BALKING AND RENEGING IN M/G/s SYSTEMS EXACT ANALYSIS AND APPROXIMATIONS

We consider the virtual queuing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multiserver system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.

[1]  Jewgeni H. Dshalalow,et al.  Frontiers in Queueing: Models and Applications in Science and Engineering , 1997 .

[2]  J. Ben Atkinson,et al.  Modeling and Analysis of Stochastic Systems , 1996 .

[3]  Daniel P. Heyman,et al.  Stochastic processes and operating characteristics , 2004 .

[4]  Ward Whitt,et al.  Engineering Solution of a Basic Call-Center Model , 2005, Manag. Sci..

[5]  B. V. Gnedenko,et al.  Introduction to queueing theory (2nd ed) , 1989 .

[6]  Avishai Mandelbaum,et al.  Designing a Call Center with Impatient Customers , 2002, Manuf. Serv. Oper. Manag..

[7]  Avishai Mandelbaum,et al.  Queueing Models of Call Centers: An Introduction , 2002, Ann. Oper. Res..

[8]  S. A. Nozaki,et al.  Approximations in finite-capacity multi-server queues by Poisson arrivals , 1978, Journal of Applied Probability.

[9]  Igor N. Kovalenko,et al.  Introduction to Queuing Theory , 1989 .

[10]  Rupert G. Miller.  Review: Lajos Takacs, Introduction to the Theory of Queues , 1964 .

[11]  A. Federgruen,et al.  Approximations for the steady-state probabilities in the M/G/c queue , 1981, Advances in Applied Probability.

[12]  A. M. Lee,et al.  Queueing Processes Associated with Airline Passenger Check-in , 1959 .

[13]  Rommert Dekker,et al.  Computing Compound Distributions Faster! , 1997 .

[14]  V. E. Beneš,et al.  General Stochastic Processes in the Theory of Queues , 1965 .

[15]  Henk Tijms,et al.  Stochastic modelling and analysis: a computational approach , 1986 .

[16]  Per Hokstad,et al.  Approximations for the M/G/m Queue , 1978, Oper. Res..

[17]  G. F. Newell,et al.  Introduction to the Theory of Queues. , 1963 .

[18]  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..

[19]  Toshikazu Kimura,et al.  Approximations for multi-server queues: System interpolations , 1994, Queueing Syst. Theory Appl..

[20]  Gordon F. Newell,et al.  Approximate Stochastic Behavior of n-Server Service Systems with Large n , 1973 .

[21]  Nam Kyoo Boots,et al.  A Multiserver Queueing System with Impatient Customers , 1999 .

[22]  Boris Gnedenko,et al.  Introduction to queueing theory , 1968 .

[23]  Arun N. Netravali.  Spline approximation to the solution of the Volterra integral equation of the second kind , 1973 .

[24]  M. Miyazawa.  Approximation of the queue-length distribution of an M/GI/s queue by the basic equations , 1986, Journal of Applied Probability.