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Cyclic queueing networks with subexponential service times

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

H. Ayhan ,
Z. Palmowski  and
S. Schlegel
H. Ayhan*
Affiliation:
Georgia Institute of Technology
Z. Palmowski*
Affiliation:
University of Wrocław
S. Schlegel*
Affiliation:
University of Ulm
*
∗ Postal address: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA. Email address: [email protected]
∗∗ Postal address: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
∗∗∗ Postal address: Department of Biometry and Medical Documentation, University of Ulm, 89069 Ulm, Germany
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Abstract

For a K-stage cyclic queueing network with N customers and general service times, we provide bounds on the nth departure time from each stage. Furthermore, we analyze the asymptotic tail behavior of cycle times and waiting times given that at least one service-time distribution is subexponential.

Keywords

Cycle timeclosed networksubexponential asymptoticsHarris Markov chain

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 791 - 801
Copyright
Copyright © Applied Probability Trust 2004 

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