A Skorokhod Problem formulation and large deviation analysis of a processor sharing model

Authors:
Paul Dupuis;Kavita Ramanan
Affiliations:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Venue:
Queueing Systems: Theory and Applications
Year:
1998

Citing 3
Cited 7

Discrete flow networks: bottleneck analysis and fluid approximations

Mathematics of Operations Research
Large deviations in high-speed communication networks

Large deviations in high-speed communication networks
Statistical analysis of the generalized processor sharing scheduling discipline

IEEE Journal on Selected Areas in Communications

A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem

Queueing Systems: Theory and Applications
Queueing Models with Multiple Waiting Lines

Queueing Systems: Theory and Applications
Explicit Solutions for Variational Problems in the Quadrant

Queueing Systems: Theory and Applications
Large deviations of the steady-state distribution of reflected processes with applications to queueing systems

Queueing Systems: Theory and Applications
Finite buffer queue with generalized processor sharing and heavy-tailed input processes

Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Beyond processor sharing

ACM SIGMETRICS Performance Evaluation Review
Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Generalized processor sharing has been proposed as a policy for distributing processing in a fair manner between different data classes in high-speed networks. In this paper we show how recent results on the Skorokhod Problem can be used to construct and analyze the mapping that takes the input processes into the buffer content. More precisely, we show how to represent the map in terms of a Skorokhod Problem, and from this infer that the mapping is well defined (existence and uniqueness) and well behaved (Lipschitz continuity). As an elementary application we present some large deviation estimates for a many data source model.