Problem
Research questions and friction points this paper is trying to address.
equilibrium joining strategies
strategic customers
two-phase random environment
queueing system
information scenarios
Equilibrium Joining Strategies for Queues in Two-Phase Random Environment
🤖 AI Summary
This study investigates the equilibrium joining decisions of strategic customers in an M/M/1 queue operating within a two-phase random environment. By integrating continuous-time Markov processes, game theory, and queueing theory, it systematically analyzes utility-based join-or-balk strategies across four information scenarios. Explicit solutions are derived for the observable-environment and fully unobservable cases under both fast-oscillation and slow-switching regimes, and the corresponding equilibrium conditions are established for each information structure. The findings reveal how the dynamic evolution of the random environment shapes customers’ equilibrium entry strategies, providing a theoretical foundation for information design and strategic optimization in stochastic service systems.
📝 Abstract
We study equilibrium joining strategies in an M/M/1-type queueing system with strategic customers operating in a two-phase random environment described as a continuous-time Markov process. Strategic customers, upon arrival, choose whether to join or to balk based on available information and anticipated utility, considering the trade-off between reward from service and waiting cost. Four observation scenarios are analysed: fully observable (both queue length and environment phase are disclosed to a customer upon arrival), queue-only observable, environment-only observable, and fully unobservable. In each case, equilibrium joining strategies are analysed. In the environment-only observable and fully unobservable cases, explicit solutions and equilibrium conditions are derived under rapid oscillations and under very slow transitions between environment phases.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Equilibrium joining strategies
Two-phase random environment
Strategic customers
M/M/1 queueing system
Information observability
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