Equilibrium Strategies in M/M/1 Priority Queues with Balking

55 Pages Posted: 6 Feb 2017 Last revised: 21 Apr 2018

See all articles by Jinting Wang

Jinting Wang

Beijing Jiaotong University; Central University of Finance and Economics

Shiliang Cui

Georgetown University - McDonough School of Business

Zhongbin Wang

Beijing Jiaotong University

Date Written: April 13, 2018

Abstract

We consider an M/M/1 queueing system with a pay-for-priority option, and study customers' joint decisions between joining/balking and pay-for-priority. The equilibrium strategies are thus two-dimensional. First, we fully characterize the equilibrium structure and identify the Pareto-dominant strategies of such a game analytically, under both the observable and unobservable settings. Interestingly, the equilibrium structure, the system throughput, and the service provider's optimal price for priority premium can all be non-monotone in the service reward, which departs from the existing models of priority queues without balking. In particular, we fi nd that an increase in service reward can actually hurt the firm's revenue (everything else being equal). Second, we compare the server's revenue between the observable and the unobservable settings. We find that the service provider is better off with the observable setting when the system load is either low or high, but benefi ts more from the unobservable setting when the system load is medium. The fact that the optimal setting switches twice as the system load increases, is rather interesting; we explain the intuitions behind it in this paper. Finally, we demonstrate the implications of these fi ndings by applying our model framework to Papa John's Pizza, based on publicly available information. Our analysis suggests that Papa John's could benefi t from providing customers with wait information while slightly decreasing its fee for Papa Priority.

Keywords: M/M/1 Queues; Priorities; Balking; Pareto-Dominant Equilibrium; Pricing

Suggested Citation

Wang, Jinting and Cui, Shiliang and Wang, Zhongbin, Equilibrium Strategies in M/M/1 Priority Queues with Balking (April 13, 2018). Available at SSRN: https://ssrn.com/abstract=2911419 or http://dx.doi.org/10.2139/ssrn.2911419

Jinting Wang

Beijing Jiaotong University ( email )

No.3 of Shangyuan Residence Haidian District
Beijing, 100089
China

Central University of Finance and Economics ( email )

Beijing, Beijing 100081
China

Shiliang Cui (Contact Author)

Georgetown University - McDonough School of Business ( email )

Washington, DC 20057
United States

Zhongbin Wang

Beijing Jiaotong University ( email )

No.3 of Shangyuan Residence Haidian District
Beijing, 100089
China

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