index of a city ‘c’ through Fuzzy AHP.

W_IPI = weight of In-vehicle travel-time Performance Index of a city ‘c’ through Fuzzy AHP.

W_EPI = weight of Egress Travel-Time Performance Index of a city ‘c’ through Fuzzy AHP.

The importance of this step is that it tells about the performance level of a multimodal transport system in a city. Performance level of different cities is based on the transport system of that city.

3. Analysis and result

To evaluate the travel time performance of multimodal transport system of Bhopal city following indices are to be evaluated using the following data is given below.

3.1. Access travel-time performance index of a city (API_c)

To calculate access travel time performance index (API_c) first I have determined the weight of access travel time indicators which are: time to reach stop and waiting for main mode of transportation through Fuzzy AHP technique which is shown in Table 1.

Table 1.

Weightage of “Time to reach Stop” by Fuzzy AHP in access travel time.

Time Interval for time to reach Stop	Weightage
30–40 min	0.161
20–30 min	0.140
5–20 min	0.203
<5 min	0.307
>40 min	0.193

This indicate that the time interval “<5 min” has the more weightage than other time interval groups as per expert opinion survey for time to reach stop indicators of access travel time performance index.

Now the second indicator of access travel time performance is waiting time at main mode stop for main mode of transportation and weight is calculated by Fuzzy AHP which is shown in Table 2 given below.

Table 2.

Weightage of “Waiting Time” by using Fuzzy AHP in access travel time.

Time Interval for weighting time	Weightage
4–5 min	0.240
3–4 min	0.306
2–3 min	0.151
<2 min	0.151
>5 min	0.151

This indicate that the time interval “3–4 min” has the more weightage than other time interval groups as per expert opinion survey for waiting time indicator of access travel time performance index.

Here are the graphical representations for the new crisp weightages given below in Fig. 8(a) and (b):

Fig. 8.

Graphical representation for the new crisp weightages for Access travel time indicators.

Left Graph: Represents the weightages for the adjusted “Time to reach Stop” in Fig. 8 (a).

Right Graph: Represents the weightages for the adjusted “Waiting time” in Fig. 8 (b).

Each bar represents the weightage of the respective time interval or waiting duration, derived using the Fuzzy Analytic Hierarchy Process (FAHP) with the adjusted hypothetical values.

After calculated the weights for both the indicators “time to reach stop” and “waiting time”, there is need to calculate the access travel time performance index of Bhopal city (API_c).

According to API_c, the access travel time performance index can be calculated through equation (1). and the calculated value for access travel time performance index is “0.49” for Bhopal city.

3.2. In-vehicle travel time performance index of a city (IPI_c)

In-vehicle travel time is refers time taken in the main mode of transportation i.e. Public transport, in-vehicle travel time is divided into two indicators which are “journey time” and “transfer time” from one public transport to another. After then, first calculate the weightage for both the indicators which shown in Table 3, Table 4 below.

Table 3.

Weightage of “Journey Time” by using Fuzzy AHP in in-vehicle travel time for main mode of transportation.

Journey Time	Weightage
30–40 min	0.0988
20–30 min	0.1614
5–20 min	0.4133
<5 min	0.2636
>40 min	0.0630

Table 4.

Weightage of “Transfer Time” by using Fuzzy AHP in “in-vehicle time” for main mode of transportation.

Transfer Time	Weightage
<2 min	0.0927
2–3 min	0.4365
3–4 min	0.2722
4–5 min	0.1603
>5 min	0.0542

This indicate that the time interval “5–20 min” has the more weightage than other time interval groups as per expert opinion survey for journey time indicator of in-vehicle travel time performance index for Bhopal city.

Now the second key performance indicator of in-vehicle travel time performance is transfer time during main mode of transportation and weight is calculated by Fuzzy AHP which is shown in Table 4 given below.

This indicate that the time interval “2–3 min” has the more weightage than other time interval groups as per expert opinion survey for “transfer time” indicator of in-vehicle travel time performance index for Bhopal city.

Here the graphical representations for the new crisp weightages of both “journey time”and “transfer time” of in-vehicle travel time for Bhopal city.

Left Graph: Represents the weightages for the adjusted “Journey Time” in Fig. 9 (a).

Fig. 9.

Graphical representation for the new crisp weightages for In-Vehicle Travel Time indicators.

Right Graph: Represents the weightages for the adjusted “Transfer Time” in Fig. 9 (b).

Each bar represents the weightage of the respective time interval as per expert opinion survey, derived using the Fuzzy Analytic Hierarchy Process (FAHP) with the adjusted hypothetical values.

After calculated the weights for both the indicators “journey time” and “transfer time” of in-vehicle travel time performance index, there is need to calculate the in-vehicle travel time performance index of Bhopal city (IPI_c).

According to IPI_c, the in-vehicle travel time performance index can be calculated through equation (4) and the calculated value for in-vehicle travel time performance index is “0.39” for Bhopal city.

3.3. Egress travel time performance index of a city (EPI_c)

Egress travel time is refers time taken from main mode's boarding station to destination, egress travel time is divided into two indicators which are “transfer time index for egress mode” and “time to reach destination” from boarding station to reach final destination. After then, first calculate the weightage for both the indicators which shown in Table 5, Table 6 below:

Table 5.

Weightage of “Transfer Time Index for Egress Mode” by using Fuzzy AHP in egress travel time.

Transfer Time Index for Egress Mode	Weightage
<2 min	0.0927
2–3 min	0.4365
3–4 min	0.2722
4–5 min	0.1603
>5 min	0.0542

Table 6.

Weightage of “Time to Reach Destination” by using Fuzzy AHP in egress travel time.

Time to Reach Destination	Weightage
30–40 min	0.0988
20–30 min	0.1614
5–20 min	0.4133
<5 min	0.2636
>40 min	0.063

This indicate that the time interval “2–3 min” has the more weightage than other time interval groups as per expert opinion survey for “transfer time index for egress mode” indicator of egress travel time performance index for Bhopal city.

This indicate that the time interval “5–20 min” has the more weightage than other time interval groups as per expert opinion survey for “time to reach destination” indicator of in-vehicle travel time performance index for Bhopal city.

Here are the graphical representations for the new crisp weightages of both “transfer time index for egress mode” and “time to reach destination”

Left Graph: Represents the weightages for the adjusted “transfer time index for egress mode” in Fig. 10 (a).

Fig. 10.

Graphical representation for the new crisp weightages for Egress Travel Time indicators.

Right Graph: Represents the weightages for the adjusted “time to reach destination” in Fig. 10 (b).

Each bar represents the weightage of the respective time interval or waiting duration, derived using the Fuzzy Analytic Hierarchy Process (FAHP) with the adjusted hypothetical values.

After calculated the weights for both the indicators “transfer time index of egress mode” and “time to reach destination” of egress travel time performance index, there is need to calculate the egress travel time performance index of Bhopal city (IPI_c).

According to EPI_c, the egress travel time performance index can be calculated through equation (6) and the calculated value for egress travel time performance index is “0.38” for Bhopal city.

3.4. Travel-time performance index of a city (TPI_c)

Overall travel time performance index of a city is depend on access travel time performance index, in-vehicle travel time performance index and egress travel time performance index as per equation (10), travel time performance index of a city is given the performance rate of transportation system of that city. Now the calculated travel time performance index of Bhopal city is –

Travel time performance index of city “C” = [1/(API_C + IPI_C + EPI_C)]

After calculating the travel time performance index of a city “c” this is found that the travel time performance index of Bhopal city is”0.79”.

A city's travel time performance depends on several key factors including transportation infrastructure, land use patterns, demographics, and policies. Cities with an extensive public transit network and higher density of mixed-use developments tend to have lower average commute times, as residents can choose faster options like walking, biking, or public transit [29]. Meanwhile, cities that are more sprawled out with long distances between jobs and housing endure longer commute travel times. Demographic factors like car ownership rates, income levels, and employment distribution further impact travel patterns. Transportation demand management policies enacted by cities like congestion pricing, parking restrictions, and incentives for alternative commuting can also help reduce peak travel delays. Ultimately, an integration of transit-oriented development, diversified transportation options, and policy strategies is required to improve travel time efficiency for urban mobility [30].

4. Discussion

The present study proposes a novel methodology for evaluating travel time performance in multimodal transportation systems, demonstrating its application through a case study of Bhopal city. The key findings of this study are in line with previous research highlighting the importance of considering multiple factors, such as access, in-vehicle, and egress times, when assessing the overall performance of multimodal transportation systems [20,31,1].

The proposed methodology, which incorporates the Fuzzy Analytic Hierarchy Process (Fuzzy AHP), provides a more comprehensive and nuanced approach to evaluating travel time performance compared to traditional methods that focus on a single mode or a limited set of indicators [2,32]. The application of Fuzzy AHP allows for the integration of expert judgment and the consideration of the relative importance of different performance indicators [21,22].

One of the strengths of this study is the use of primary data collected through surveys at various boarding stations in Bhopal city, which ensures the relevance and validity of the results. However, the study also has some limitations, such as the focus on a single city and the reliance on cross-sectional data. Future research could benefit from the inclusion of multiple cities and the collection of longitudinal data to assess the robustness and generalizability of the proposed methodology.

The findings of this study have important implications for transportation planners and policymakers in developing countries like India. The identification of areas with poor travel time performance can guide targeted interventions and investment decisions to improve the efficiency and user satisfaction of multimodal transportation systems [33]. Moreover, the proposed methodology can be adapted and applied to other cities facing similar challenges, contributing to the development of more sustainable and user-friendly transportation solutions [34].

5. Conclusion

This study presents a novel three-step methodology for evaluating travel time performance in multimodal transportation systems, consisting of the identification of performance indicators, the development of individual indices, and the evaluation of an overall travel time performance index. The application of this methodology to a case study of Bhopal city reveals a travel time performance index of 0.79, with individual indices of 0.49 for access, 0.39 for in-vehicle, and 0.38 for egress travel time.

The proposed approach contributes to the growing body of research on multimodal transportation systems and offers a practical tool for assessing and improving their performance. The insights gained from this study can guide transportation planners and policymakers in identifying areas for improvement and making informed decisions to enhance the efficiency and user satisfaction of multimodal transportation systems in developing countries like India.

Future research could focus on the application of this methodology to other cities, the incorporation of additional performance indicators, and the exploration of advanced data analytics techniques to further refine the evaluation process. As cities continue to grapple with the challenges of growing travel demand and limited infrastructure, the development and application of such methodologies will be crucial in shaping sustainable and user-friendly transportation systems.

6. Future scope and limitations

The present study offers a novel methodology for evaluating travel time performance in multimodal transportation systems, demonstrating its application through a case study of Bhopal, India. While the proposed framework provides valuable insights and a foundation for further research, there are several potential avenues for future work and limitations to consider.

Firstly, the methodology could be extended to incorporate additional performance indicators, such as reliability, comfort, and safety, to provide a more comprehensive assessment of the overall user experience in multimodal networks. Secondly, future studies could explore the integration of real-time data from various sources, such as GPS tracking and smart card systems, to enable dynamic monitoring and optimization of travel times.

Furthermore, the application of advanced data analytics techniques, such as machine learning and predictive modeling, could help identify patterns and forecast travel time variations under different scenarios. This would enable proactive decision-making and resource allocation to mitigate potential disruptions and improve system resilience.

However, it is important to acknowledge the limitations of the current study. The analysis relies on data collected through surveys and secondary sources, which may be subject to biases and inaccuracies. Future research could benefit from more extensive and representative data collection efforts, including longitudinal studies to capture temporal variations in travel behavior and performance.

Additionally, the case study focuses on a single city, which may limit the generalizability of the findings to other contexts with different socio-economic, cultural, and infrastructural characteristics. Comparative studies across multiple cities and regions would help validate the robustness and transferability of the proposed methodology.

Despite these limitations, the present study makes a significant contribution to the field of multimodal transportation planning by providing a systematic framework for evaluating travel time performance. The insights gained from this research can inform policy decisions and investment priorities to enhance the efficiency and sustainability of urban mobility systems. As cities continue to grapple with the challenges of congestion, pollution, and accessibility, the development and application of such analytical tools will be crucial in shaping the future of transportation.

Funding

This work has no funding resources.

Ethics statement

This material has not been published in whole or in part elsewhere; The manuscript is not currently being considered for publication in another journal; All authors have been personally and actively involved in substantive work leading to the manuscript, and will hold themselves jointly and individually responsible for its content.

Availability of data and materials

Data sharing is applicable to this article on request to corresponding author.

CRediT authorship contribution statement

Rahul Tanwar: Writing – original draft, Validation, Software, Methodology, Investigation, Data curation, Conceptualization. Pradeep Kumar Agarwal: Writing – review & editing, Visualization, Supervision, Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article: