, Volume 40, Issue 1, pp 531
WaitingTime Asymptotics for the M/G/2 Queue with Heterogeneous Servers
 O.J. BoxmaAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of TechnologyCWI
 , Q. DengAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology
 , A.P. ZwartAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology
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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 semiexponential 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.
 Title
 WaitingTime Asymptotics for the M/G/2 Queue with Heterogeneous Servers
 Journal

Queueing Systems
Volume 40, Issue 1 , pp 531
 Cover Date
 200202
 DOI
 10.1023/A:1017913826973
 Print ISSN
 02570130
 Online ISSN
 15729443
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 M/G/2 queue
 heterogeneous servers
 queue length
 waiting time
 tail behaviour
 slowly varying function
 regularly varying distribution
 semiexponential distribution
 Industry Sectors
 Authors

 O.J. Boxma ^{(1)} ^{(2)}
 Q. Deng ^{(1)}
 A.P. Zwart ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
 2. CWI, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands