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On the optimal assignment of customers to parallel servers

Published online by Cambridge University Press:  14 July 2016

Richard R. Weber
Richard R. Weber*
Affiliation:
University of Cambridge
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Abstract

We consider a queuing system with several identical servers, each with its own queue. Identical customers arrive according to some stochastic process and as each customer arrives it must be assigned to some server's queue. No jockeying amongst the queues is allowed. We are interested in assigning the arriving customers so as to maximize the number of customers which complete their service by a certain time. If each customer's service time is a random variable with a non-decreasing hazard rate then the strategy which does this is one which assigns each arrival to the shortest queue.

Keywords

QUEUINGSHORTEST LINESTOCHASTIC ORDERMULTI-SERVER
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 406 - 413
Copyright
Copyright © Applied Probability Trust 1978 

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References

Glazebrook, K. D. and Nash, P. (1976) On multi-server stochastic scheduling. J. R. Statist. Soc. B 38, 67–72.Google Scholar
Weber, R. R. and Nash, P. (1978) An optimal strategy in multi-server stochastic scheduling. To appear.CrossRefGoogle Scholar
Winston, W. (1977) Optimality of the shortest line discipline. J. Appl. Prob. 14, 181–189.Google Scholar