Equilibrium balking strategies in the single server Markovian queue with catastrophes

TL;DR

This paper analyzes customer balking strategies in a Markovian queue with Poisson catastrophes, deriving Nash equilibrium strategies considering reward and cost factors for customers.

Contribution

It introduces a model for customer decision-making in queues affected by catastrophes and derives equilibrium strategies, a novel approach in this context.

Findings

Characterization of Nash equilibrium balking strategies

Impact of catastrophe rate on customer behavior

Analytical expressions for system performance metrics

Abstract

We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies.