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A Lindley-type equation arising from a carousel problem

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

M. Vlasiou ,
I. J. B. F. Adan  and
J. Wessels
M. Vlasiou*
Affiliation:
EURANDOM
I. J. B. F. Adan*
Affiliation:
EURANDOM and Eindhoven University of Technology
J. Wessels*
Affiliation:
EURANDOM
*
∗ Postal address: EURANDOM, PO Box 513, 5600 MB Eindhoven, The Netherlands
∗∗∗ Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: iadan@win.tue.nl
∗ Postal address: EURANDOM, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, we show that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue depends on the complete interarrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution.

Keywords

CarouselLindley's equationthroughputautomated storage/retrieval system

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1171 - 1181
Copyright
Copyright © Applied Probability Trust 2004 

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