Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers

Authors:
O. J. Boxma;Q. Deng;A. P. Zwart
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands q.deng@tue.nl;Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands a.p.zwart@tue.nl
Venue:
Queueing Systems: Theory and Applications
Year:
2002

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Abstract

This paper considers a heterogeneous M/G/2 queue. The service times at server 1 are exponentially distributed, and at server 2 they have a general distribution B(⋅). We present an exact analysis of the queue length and waiting time distribution in case B(⋅) has a rational Laplace–Stieltjes transform. When B(⋅) is regularly varying at infinity of index −ν, we determine the tail behaviour of the waiting time distribution. This tail is shown to be semi-exponential if the arrival rate is lower than the service rate of the exponential server, and regularly varying at infinity of index 1−ν if the arrival rate is higher than that service rate.