Annals of Applied Probability

Heavy traffic limit for a processor sharing queue with soft deadlines

H. Christian Gromoll and Łukasz Kruk

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This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.

Article information

Ann. Appl. Probab., Volume 17, Number 3 (2007), 1049-1101.

First available in Project Euclid: 22 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F17: Functional limit theorems; invariance principles 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]

Processor sharing real-time queue deadlines heavy traffic measure valued process empirical process


Gromoll, H. Christian; Kruk, Łukasz. Heavy traffic limit for a processor sharing queue with soft deadlines. Ann. Appl. Probab. 17 (2007), no. 3, 1049--1101. doi:10.1214/105051607000000014.

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