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A note on many-server queueing systems with ordered entry, with an application to conveyor theory

Published online by Cambridge University Press:  14 July 2016

W. M. Nawijn
W. M. Nawijn*
Affiliation:
Twente University of Technology
*
∗ Department of Mechanical Engineering, Twente University of Technology, P.O. Box 217, 7500 AE Enschede, The Netherlands.
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Abstract

Consider a many-server queueing system in which the servers are numbered. If a customer arrives when two or more servers are idle he selects the server with lowest index (this is called the ordered entry selection rule). An explicit expression for the traffic handled by the various servers in a GI/M/s queueing system with ordered entry is derived. For the M/M/s queueing system the probability distribution of the number of busy servers among the first k(k = 1, 2,…, s) servers will be given. Finally, a formula for the traffic handled by the first server in an M/D/s system will be derived. All results are derived under steady-state conditions. As an application some numerical data for the server utilizations will be given and compared to data obtained from simulation studies of a closed-loop continuous belt-conveyor.

Keywords

SERVER UTILIZATIONCONVEYOR THEORY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 144 - 152
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[2] Disney, R. L. (1963) Some results of multichannel queueing problems with ordered entry — an application to conveyor theory. J. Industrial Engineering 14, 105–108.Google Scholar
[3] Cooper, R. B. (1972) Introduction to Queueing Theory. Macmillan, New York.Google Scholar
[4] Cooper, R. B. (1976) Queues with ordered servers that work at different rates. Opsearch 13, 69–78.Google Scholar
[5] Nawijn, W. M. and Eelkman Rooda, J. (1980) An analysis of operating characteristics of closed-loop continuous conveyors, using simulation and queueing approximations. Mechanical Comm. 6, Twente University of Technology, Enschede, The Netherlands.Google Scholar
[6] Phillips, D. T. and Skeith, R. W. (1969) Ordered entry queueing networks with multiple services and multiple queues. AIIE Trans. 1, 333–342.CrossRefGoogle Scholar
[7] Pritsker, A. A. B. (1966) Applications of multichannel queueing results to the analysis of conveyor systems. J. Industrial Engineering 17, 14–21.Google Scholar
[8] Proctor, C. L., El Sayed, E. A. and Elayat, H. A. (1977) A conveyor system with homogeneous and heterogeneous servers with dual input. Internat. J. Production Res. 15, 73–85.CrossRefGoogle Scholar
[9] Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar
[10] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[11] Wilkinson, R. I. (1956) Theories for toll traffic engineering in the U.S.A. Bell System Tech. J. 35, 796–802.CrossRefGoogle Scholar