Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority

Biao Xu,Zhong Yao,Xiuli Xu

doi:10.3934/jimo.2018113

Abstract

This paper investigates the low-priority customers' strategic behavior in the single-server queueing system with general service time and two customer types. The priority system is preemptive resume, which means that if a high-priority customer enters the system that are serving a low-priority customer, the arriving customer preempts the service facility and the preempted customer returns to the head of the queue for his own class. The customer who is preempted resumes service at the point of interruption upon reentering the system. The low-priority customer's dilemma is whether to join or balk based on a linear reward-cost structure. Two cases are distinguished based on the different levels of information that the low-priority customers acquire before joining the system. The equilibrium threshold strategy in the observable case and the equilibrium balking strategy as well as the socially optimal balking strategy in the unobservable case for the low-priority customers are derived finally.

Highlights

Due to the wide applications in service system, production management, electronic commerce and so forth, a growing number of papers that study customers strategic behavior in queueing models from an economic viewpoint have emerged
Our work considers the strategic decisions of customers in an M/G/1 queue, and contributes to the literature on the non-Markovian queueing systems
Based on the prior literatures, we examine the low-priority customers strategic behavior in M/G/1 queue serving two customer classes with preemption policy

Summary

Introduction

Due to the wide applications in service system, production management, electronic commerce and so forth, a growing number of papers that study customers strategic behavior in queueing models from an economic viewpoint have emerged. In the observable M/G/1 queue with two classes of customers and preemptive priority, there exists a unique equilibrium threshold ne, which is given by ne = In the unobservable queueing system, we suppose that the class-1 customers follow a mixed strategy with a joining probability q.

Results

Conclusion