A many-server fluid limit for the Gt/G//st+G/ queueing model experiencing periods of overloading

Abstract A many-server heavy-traffic functional weak law of large numbers is established for the G t / G I / s t + G I queueing model, which has customer abandonment (the + G I ), time-varying arrival rate and staffing (the subscript t ) and non-exponential service and patience distributions (the two G I ’s). This limit provides support for a previously proposed deterministic fluid approximation, and extends a previously established limit for the special case of exponential service times.

[1]  K. Ramanan,et al.  Fluid limits of many-server queues with reneging , 2010, 1011.2921.

[2]  J. Reed,et al.  The G/GI/N queue in the Halfin–Whitt regime , 2009, 0912.2837.

[3]  Avishai Mandelbaum,et al.  Strong approximations for Markovian service networks , 1998, Queueing Syst. Theory Appl..

[4]  W. Whitt,et al.  Martingale proofs of many-server heavy-traffic limits for Markovian queues ∗ , 2007, 0712.4211.

[5]  H. Kaspi,et al.  SPDE Limits of Many Server Queues , 2010, 1010.0330.

[6]  Ward Whitt,et al.  Fluid Models for Multiserver Queues with Abandonments , 2006, Oper. Res..

[7]  Ward Whitt,et al.  A Network of Time-Varying Many-Server Fluid Queues with Customer Abandonment , 2011, Oper. Res..

[8]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[9]  Ward Whitt,et al.  Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System , 2007 .

[10]  Kavita Ramanan,et al.  Law of large numbers limits for many-server queues , 2007, 0708.0952.

[11]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[12]  Gerhard J. Woeginger,et al.  Operations Research Letters , 2011 .

[13]  Anatolii A. Puhalskii,et al.  A heavy-traffic analysis of a closed queueing system with a GI/∞ service center , 1997, Queueing Syst. Theory Appl..

[14]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[15]  Ward Whitt,et al.  The Gt/GI/st+GI many-server fluid queue , 2012, Queueing Syst. Theory Appl..

[16]  Guodong Pang,et al.  Two-parameter heavy-traffic limits for infinite-server queues , 2008, Queueing Syst. Theory Appl..

[17]  Jiheng Zhang.  Fluid models of many-server queues with abandonment , 2013, Queueing Syst. Theory Appl..

[18]  Anatolii A. Puhalskii,et al.  On many-server queues in heavy traffic , 2010, 1001.2163.

[19]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .

[20]  Ward Whitt,et al.  Many-server heavy-traffic limit for queues with time-varying parameters , 2014, 1401.3933.

[21]  A. Skorokhod.  Limit Theorems for Stochastic Processes , 1956 .

[22]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[23]  Ward Whitt,et al.  Heavy-traffic limits for waiting times in many-server queues with abandonment , 2009 .