## The Annals of Applied Probability

### Multiple-input heavy-traffic real-time queues

#### Abstract

A single queueing station that serves K input streams is considered. Each stream is an independent renewal process, with customers having random lead times. Customers are served by processor sharing across streams. Within each stream, two disciplines are considered--earliest deadline first and first-in, first-out. The set of current lead times of the K streams is modeled as a K-dimensional vector of random counting measures on $\mathbb{R}$, and the limit of this vector of measure-valued processes is obtained under heavy traffic conditions.

#### Article information

Source
Ann. Appl. Probab., Volume 13, Number 1 (2003), 54-99.

Dates
First available in Project Euclid: 16 January 2003

https://projecteuclid.org/euclid.aoap/1042765663

Digital Object Identifier
doi:10.1214/aoap/1042765663

Mathematical Reviews number (MathSciNet)
MR1951994

Zentralblatt MATH identifier
1046.60082

#### Citation

Kruk, Lukasz; Lehoczky, John; Shreve, Steven; Yeung, Shu-Ngai. Multiple-input heavy-traffic real-time queues. Ann. Appl. Probab. 13 (2003), no. 1, 54--99. doi:10.1214/aoap/1042765663. https://projecteuclid.org/euclid.aoap/1042765663

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• PITTSBURGH, PENNSy LVANIA 15213 E-MAIL: jpl@stat.cmu.edu
• PITTSBURGH, PENNSy LVANIA 15213 E-MAIL: shreve@cmu.edu S.-N. YEUNG AT&T LABS 180 PARK AVENUE
• FLORHAM PARK, NEW JERSEY 07932 E-MAIL: sy eung@homer.att.com