The Annals of Applied Probability

On many-server queues in heavy traffic

Anatolii A. Puhalskii and Josh E. Reed

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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.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 1 (2010), 129-195.

Dates
First available in Project Euclid: 8 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1262962320

Digital Object Identifier
doi:10.1214/09-AAP604

Mathematical Reviews number (MathSciNet)
MR2582645

Zentralblatt MATH identifier
1201.60088

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F17: Functional limit theorems; invariance principles 60G15: Gaussian processes 60G44: Martingales with continuous parameter

Keywords
Many-server queues heavy traffic weak convergence Skorohod space martingales Gaussian processes

Citation

Puhalskii, Anatolii A.; Reed, Josh E. On many-server queues in heavy traffic. Ann. Appl. Probab. 20 (2010), no. 1, 129--195. doi:10.1214/09-AAP604. https://projecteuclid.org/euclid.aoap/1262962320


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