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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
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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