Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T03:08:23.278Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Operations research and management science Special processes

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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