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January 2003 Fluid and heavy traffic diffusion limits for a generalized processor sharing model
Kavita Ramanan, Martin I. Reiman
Ann. Appl. Probab. 13(1): 100-139 (January 2003). DOI: 10.1214/aoap/1042765664


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.


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Kavita Ramanan. Martin I. Reiman. "Fluid and heavy traffic diffusion limits for a generalized processor sharing model." Ann. Appl. Probab. 13 (1) 100 - 139, January 2003.


Published: January 2003
First available in Project Euclid: 16 January 2003

zbMATH: 1016.60083
MathSciNet: MR1951995
Digital Object Identifier: 10.1214/aoap/1042765664

Primary: 60F05 , 60F17
Secondary: 60K25 , 68M20 , 90B22

Keywords: diffusion approximations , Extended Skorokhod problem , fluid limits , generalized processor sharing , heavy traffic , Queueing networks , Semimartingales , Skorokhod map , Skorokhod problem

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 1 • January 2003
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