Performance analysis and optimal control of the Geo/Geo/c queue

Discrete-time multiserver queues have been used for many years to investigate the behavior of communication and computer systems in which time is slotted. In this paper, we consider the discrete-time Geo/Geo/c queue. We first develop an efficient recursive procedure to obtain the steady-state probabilities and prove the convergence to the continuous-time counterpart. We also deal with the infinite-horizon discounted cost criterion for the arrival and service rate control problems. Optimal stationary policies and Value functions are determined. This allows us to compare both control problems.

[1]  J.R. Artalejo,et al.  G-networks: A versatile approach for work removal in queueing networks , 2000, Eur. J. Oper. Res..

[2]  Annie Gravey,et al.  Simultaneity in Discrete-Time Single Server Queues with Bernoulli Inputs , 1992, Perform. Evaluation.

[3]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[4]  Mohan L. Chaudhry,et al.  Algorithmic Discussions Of Distributions Of Numbers Of Busy Channels For GI/Geom/m/m Queues , 2000 .

[5]  V. Kulkarni.  Modeling and Analysis of Stochastic Systems , 1996 .

[6]  D. Y. Maa,et al.  The GI/Geom/N Queue In Discrete Time , 1978 .

[7]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[8]  Mohan L. Chaudhry,et al.  On Numerical Computations of Some Discrete-Time Queues , 2000 .

[9]  L. Sennott.  Stochastic Dynamic Programming and the Control of Queueing Systems , 1998 .

[10]  Izhak Rubin,et al.  Message delay and queue-size analysis for circuit-switched TDMA systems , 1991, IEEE Trans. Commun..

[11]  Herwig Bruneel,et al.  Discrete-Time Multiserver Queues with Priorities , 1998, Perform. Evaluation.

[12]  Herwig Bruneel,et al.  Analysis of discrete-time multiserver queueing models with constant service times , 1994, Oper. Res. Lett..

[13]  M. E. Woodward,et al.  Communication and computer networks - modelling with discrete-time queues , 1993 .

[14]  Guy Pujolle,et al.  Introduction to queueing networks , 1987 .

[15]  Herwig Bruneel,et al.  Discrete-time models for communication systems including ATM , 1992 .