The Annals of Applied Probability

Fluid and heavy traffic diffusion limits for a generalized processor sharing model

Kavita Ramanan and Martin I. Reiman

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Abstract

Under fairly general assumptions on the arrival and service time processes, we prove fluid and heavy traffic limit theorems for the unfinished work, queue length, sojourn time and waiting time processes associated with a single station multiclass generalized processor sharing model. The fluid limit of the unfinished work process is characterized by the Skorokhod map associated with a Skorokhod problem formulation of the generalized processor sharing model, while the heavy traffic diffusion limit is characterized using the corresponding extended Skorokhod map. An interesting feature of the diffusion limits is that they may fail to be semimartingales.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 1 (2003), 100-139.

Dates
First available in Project Euclid: 16 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1042765664

Digital Object Identifier
doi:10.1214/aoap/1042765664

Mathematical Reviews number (MathSciNet)
MR1951995

Zentralblatt MATH identifier
1016.60083

Subjects
Primary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 90B22: Queues and service [See also 60K25, 68M20] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Keywords
Diffusion approximations heavy traffic fluid limits generalized processor sharing queueing networks Skorokhod problem Skorokhod map extended Skorokhod problem semimartingales

Citation

Ramanan, Kavita; Reiman, Martin I. Fluid and heavy traffic diffusion limits for a generalized processor sharing model. Ann. Appl. Probab. 13 (2003), no. 1, 100--139. doi:10.1214/aoap/1042765664. https://projecteuclid.org/euclid.aoap/1042765664


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  • MURRAY HILL, NEW JERSEY 07974 E-MAIL: kavita@lucent.com marty@lucent.com