Equilibrium customers’ choice between FCFS and random servers

Consider two servers of equal service capacity, one serving in a first-come first-served order (FCFS), and the other serving its queue in random order. Customers arrive as a Poisson process and each arriving customer observes the length of the two queues and then chooses to join the queue that minimizes its expected queueing time. Assuming exponentially distributed service times, we numerically compute a Nash equilibrium in this system, and investigate the question of which server attracts the greater share of customers. If customers who arrive to find both queues empty independently choose to join each queue with probability 0.5, then we show that the server with FCFS discipline obtains a slightly greater share of the market. However, if such customers always join the same queue (say of the server with FCFS discipline) then that server attracts the greater share of customers.

[1]  Ady Pauzner,et al.  Resolving Indeterminacy in Dynamic Settings: The Role of Shocks , 2000 .

[2]  Refael Hassin,et al.  Equilibrium strategies and the value of information in a two line queueing system with threshold jockeying , 1994 .

[3]  Benjamin Avi-Itzhak,et al.  A resource allocation queueing fairness measure: properties and bounds , 2007, Queueing Syst. Theory Appl..

[4]  Refael Hassin,et al.  ON THE OPTIMALITY OF FIRST COME LAST SERVED QUEUES , 1985 .

[5]  P. Naor.  The Regulation of Queue Size by Levying Tolls , 1969 .

[6]  Timothy J. Kehoe,et al.  An Index Theorem for General Equilibrium Models with Production , 1980 .

[7]  Pengfei Guo,et al.  Analysis and Comparison of Queues with Different Levels of Delay Information , 2007, Manag. Sci..

[8]  Eitan Altman,et al.  Optimal Routing Among ⋅/M/1 Queues with Partial Information , 2004 .

[9]  C. Larsen.  Investigating sensitivity and the impact of information on pricing decisions in an M/M/1/ ∞ queueing model , 1998 .

[10]  John Whalley,et al.  Uniqueness of equilibrium in large-scale numerical general equilibrium models , 1985 .

[11]  Refael Hassin.  Consumer Information in Markets with Random Product Quality: The Case of Queues and Balking , 1986 .

[12]  D. K. Hildebrand,et al.  Congestion Tolls for Poisson Queuing Processes , 1975 .

[13]  André de Palma,et al.  Information and Time-of-Usage Decisions in the Bottleneck Model with Stochastic Capacity and Demand , 1999 .

[14]  Hanna Alperstein.  Note-Optimal Pricing Policy for the Service Facility Offering a Set of Priority Prices , 1988 .

[15]  Refael Hassin,et al.  To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems , 2002 .

[16]  Frank Heinemann,et al.  American Economic Association Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks : Comment , 2015 .

[17]  Nicolas Vieille,et al.  Social Learning in One-Arm Bandit Problems , 2007 .

[18]  André de Palma,et al.  INFORMATION AND USAGE OF FREE-ACCESS CONGESTIBLE FACILITIES WITH STOCHASTIC CAPACITY AND DEMAND* , 1993 .

[19]  J. Gittins,et al.  A dynamic allocation index for the discounted multiarmed bandit problem , 1979 .

[20]  Refael Hassin,et al.  Equilibrium Threshold Strategies: The Case of Queues with Priorities , 1997, Oper. Res..

[21]  Benjamin Avi-Itzhak,et al.  QUANTIFYING FAIRNESS IN QUEUING SYSTEMS , 2008, Probability in the Engineering and Informational Sciences.

[22]  Refael Hassin,et al.  On the advantage of being the first server , 1996 .