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Time-dependent solution and optimal control of a bulk service queue

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Shokri Z. Selim
Shokri Z. Selim*
Affiliation:
King Fahd University of Petroleum and Minerals
*
∗Postal address: Department of Systems Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
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Abstract

We consider the queueing system denoted by M/MN/1/N where customers are served in batches of maximum size N. The model is motivated by a traffic application. The time-dependent probability distribution for the number of customers in the system is obtained in closed form. The solution is used to predict the optimal service rates during a finite time horizon.

Keywords

BULK SERVICEBULK QUEUESTRANSIENT SOLUTIONCONTROL OF QUEUESQUEUEING APPLICATIONS

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 258 - 266
Copyright
Copyright © Applied Probability Trust 1997 

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References

[1] Abolnikov, L. M. and Dshalalow, J. H. (1993) Semiregenerative analysis of controlled bulk queuing-systems with a bilevel service delay discipline and some ergodic theorems. Comput. Math. Appl. 25, 107–116.CrossRefGoogle Scholar
[2] Abolnikov, L. M., Dshalalow, J. H. and Dukhovny, A. M. (1993) A multilevel control bulk queueing system with vacationing server. Operat. Res. Lett. 13, 183–188.Google Scholar
[3] Bailey, N. T. J. (1954) On queueing processes with bulk service. J. R. Statist. Soc. B 16, 80–87.Google Scholar
[4] Bhat, U. N. (1968) A Study of the Queueing Systems M/G/1 and G1/M/1. (Lecture Notes in Operations Research and Mathematical Economics 2.) Springer, New York.Google Scholar
[5] Chaudhry, M. L. and Templeton, J. G. C. (1983) A First Course in Bulk Queues. Wiley, New York.Google Scholar
[6] Deb, R. K. and Serfozo, R. F. (1973) Optimal control of batch service queues. Adv. Appl. Prob. 5, 340–361.Google Scholar
[7] Dshalalow, J. H. (1994) First excess level analysis of random processes in a class of stochastic service processes with global control. Stoch. Anal. Appl. 12, 75–101.Google Scholar
[8] Finch, P. D. (1962) On the transient behaviour of a queueing system with bulk service and finite capacity. Ann. Math. Statist. 33, 973–985.Google Scholar
[9] Handa, J. M. (1971) Optimal control of service rate and service batch size in the single channel stochastic service systems. MSc thesis. Department of Industrial Engineering, University of Toronto.Google Scholar
[10] Jaiswal, N. K. (1960) Time-dependent solution of the bulk-service queueing problem. Operat. Res. 8, 773–781.Google Scholar
[11] Kleinrock, L. (1976) Queueing Systems. Vol II: Computer Applications. Wiley, New York.Google Scholar
[12] Madan, K. C. (1989) A single channel queue with bulk service subject to interruptions. Microelec. Reliab. 29, 813–818.Google Scholar
[13] Madan, K. C. (1992) A bulk queueing system with random failures and 2 phase repairs. Microelec. Reliab. 32, 669–677.Google Scholar
[14] Medhi, J. (1975) Waiting time distribution in a Poisson queue with a general bulk service rule. Management Sci. 21, 777–782.Google Scholar
[15] Medhi, J. and Borthakur, A. (1972) On a two server Markovian queue with a general bulk services rule. Cahiers Centre Etudes Rech. Opérat. 14, 151–158.Google Scholar
[16] Moran, P. A. P. (1959) The Theory of Storage. Methuen, London.Google Scholar
[17] Nadarajan, R. and Jayaraman, D. (1991) Series queues with general bulk service, random breakdown and vacation. Microelec. Reliab. 31, 861–863.CrossRefGoogle Scholar
[18] Neuts, M. F. (1967) A general class of bulk queues with Poisson input. Ann. Math. Statist. 38, 759–770.CrossRefGoogle Scholar
[19] Prabhu, N. U. (1965) Queues and Inventories – A Study of Their Basic Stochastic Processes. Wiley, New York.Google Scholar
[20] Radmilovich, Z. R. (1992) Ship-berth link as bulk queueing system in ports. Waterway Fort. Coastal Ocean Eng. 118, 474–495.Google Scholar
[21] Reddy, G. V. K., Nadarajan, R. and Kandasamy, P. R. (1993) Tandem queue with 3 multiserver units and bulk service in unit III. Microelec. Reliab 33, 513–519.Google Scholar
[22] Singh, I. P. and Ram, C. (1991) 3-server bulk service queue with service interruptions and exponential repairs. Microelec. Reliab 31, 257–259.Google Scholar
[23] Weiss, H. J. (1979) The computation of optimal control limits for a queue with batch services. Management Sci. 25, 220–238.Google Scholar