Customers' strategic behavior in batch arrivals M2/M/1 queue

The investigated problem is the analysis of customers’ strategic behavior in a single server Markovian M2/M/1 queue with batch arrivals of two customers with a reward-cost structure. At their arrival time, customers can decide to join the queue or to balk. The utility of each one depends on his decision, on his partner’s decision and on the system state. Two cases are considered: when the system provides the information about its state (observable case), and when this information is not provided (unobservable case). Both problems are modeled as games in extensive form with complete and imperfect information. We give the Nash equilibria for each corresponding game and we compare between both cases in order to determine the policy which arranges the system’s manager.

[1]  Naishuo Tian,et al.  Equilibrium analysis in batch-arrival queues with complementary services , 2009 .

[2]  Laurens G. Debo,et al.  Equilibrium in Queues Under Unknown Service Times and Service Value , 2014, Oper. Res..

[3]  Antonis Economou,et al.  Equilibrium customer strategies in a single server Markovian queue with setup times , 2007, Queueing Syst. Theory Appl..

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

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

[6]  Refael Hassin,et al.  Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers , 2012, Eur. J. Oper. Res..

[7]  Refael Hassin.  Information And Uncertainty In A Queuing System , 2007 .

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

[9]  Amnon Rapoport,et al.  Batch Queues with Choice of Arrivals: Equilibrium Analysis and Experimental Study , 2004 .

[10]  Y. Dimitrakopoulos,et al.  Customer equilibrium and optimal strategies in an M/M/1 queue with dynamic service control , 2016, Eur. J. Oper. Res..

[11]  John J. Hasenbein,et al.  Admission control and pricing in a queue with batch arrivals , 2010, Oper. Res. Lett..

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

[13]  Apostolos Burnetas,et al.  Dynamic admission control for loss systems with batch arrivals , 2005, Advances in Applied Probability.

[14]  Vincent A. Knight,et al.  Comparisons between observable and unobservable M/M/1 queues with respect to optimal customer behavior , 2013, Eur. J. Oper. Res..

[15]  Refael Hassin,et al.  Strategic Behavior and Social Optimization in Markovian Vacation Queues , 2011, Oper. Res..

[16]  Antonis Economou,et al.  Optimal balking strategies and pricing for the single server Markovian queue with compartmented waiting space , 2008, Queueing Syst. Theory Appl..

[17]  Apostolos Burnetas,et al.  Admission control with batch arrivals , 2004, Oper. Res. Lett..

[18]  Antonis Economou,et al.  Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes , 2012, Eur. J. Oper. Res..

[19]  Fikri Karaesmen,et al.  Structural results on a batch acceptance problem for capacitated queues , 2007, Math. Methods Oper. Res..

[20]  Refael Hassin,et al.  Equilibrium in Queueing Systems with Complementary Products , 2005, Queueing Syst. Theory Appl..

[21]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .