Queueing system with impatient customers: A review

In this paper, queueing systems with impatient customers is surveyed in accordance with various dimensions. First, we introduce the impatient behaviors (balking and reneging) and their various rules proposed in literature. Second, analytic solutions, numerical solutions and simulation modeling of the queue with impatient customers are investigated. Third, we propose the optimization both from the perspective of customers and providers. Finally, some research trendencies in the field are included.

[1]  Jau-Chuan Ke,et al.  Modified vacation policy for M/G/1 retrial queue with balking and feedback , 2009, Comput. Ind. Eng..

[2]  Sunggon Kim,et al.  The Virtual Waiting Time of the M/G/1 Queue with Impatient Customers , 2001, Queueing Syst. Theory Appl..

[3]  Gabriel R. Bitran,et al.  A review of open queueing network models of manufacturing systems , 1992, Queueing Syst. Theory Appl..

[4]  Jacques Teghem Use of discrete transforms for the study of aGI/M/S queue with impatient customer phenomena , 1979, Z. Oper. Research.

[5]  Donald L. Iglehart,et al.  Simulation methods for queues: An overview , 1988, Queueing Syst. Theory Appl..

[6]  Yves Dallery,et al.  Queueing models for full-flexible multi-class call centers with real-time anticipated delays , 2009 .

[7]  Avishai Mandelbaum,et al.  Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers , 2009, Oper. Res..

[8]  Erica L. Plambeck,et al.  Sensitivity of Optimal Capacity to Customer Impatience in an Unobservable M/M/S Queue (Why You Shouldn't Shout at the DMV) , 2009, Manuf. Serv. Oper. Manag..

[9]  Douglas G. Woolford,et al.  A preemptive priority queue with balking , 2005, Eur. J. Oper. Res..

[10]  Uri Yechiali,et al.  Queues with slow servers and impatient customers , 2010, Eur. J. Oper. Res..

[11]  Kuo-Hsiung Wang,et al.  Cost analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns , 2002, Math. Methods Oper. Res..

[12]  Jesus R. Artalejo,et al.  On the impact of customer balking, impatience and retrials in telecommunication systems , 2009, Comput. Math. Appl..

[13]  Opher Baron,et al.  Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements , 2009, Oper. Res..

[14]  Y. Shin,et al.  M/M/s queue with impatient customers and retrials , 2009 .

[15]  Moshe Haviv,et al.  On balking from an empty queue , 2007, Queueing Syst. Theory Appl..

[16]  J. Templeton Retrial queues , 1999 .

[17]  Gennadi Falin,et al.  A survey of retrial queues , 1990, Queueing Syst. Theory Appl..

[18]  Pengfei Guo,et al.  The effects of the availability of waiting-time information on a balking queue , 2009, Eur. J. Oper. Res..

[19]  Pilar Moreno,et al.  A discrete time single-server queue with balking: economic applications , 2008 .

[20]  Sherif I. Rabia,et al.  A discrete time Geo/G/1 retrial queue with general retrial times and balking customers , 2008 .

[21]  W. Whitt,et al.  Improving Service by Informing Customers About Anticipated Delays , 1999 .

[22]  Walid F. Nasrallah How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging , 2009, Eur. J. Oper. Res..

[23]  Hong Chen,et al.  Capacity competition of make-to-order firms , 2005, Oper. Res. Lett..

[24]  Baris Balcioglu,et al.  On priority queues with impatient customers , 2008, Queueing Syst. Theory Appl..

[25]  Avishai Mandelbaum,et al.  Statistical Analysis of a Telephone Call Center , 2005 .

[26]  Peter W. Glynn,et al.  A Diffusion Approximation for a GI/GI/1 Queue with Balking or Reneging , 2005, Queueing Syst. Theory Appl..

[27]  J. R. Artalejo,et al.  Approximations for multiserver queues with balking/retrial discipline , 1995 .

[28]  Long Gao,et al.  Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers , 2007, Manag. Sci..

[29]  Ragab Omarah Al-Seedy,et al.  Transient solution of the M/M/c queue with balking and reneging , 2009, Comput. Math. Appl..

[30]  Martien van Tits,et al.  Simulation of a queueing problem with balking , 1979 .

[31]  Vidyadhar G. Kulkarni,et al.  BALKING AND RENEGING IN M/G/s SYSTEMS EXACT ANALYSIS AND APPROXIMATIONS , 2008, Probability in the Engineering and Informational Sciences.

[32]  Marcel F. Neuts,et al.  Matrix-analytic methods in queuing theory☆ , 1984 .

[33]  U. Narayan Bhat,et al.  Sixty Years of Queueing Theory , 1969 .

[34]  Jau-Chuan Ke Operating characteristic analysis on the M[x]/G/1 system with a variant vacation policy and balking , 2007 .

[35]  Avishai Mandelbaum,et al.  Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue , 2005, Queueing Syst. Theory Appl..

[36]  Joseph D. Blackburn Optimal Control of a Single-Server Queue with Balking and Reneging , 1972 .

[37]  Ward Whitt,et al.  Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments , 2009, Manag. Sci..

[38]  C. J. Ancker,et al.  Some Queuing Problems with Balking and Reneging. I , 1963 .

[39]  Paul H. Zipkin,et al.  THE IMPACTS OF CUSTOMERS’ DELAY-RISK SENSITIVITIES ON A QUEUE WITH BALKING , 2009, Probability in the Engineering and Informational Sciences.

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

[41]  Zhe George Zhang,et al.  Matrix Analytic Method and Working Vacation Queues - A Survey , 2009 .

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

[43]  D. S. Robson,et al.  A single server queue with random arrivals and balking: Confidence interval estimation , 1990, Queueing Syst. Theory Appl..

[44]  Pengfei Guo,et al.  The effects of information on a queue with balking and phase‐type service times , 2008 .

[45]  Vijendra P. Singh Two-Server Markovian Queues with Balking: Heterogeneous vs. Homogeneous Servers , 1970, Oper. Res..

[46]  Jaejin Jang,et al.  Estimation of the mean waiting time of a customer subject to balking: a simulation study , 2007 .

[47]  Pen-Yuan Liao,et al.  Optimal pricing strategy for queuing systems with balking loss and reneging loss , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

[48]  Shaler Stidham,et al.  A survey of Markov decision models for control of networks of queues , 1993, Queueing Syst. Theory Appl..

[49]  Wei Xiong,et al.  An approximation for multi-server queues with deterministic reneging times , 2009, Ann. Oper. Res..

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

[51]  Frank A. Haight,et al.  QUEUEING WITH BALKING , 1957 .

[52]  Thomas L. Saaty,et al.  Elements of queueing theory , 2003 .

[53]  Vidyadhar G. Kulkarni,et al.  Explicit solutions for the steady state distributions in M/PH/1 queues with workload dependent balking , 2006, Queueing Syst. Theory Appl..

[54]  David J. Worthington,et al.  Reflections on queue modelling from the last 50 years , 2009, J. Oper. Res. Soc..

[55]  Vidyadhar G. Kulkarni,et al.  Busy period analysis for M/PH/1 queues with workload dependent balking , 2008, Queueing Syst. Theory Appl..

[56]  A. M. A. Hariri,et al.  The M/M/c/N queue with balking and reneging , 1992, Comput. Oper. Res..

[57]  Uri Yechiali,et al.  Queues with system disasters and impatient customers when system is down , 2007, Queueing Syst. Theory Appl..

[58]  S. Subba Rao,et al.  Queuing Models with Balking, Reneging, and Interruptions , 1965 .

[59]  Leslie D. Servi,et al.  Moment estimation of customer loss rates from transactional data , 1998 .

[60]  Rosa E. Lillo Optimal control of an M/G/1 queue with impatient priority customers , 2001 .

[61]  Ragab Omarah Al-Seedy A transient solution of queues with variable channel considering balking concept when S , 2006, Appl. Math. Comput..

[62]  Antonis Economou,et al.  Synchronized reneging in queueing systems with vacations , 2009, Queueing Syst. Theory Appl..

[63]  François Baccelli,et al.  Elements Of Queueing Theory , 1994 .

[64]  Andreas Brandt,et al.  On the M(n)/M(n)/s Queue with Impatient Calls , 1999, Perform. Evaluation.

[65]  Ernest Koenigsberg,et al.  Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review , 1982 .

[66]  Jihong Ou,et al.  Benefits of providing amenities to impatient waiting customers , 2003, Comput. Oper. Res..

[67]  Sunggon Kim,et al.  The stationary workload of the G/M/1 queue with impatient customers , 2010, Queueing Syst. Theory Appl..

[68]  Hui Li,et al.  A Retrial Queue with a Constant Retrial Rate, Server Downs and Impatient Customers , 2005 .

[69]  M. H. L. van Tits,et al.  Simulation of a queueing problem with balking , 1979, SIML.

[70]  Antonis Economou,et al.  Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs , 2008, Oper. Res. Lett..

[71]  Apostolos Burnetas,et al.  Priority option pricing in an M/M/m , 2008, Oper. Res. Lett..

[72]  S. S. Rao,et al.  Queuing with balking and reneging in M|G|1 systems , 1967 .

[73]  J. R. Artalejo,et al.  On The Single Server Retrial Queue With Balking , 2000 .

[74]  Avishai Mandelbaum,et al.  Adaptive Behavior of Impatient Customers in Tele-Queues: Theory and Empirical Support , 2002, Manag. Sci..

[75]  Thomas L. Saaty,et al.  Seven more years of queues. A lament and a bibliography , 1966 .

[76]  Refael Hassin,et al.  Equilibrium strategies for queues with impatient customers , 1995, Oper. Res. Lett..

[77]  Benjamin Avi-Itzhak,et al.  Strategic Equilibrium for a Pair of Competing Servers with Convex Cost and Balking , 2002, Manag. Sci..

[78]  Boyan N. Dimitrov Queues with resequencing: a survey and recent results , 1997 .

[79]  Kuo-Hsiung Wang,et al.  Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers , 2004, RAIRO Oper. Res..

[80]  Ken'ichi Kawanishi,et al.  QBD approximations of a call center queueing model with general patience distribution , 2008, Comput. Oper. Res..

[81]  Ronald Stewart Dick,et al.  Some Theorems on a Single-Server Queue with Balking , 1970, Oper. Res..

[82]  Bara Kim,et al.  MAP/M/c Queue with Constant Impatient Time , 2004, Math. Oper. Res..

[83]  Lee K. Jones,et al.  Inferring Balking Behavior From Transactional Data , 1999, Oper. Res..

[84]  Amit Pazgal,et al.  Comparison of customer balking and reneging behavior to queueing theory predictions: An experimental study , 2008, Comput. Oper. Res..

[85]  Gyutai Kim,et al.  Empirical Analysis for Individual Behavior of Impatient Customers in a Call Center , 2004, AsiaSim.

[86]  Hayriye Ayhan,et al.  A monotonicity result for a G/GI/c queue with balking or reneging , 2006, Journal of Applied Probability.

[87]  Ward Whitt,et al.  The Impact of Delay Announcements in Many-Server Queues with Abandonment , 2009, Oper. Res..

[88]  Frank A. Haight,et al.  Queueing with reneging , 1959 .

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

[90]  Martin J. Fischer,et al.  Approximation Techniques in the Solution of Queueing Problems. Revision. , 1978 .

[91]  Al-Seedy Ragab Omarah A transient solution of queues with variable channel considering balking concept when S = 2 and σ = 1 , 2006 .

[92]  R. O. Al-Seedy Analytical solution of the state-dependent Erlangian queue: M/Ej/1/N with balking , 1996 .

[93]  Nam Kyoo Boots,et al.  AnM/M/c queue with impatient customers , 1999 .