On many-server queues in heavy traffic
Anatolii A. Puhalskii and Josh E. Reed
Source: Ann. Appl. Probab. Volume 20, Number 1 (2010), 129-195.
Abstract
We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit process does not have trajectories in the Skorohod space. We give conditions for the convergence to hold in the topology of compact convergence. Some new results for an infinite server are also provided.
Primary Subjects: 60K25
Secondary Subjects: 60F17, 60G15, 60G44
Keywords: Many-server queues; heavy traffic; weak convergence; Skorohod space; martingales; Gaussian processes
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1262962320
Digital Object Identifier: doi:10.1214/09-AAP604
Zentralblatt MATH identifier:
05678701
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