M/G/1 queue with deterministic reneging times

We consider a single-server queue with a deterministic reneging time motivated by the timeout mechanism used in application servers in distributed computing environments. We have employed a Volterra integral equation to study the M/G/1 queue with reneging using level crossing analysis. An analytical solution is given for the M/H"2/1 queue with deterministic reneging times and a numerical approach is presented for the more general M/G/1 queue. The numerical approach is verified via simulation and the results reveal that predictions are highly accurate with errors that are in general below 0.5%.

[1]  P. H. Brill,et al.  Level Crossings in Point Processes Applied to Queues: Single-Server Case , 1977, Oper. Res..

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

[3]  F. Baccelli,et al.  Single-server queues with impatient customers , 1984, Advances in Applied Probability.

[4]  Ali Movaghar-Rahimabadi.  On queueing with customer impatience until the beginning of service , 1998, Queueing Syst. Theory Appl..

[5]  Robert E. Stanford,et al.  Reneging Phenomena in Single Channel Queues , 1979, Math. Oper. Res..

[6]  D. Y. Barrer.  Queuing with Impatient Customers and Ordered Service , 1957 .

[7]  Onno Boxma,et al.  Multiserver queues with impatient customers , 1993 .

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

[9]  Walter Ledermann,et al.  Handbook of applicable mathematics , 1980 .

[10]  O. J. Boxma,et al.  Approximations of the Mean Waiting Time in an M/G/s Queueing System , 1979, Oper. Res..

[11]  B. Melamed,et al.  Models and Approximations for Call Center Design , 2003 .

[12]  R. Haugen,et al.  Queueing Systems with Stochastic Time out , 1980, IEEE Trans. Commun..

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

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

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

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

[17]  Oj Onno Boxma,et al.  Teletraffic Analysis and Computer Performance Evaluation , 1988 .

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

[19]  P. D. Finch.  Deterministic customer impatience in the queueing system GI/M/1; a correction , 1961 .

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

[21]  P. D. Finch.  Deterministic customer impatience in the queueing system GI/M/1 , 1960 .

[22]  D. Y. Barrer.  Queuing with Impatient Customers and Indifferent Clerks , 1957 .

[23]  B T Doshi,et al.  An M/G/1 queue with class dependent balking (reneging) , 1986 .

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

[25]  R. E. Stanford.  On queues with impatience , 1990, Advances in Applied Probability.

[26]  K. Fernow.  New York , 1896, American Potato Journal.

[27]  David L. Jagerman.  Difference equations with applications to queues , 2000 .

[28]  Ronald W. Wolff,et al.  The M/G/c queue in light traffic , 1998, Queueing Syst. Theory Appl..

[29]  Ward Whitt,et al.  Understanding the Efficiency of Multi-Server Service Systems , 1992 .

[30]  A. Federgruen,et al.  Approximations for the steady-state probabilities in the multi-server m/g/c queue : (preprint) , 1979 .

[31]  Henk C. Tijms,et al.  A Two-Moment Approximation for a Buffer Design Problem Requiring a Small Rejection Probability , 1985, Perform. Evaluation.