Stationary delays for a two-class priority queue with impatient customers

We consider a Markovian multiserver queue with two types of impatient customers, high and low priority ones. The first type of customers has a non-preemptive strict priority over the other type. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time he will renege and be lost. We focus on deriving performance measures in terms of the sojourn times of customers in queue, either before starting service, or before reneging. We provide an exact analysis for systems where customers within each type are served under the FCFS discipline of service.

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

[2]  Andreas Brandt,et al.  On the Two-Class M/M/1 System under Preemptive Resume and Impatience of the Prioritized Customers , 2004, Queueing Syst. Theory Appl..

[3]  Andrei Sleptchenko,et al.  Multi-class, multi-server queues with non-preemptive priorities , 2003 .

[4]  Ward Whitt,et al.  Heavy-Traffic Limits for Queues with Many Exponential Servers , 1981, Oper. Res..

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

[6]  Eitan Altman,et al.  On the stability of retrial queues , 1997, Queueing Syst. Theory Appl..

[7]  François Baccelli,et al.  ON QUEUES WITH IMPATIENT CUSTOMERS. , 1981 .

[8]  Carl M. Harris,et al.  Fundamentals of queueing theory (2nd ed.). , 1985 .

[9]  Peter W. Glynn,et al.  A Diffusion Approximation for a Markovian Queue with Reneging , 2003, Queueing Syst. Theory Appl..

[10]  Richard H. Davis.  Waiting-Time Distribution of a Multi-Server, Priority Queuing System , 1966, Oper. Res..

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

[12]  Onno Boxma,et al.  Queueing-theoretic solution methods for models of parallel and distributed systems , 1994 .

[13]  U. Yechiali,et al.  Waiting Times in the Non-Preemptive Priority M/M/c Queue , 1985 .

[14]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[15]  Adam Wierman,et al.  Multi-Server Queueing Systems with Multiple Priority Classes , 2005, Queueing Syst. Theory Appl..

[16]  D. Daley.  General customer impatience in the queue GI/G/ 1 , 1965 .

[17]  Tetsuya Takine,et al.  The Nonpreemptive Priority MAP/G/1 Queue , 1999, Oper. Res..

[18]  Bara Kim,et al.  M/M/1 Queue with Impatient Customers of Higher Priority , 2001, Queueing Syst. Theory Appl..

[19]  Ali Movaghar.  On queueing with customer impatience until the beginning of service , 1996 .

[20]  Leonard Kleinrock,et al.  Theory, Volume 1, Queueing Systems , 1975 .

[21]  H. Tijms,et al.  A queueing system with impatient customers , 1985 .

[22]  Yves Dallery,et al.  Moments of first passage times in general birth–death processes , 2008, Math. Methods Oper. Res..

[23]  Matthieu van der Heijden,et al.  An Exact Solution for the State Probabilities of the Multi-Class, Multi-Server Queue with Preemptive Priorities , 2005, Queueing Syst. Theory Appl..

[24]  Andreas Brandt,et al.  Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System , 2002, Queueing Syst. Theory Appl..

[25]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[26]  D. Wagner.  Analysis of mean values of a multi-server model with non-preemptive priorities and non-renewal input , 1997 .