The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 13, Number 1 (2003), 100-139.
Fluid and heavy traffic diffusion limits for a generalized processor sharing model
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.
Ann. Appl. Probab., Volume 13, Number 1 (2003), 100-139.
First available in Project Euclid: 16 January 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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