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Heavy traffic analysis of a queueing system with bounded capacity for two types of customers

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

David Perry  and
Wolfgang Stadje
David Perry*
Affiliation:
University of Osnabrück
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗Postal address: Department of Mathematics, Universität Osnabrück, FB-6, D49069 Osnabrück, Germany.
∗Postal address: Department of Mathematics, Universität Osnabrück, FB-6, D49069 Osnabrück, Germany.
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Abstract

We study a service system with a fixed upper bound for its workload and two independent inflows of customers: frequent ‘small’ ones and occasional ‘large’ ones. The workload process generated by the small customers is modelled by a Brownian motion with drift, while the arrival times of the large customers form a Poisson process and their service times are exponentially distributed. The workload process is reflected at zero and at its upper capacity bound. We derive the stationary distribution of the workload and several related quantities and compute various important characteristics of the system.

Keywords

Queueingworkload processheavy trafficBrownian motionPoisson process

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1155 - 1166
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

D. Perry is on leave from the University of Haifa. His stay at the University of Osnabrück, is supported by the Deutsche Forschungsgemeinschaft.

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