Artalejo, Jesús R. and Hernández-Lerma , O.
(2003)
*Performance analysis and optimal control of the Geo/Geo/c queue.*
Performance Evaluation, 52
(1).
pp. 15-39.
ISSN 0166-5316

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Official URL: http://www.sciencedirect.com/science/article/pii/S016653160200161X

## Abstract

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/cqueue. 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.

Item Type: | Article |
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Additional Information: | The authors thank the referee for his comments on an earlier version of this paper. It was finished during |

Uncontrolled Keywords: | Discrete queues; Multiple servers; Optimal control; Steady-state distribution |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15729 |

References: | J.R. Artalejo. G-networks: a versatile approach for work removal in queueing networks. Eur. J. Oper. Res., 126 (2000), pp. 233–249 H. Bruneel, B.G. Kim, Discrete-time Models for Communication Systems including ATM, Kluwer Academic Publishers, Boston, 1993. H. Bruneel, I. Wuyts. Analysis of discrete-time multiserver queueing models with constant service times. Oper. Res. Lett., 15 (1994), pp. 231–236 W.C. Chan, D.Y. Maa, The GI/Geom/N queue in discrete time, Infor 16 (1978) 232–252. M.L. Chaudhry, On numerical computations of some discrete-time queues, in: W.K. Grassmann (Ed.), Computational Probability, Kluwer Academic Publishers, Boston, 2000, pp. 365–407. M.L. Chaudrhy, U. C. Gupta, Algorithmic discussions of distributions of numbers of busy channels for GI/Geom/m/n queues, Infor 38 (2000) 51-63. P. Gao, S. Wittevrongel, H. Bruneel, Analysis of discrete-time buffers with geometric service times and multiple servers, in: Proceedings of the High Performance Computing Symposium (HPC 2002), San Diego, April 2002, pp. 294–299. E. Gelenbe, G. Pujolle, Introduction to Queueing Networks, Wiley, Chichester, UK, 1998. A. Gravey, G. Hébuterne. Simultaneity in discrete time single server queues with Bernoulli inputs. Perform. Eval., 14 (1992), pp. 123–131 O. Hernández-Lerma, J. Lasserre, Discrete-time Markov Control Processes, Springer, New York, 1996. V.G. Kulkarni, Modeling and Analysis of Stochastic Systems, Chapman & Hall, London, 1995. K. Laevens, H. Bruneel. Discrete-time multiserver queues with priorities. Perform. Eval., 33 (1998), pp. 249–275 R.D. Nobel, Optimalcontrol of an MX/G/1 queue with varying arrival rate and service mode, in: A. Krishnamoorthy, N. Raju, V. Ramaswami (Eds.), Advances in Probability and Stochastic Processes, Notable Publications, Neshanic Station, NJ, 2001, pp. 125–142. M. Puterman, Markov Decision Processes, Wiley, New York, 1994. I. Rubin, Z. Zhang. Message delay and queue-size analysis for circuit-switched TDMA systems. IEEE Trans. Commun., 39 (1991), pp. 905–914 L.I. Sennott, Stochastic Dynamic Programming and the Control of Queueing Systems, Wiley, New York, 1999. H. Takagi, Queueing Analysis—A Foundation of Performance Evaluation, vol. 3, Discrete-time Systems, North-Holland, New York, 1993. M.E. Woodward, Communication and Computer Networks: Modelling with Discrete-time Queues, IEEE Computer Society Press, Los Alamitos, 1994. |

Deposited On: | 22 Jun 2012 08:22 |

Last Modified: | 06 Feb 2014 10:30 |

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