Duopoly Competition Considering Waiting Cost

Abstract

In this paper we consider two queueing systems that serve a large number of customers. Those two queueing systems compete for customers. Prices, (p1, p2), for each queueing system are announced, and each individual user makes a decision whether to join the queueing systems. In case a user decides to enter, he should determine which of the two queueing systems to join. Mendelson(1985) analyzes internal pricing scheme to control the job flow into a queueing system. Mendelson model considers the special case where all jobs are homogeneous in their time values and expected service requirements. But jobs usually have heterogeneous values specifying the gross value gained by system users per unit time. An important extension of Mendelson model was made by Mendelson and Whang. Mendelson and Whang(1990) consider an M/M/1 queueing system with multiple user classes. Each class is characterized by its delay cost per unit of time, its expected service time and its demand function. They derive a pricing mechanism which is optimal and incentive-compatible in the sense that the arrival rates and execution priorities jointly maximize the expected net value of the system while being determined, on a decentralized basis, by individual users.