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The M/G/1 queue with two service speeds

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  01 July 2016

O. J. Boxma  and
I. A. Kurkova
O. J. Boxma*
Affiliation:
Eindhoven University of Technology
I. A. Kurkova*
Affiliation:
EURANDOM
*
∗ Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
∗∗ Current address: Laboratoire de Probabilités et Modèles Aléatoires, Université Paris IV, BC 188, 4, Place Jussieu, 75252 Paris Cedex 05, France. Email address: kurkova@ccr.jussieu.fr
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Abstract

We consider an M/G/1 queue with the special feature that the speed of the server alternates between two constant values sL and sH > sL. The high-speed periods are exponentially distributed, and the low-speed periods have a general distribution. Our main results are: (i) for the case that the distribution of the low-speed periods has a rational Laplace–Stieltjes transform, we obtain the joint distribution of the buffer content and the state of the server speed; (ii) for the case that the distribution of the low-speed periods and/or the service request distribution is regularly varying at infinity, we obtain explicit asymptotics for the tail of the buffer content distribution. The two cases in which the offered traffic load is smaller or larger than the low service speed are shown to result in completely different asymptotics.

Keywords

M/G/1 queuevariable speedbuffer contentregular variation

MSC classification

Primary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 520 - 540
Copyright
Copyright © Applied Probability Trust 2001 

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