Summary of Mathematical Models Considered in the Study.

Model/Approach	Description	Main expressions/Features
Classical Queueing Models	Stochastic formulations such as M/M/1, M/G/1, and G/G/1 commonly used in analytical evaluations of queueing delay and system load.	Non-adaptive; assumes immediate service readiness.
Standard Queue Management Policies	Telecommunication algorithms (DropTail, RED, CoDel) adapted to IoT systems; make decisions based on macrometrics like queue length.	Rule-based logic; ignores device availability state.
Protocol-Constrained Buffers	Models incorporating protocol-imposed inactivity (e.g., PSM, eDRX, duty-cycle); device unavailability is fixed and non-controllable.	Structured delays, but outside algorithmic control.
Heuristic Queue Strategies	Local, fixed-threshold decision rules (e.g., delay/drop when buffer exceeds a limit); lacks dynamic adaptation.	Empirical, non-formalised rules; rigid and context-dependent.
Task Offloading Mechanisms	Offloading to fog/cloud peers based on external metrics; does not model delay at the receiving node or internal queue dynamics.	External balancing; delay shifts not modelled.
RL-Based Delay Management	Reinforcement learning agents optimising QoS metrics; typically lack parameterised control over structural service delay.	Learning-based; focuses on external performance indicators.
Proposed Model (This Study)	G/G/1 queue with parameterised delay shift (θ); decentralised DQN-based agent controls service timing based on local queue state in real time.	Expressions (2)–(6), (10), (14), (19), (22)–(25); includes θ.