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Multiple-server system with flexible arrivals

Published online by Cambridge University Press:  01 July 2016

Osman T. Akgun*
Affiliation:
University of California, Berkeley
Rhonda Righter*
Affiliation:
University of California, Berkeley
Ronald Wolff*
Affiliation:
University of California, Berkeley
*
Postal address: Department of Industrial Engineering and Operations Research, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
Postal address: Department of Industrial Engineering and Operations Research, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
Postal address: Department of Industrial Engineering and Operations Research, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
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Abstract

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In many service, production, and traffic systems there are multiple types of customers requiring different types of ‘servers’, i.e. different services, products, or routes. Often, however, a proportion of the customers are flexible, i.e. they are willing to change their type in order to achieve faster service, and even if this proportion is small, it has the potential of achieving large performance gains. We generalize earlier results on the optimality of ‘join the shortest queue’ (JSQ) for flexible arrivals to the following: arbitrary arrivals where only a subset are flexible, multiple-server stations, and abandonments. Surprisingly, with abandonments, the optimality of JSQ for minimizing the number of customers in the system depends on the relative abandonment and service rates. We extend our model to finite buffers and resequencing. We assume exponential service. Our optimality results are very strong; we minimize the queue length process in the weak majorization sense.

MSC classification

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2011 

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