Equilibrium balking strategies for a clearing queueing system in alternating environment

TL;DR

This paper analyzes customer balking strategies in a Markovian clearing queue with an alternating environment, deriving Nash equilibrium strategies based on information levels and a reward-cost framework.

Contribution

It introduces a model for customer decision-making in a clearing queue with environment-dependent rates and derives equilibrium strategies under different information scenarios.

Findings

Derived Nash equilibrium balking strategies.

Analyzed impact of environment on customer behavior.

Provided insights into decision-making in clearing queues.

Abstract

We consider a Markovian clearing queueing system, where the customers are accumulated according to a Poisson arrival process and the server removes all present customers at the completion epochs of exponential service cycles. This system may represent the visits of a transportation facility with unlimited capacity at a certain station. The system evolves in an alternating environment that influences the arrival and the service rates. We assume that the arriving customers decide whether to join the system or balk, based on a natural linear reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies under various levels of information.