Artalejo, Jesús R. and Economou, Antonis (2005) Markovian Controllable Queueing Systems with Hysteretic Policies: Busy Period and Waiting Time Analysis. Methodology and computing in applied probability, 7 (3). pp. 353-378. ISSN 1387-5841
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We study Markovian queueing systems in which the service rate varies whenever the queue length changes. More specifically we consider controllable queues operating under the so-called hysteretic policy which provides a rather versatile class of operating rules for increasing and decreasing service rate at the arrival and service completion times. The objective of this paper is to investigate algorithmically the busy period and the waiting time distributions. Our analysis supplements the classical work of Yadin and Naor (1967) who focused on the steady-state probabilities of the system state.
|Additional Information:||The authors thank the referee for the constructive suggestions on the earlier version of this paper. Jesus Artalejo thanks the support received from the research project BFM2002-02189. Antonis Economou was supported by the University of Athens grant ELKE/70/4/6415 and by the European Union and the Greek Ministry of Education program PYTHAGORAS/2004.|
|Uncontrolled Keywords:||Queueing, Hysteretic Policy, Busy Period, Waiting Time, Removable Servers|
|Subjects:||Sciences > Mathematics > Operations research|
J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, ORSA Journal on Computing vol. 7 pp. 36-43, 1995.
J. R. Artalejo and M. J. Lopez-Herrero, Analysis of the busy period for the M/M/c queue: An algorithmic approach, Journal of Applied Probability vol. 38 pp. 209-222, 2001.
J. R. Artalejo and M. J. Lopez-Herrero, On the M/M/m queue with removable servers.In S.K. Srinivasan and A. Vijayakumar (eds.), Stochastic Point Processes, pp. 124-144, Narosa Publishing House: New Delhi, 2003.
F. Ball and V. T. Stefanov, Further approaches to computing fundamental characteristics of birth-death processes, Journal of Applied Probability vol. 38 pp. 995-1005, 2001.
Ch. A. Charalambides, Enumerative Combinatorics, Chapman and Hall: Boca Raton, 2002.
T. Crabill, D. Gross, and M. Magazine, A classified bibliography of research on optimal design and control of queues, Operational Research vol. 25 pp. 219-232, 1977.
M. Yu Kitaev and R. F. Serfozo, M/M/1 queues with switching costs and hysteretic optimal control, Operational Research vol. 47 pp. 310-312, 1999.
R. B. Lenin and P. R. Parthasarathy, Transient analysis in discrete time of Markovian queues with quadratic rates, Southwest Journal of Pure and Applied Mathematics vol. 3, pp. 1-15, 2000.
F. V. Lu and R. F. Serfozo, M /M /1 queueing decision processes with monotone hysteretic optimal policies, Operational Research vol. 32 pp. 1116-1132, 1984.
B. Natvig, On the waiting-time and busy period distributions for a general birth-and-death queueing model, Journal of Applied Probability vol. 12 pp. 524-532, 1975a.
B. Natvig, A Contribution to the Theory of Birth-and-Death Queueing Models, Doctoral Thesis, University of Sheffield, 1975b.
H. K. Rhee and B. D. Sivazlian, Distribution of the busy period in a controllable M/M/2 queue operating under the triadic (0, K, M, N ) policy, Journal of Applied Probability vol. 27 pp. 425-432, 1990.
J. Romani, A queueing model with a variable number of channels, Trabajos de Estadística vol. 8 pp. 175-189, 1957 (in Spanish).
L. I. Sennott, Stochastic Dynamic Programming and the Control of Queueing Systems, Wiley: New York, 1999.
J. Teghem, Control of the service process in a queueing system, European Journal of Operational Research vol. 23 pp. 141-158, 1986.
H. C. Tijms, A First Course in Stochastic Models, Wiley: Chichester, 2003.
M. Yadin and P. Naor, On queueing systems with variable service capacities, Naval Research Logistics Quarterly vol. 14 pp. 43-53, 1967.
|Deposited On:||14 Jun 2012 08:58|
|Last Modified:||06 Feb 2014 10:28|
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