Inefficiency in stochastic queueing systems with strategic customers

Abstract This paper summarizes the literature on efficiency loss when agents selfishly optimize their utility in stochastic queueing systems. The price of anarchy is the most popular measure for quantifying this loss, but we also discuss other measures. The queueing models are introduced briefly and results on the loss of efficiency are discussed.

[1]  Yu Wu,et al.  Heavy Traffic Approximation of Equilibria in Resource Sharing Games , 2012, IEEE J. Sel. Areas Commun..

[2]  Shaler Stidham,et al.  The Price of Anarchy for a Network of Queues in Heavy Traffic , 2014, Essays in Production, Project Planning and Scheduling.

[3]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2005, IEEE Trans. Autom. Control..

[4]  Antonis Economou,et al.  Strategic customer behavior in a queueing system with delayed observations , 2017, Queueing Syst. Theory Appl..

[5]  Dusit Niyato,et al.  Strategic Access and Pricing in Internet of Things (IoT) Service With Energy Harvesting , 2019, IEEE Access.

[6]  Tricha Anjali,et al.  Price of Anarchy in network routing with class based capacity guarantees , 2014, IEEE INFOCOM 2014 - IEEE Conference on Computer Communications.

[7]  Li Xia,et al.  Service rate control of closed Jackson networks from game theoretic perspective , 2014, Eur. J. Oper. Res..

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

[9]  Joel E. Cohen,et al.  A paradox of congestion in a queuing network , 1990, Journal of Applied Probability.

[10]  D. Manjunath,et al.  To Lounge or to Queue Up , 2016, PERV.

[11]  Liron Ravner,et al.  Equilibrium arrival times to a queue with order penalties , 2013, Eur. J. Oper. Res..

[12]  Nicholas Bambos,et al.  Game based capacity allocation for utility computing environments , 2008, Valuetools 2008.

[13]  Tim Roughgarden,et al.  The price of anarchy in an exponential multi-server , 2007, Oper. Res. Lett..

[14]  Refael Hassin,et al.  Regulation under partial cooperation: The case of a queueing system , 2014, Oper. Res. Lett..

[15]  Yezekael Hayel,et al.  Decentralized optimization of last-mile delivery services with non-cooperative bounded rational customers , 2016, Ann. Oper. Res..

[16]  Refael Hassin,et al.  ?/M/1: On the equilibrium distribution of customer arrivals , 1983 .

[17]  Sandeep Juneja,et al.  The concert queueing game: strategic arrivals with waiting and tardiness costs , 2013, Queueing Syst. Theory Appl..

[18]  Tim Roughgarden,et al.  On the severity of Braess's Paradox: Designing networks for selfish users is hard , 2006, J. Comput. Syst. Sci..

[19]  Yi Gai,et al.  A packet dropping mechanism for efficient operation of M/M/1 queues with selfish users , 2011, Comput. Networks.

[20]  Pelin G. Canbolat.  Bounded rationality in clearing service systems , 2020, Eur. J. Oper. Res..

[21]  Uri Yechiali,et al.  On Optimal Balking Rules and Toll Charges in the GI/M/1 Queuing Process , 1971, Oper. Res..

[22]  Jie Li,et al.  Numerical studies on a paradox for non-cooperative static load balancing in distributed computer systems , 2006, Comput. Oper. Res..

[23]  Refael Hassin,et al.  Profit maximization in the M/M/1 queue , 2017, Oper. Res. Lett..

[24]  Jr. Shaler Stidham.  Optimal control of admission to a queueing system , 1985 .

[25]  Refael Hassin,et al.  A strategic model of job arrivals to a single machine with earliness and tardiness penalties , 2017, 1701.04776.

[26]  Eitan Altman,et al.  Inefficient Noncooperation in Networking Games of Common-Pool Resources , 2008, IEEE Journal on Selected Areas in Communications.

[27]  Parijat Dube,et al.  Bertrand equilibria and efficiency in markets for congestible network services , 2014, Autom..

[28]  Balakrishna J. Prabhu,et al.  A resource-sharing game with relative priorities , 2014, Perform. Evaluation.

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

[30]  Moshe Haviv,et al.  Strategic timing of arrivals to a finite queue multi-server loss system , 2015, Queueing Syst. Theory Appl..

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

[32]  Adam Wierman,et al.  Competition yields efficiency in load balancing games , 2011, Perform. Evaluation.

[33]  Eitan Altman,et al.  Braess-like paradoxes in distributed computer systems , 2000, IEEE Trans. Autom. Control..

[34]  Vincent A. Knight,et al.  Measuring the price of anarchy in critical care unit interactions , 2017, J. Oper. Res. Soc..

[35]  Eitan Altman,et al.  Mean-Field Game Approach to Admission Control of an M/M/$$\infty $$∞ Queue with Shared Service Cost , 2016 .

[36]  S. Gavirneni,et al.  Self‐Selecting Priority Queues with Burr Distributed Waiting Costs , 2014 .

[37]  David Starobinski,et al.  Advance Reservation Games , 2017, ACM Trans. Model. Perform. Evaluation Comput. Syst..

[38]  Refael Hassin,et al.  Strategic customer behavior in a queueing system with a loss subsystem , 2017, Queueing Syst. Theory Appl..

[39]  Hyun-Soo Ahn,et al.  The potentially negative effects of cooperation in service systems , 2020, Advances in Applied Probability.

[40]  Kashi R. Balachandran,et al.  Public and private optimization at a service facility with approximate information on congestion , 1980 .

[41]  Urtzi Ayesta,et al.  Load balancing in processor sharing systems , 2011, Telecommun. Syst..

[42]  Balakrishna J. Prabhu,et al.  Worst-case analysis of non-cooperative load balancing , 2014, Annals of Operations Research.

[43]  Berthold Vöcking,et al.  Selfish Traffic Allocation for Server Farms , 2010, SIAM J. Comput..

[44]  Refael Hassin,et al.  On Optimal and Equilibrium Retrial Rates in a Queueing System , 1996 .

[45]  I. Ziedins,et al.  Braess's Paradox in a Queueing Network with State-Dependent Routing , 1997 .

[46]  Tim Roughgarden,et al.  The price of anarchy is independent of the network topology , 2002, STOC '02.

[47]  Tao Wu,et al.  A Comparative Analysis of Server Selection in Content Replication Networks , 2008, IEEE/ACM Transactions on Networking.

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

[49]  Paul R. Harper,et al.  Selfish routing in public services , 2013, Eur. J. Oper. Res..

[50]  Balakrishna J. Prabhu,et al.  Is the Price of Anarchy the Right Measure for Load-Balancing Games? , 2014, TOIT.

[51]  Hisao Kameda,et al.  Paradoxes in distributed decisions on optimal load balancing for networks of homogeneous computers , 2002, JACM.

[52]  Refael Hassin,et al.  Equilibrium and optimal arrival patterns to a server with opening and closing times , 2010 .

[53]  Mahnoosh Alizadeh,et al.  Congestion control and pricing in a network of electric vehicle public charging stations , 2017, 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[54]  Refael Hassin,et al.  On the price of anarchy in a single-server queue with heterogeneous service valuations induced by travel costs , 2018, Eur. J. Oper. Res..

[55]  Refael Hassin,et al.  The Price of Anarchy in the Markovian Single Server Queue , 2014, IEEE Transactions on Automatic Control.

[56]  Hamid Garmani,et al.  A Stackelberg game-based approach for interactions among Internet service providers and content providers , 2019, NETNOMICS: Economic Research and Electronic Networking.

[57]  Hisao Kameda,et al.  A paradox in optimal flow control of M/M/m queues , 2006, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[58]  David Starobinski,et al.  Social Welfare and Price of Anarchy in Preemptive Priority Queues , 2020, Oper. Res. Lett..

[59]  Balakrishna J. Prabhu,et al.  Price of anarchy in non-cooperative load balancing games , 2011, Perform. Evaluation.

[60]  S. Stidham,et al.  Individual versus Social Optimization in the Allocation of Customers to Alternative Servers , 1983 .

[61]  Ping Huang,et al.  Strategic behavior and social optimization in a constant retrial queue with the N-policy , 2017, Eur. J. Oper. Res..

[62]  Eitan Altman,et al.  Joint Operator Pricing and Network Selection Game in Cognitive Radio Networks: Equilibrium, System Dynamics and Price of Anarchy , 2013, IEEE Transactions on Vehicular Technology.

[63]  Clark Jeffries,et al.  Congestion resulting from increased capacity in single-server queueing networks , 1997, TNET.

[64]  Hisao Kameda,et al.  Coincident Cost Improvement vs. Degradation by Adding Connections to Noncooperative Networks and Distributed Systems , 2009 .

[65]  Bruno Gaujal,et al.  The price of forgetting in parallel and non-observable queues , 2011, Perform. Evaluation.