Open Access
February 2010 On many-server queues in heavy traffic
Anatolii A. Puhalskii, Josh E. Reed
Ann. Appl. Probab. 20(1): 129-195 (February 2010). DOI: 10.1214/09-AAP604

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.

Citation

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Anatolii A. Puhalskii. Josh E. Reed. "On many-server queues in heavy traffic." Ann. Appl. Probab. 20 (1) 129 - 195, February 2010. https://doi.org/10.1214/09-AAP604

Information

Published: February 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1201.60088
MathSciNet: MR2582645
Digital Object Identifier: 10.1214/09-AAP604

Subjects:
Primary: 60K25
Secondary: 60F17 , 60G15 , 60G44

Keywords: Gaussian processes , heavy traffic , Many-server queues , Martingales , Skorohod space , weak convergence

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.20 • No. 1 • February 2010
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