A note on the event horizon for a processor sharing queue

Authors:
Robert C. Hampshire;William A. Massey
Affiliations:
Heinz School of Public Policy and Management, Carnegie Mellon University, Pittsburgh, USA;Department of Operations Research and Financial Engineering, Princeton University, Princeton, USA
Venue:
Queueing Systems: Theory and Applications
Year:
2008

Citing 2
Cited 1

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

Queueing Systems: Theory and Applications
The Fluid Limit of an Overloaded Processor Sharing Queue

Mathematics of Operations Research

Additive functionals with application to sojourn times in infinite-server and processor sharing systems

Queueing Systems: Theory and Applications

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Abstract

In this note we identify a phenomenon for processor sharing queues that is unique to ones with time-varying rates. This property was discovered while correcting a proof in Hampshire, Harchol-Balter and Massey (Queueing Syst. 53(1---2), 19---30, 2006). If the arrival rate for a processor sharing queue has unbounded growth over time, then it is possible for the number of customers in a processor sharing queue to grow so quickly that a newly entering job never finishes. We define the minimum size for such a job to be the event horizon for a processor sharing queue. We discuss the use of such a concept and develop some of its properties. This short article serves both as errata for Hampshire, Harchol-Balter and Massey (Queueing Syst. 53(1---2), 19---30, 2006) and as documentation of a characteristic feature for some processor sharing queues with time varying rates.