Adventures in stochastic processes
Adventures in stochastic processes
Fluid approximations for a processor-sharing queue
Queueing Systems: Theory and Applications
Large deviations of sojourn times in processor sharing queues
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Performance Evaluation
Large deviations of sojourn times in processor sharing queues
Queueing Systems: Theory and Applications
Bandwidth-sharing networks in overload
Performance Evaluation
A note on the event horizon for a processor sharing queue
Queueing Systems: Theory and Applications
Fluid Limits for Shortest Remaining Processing Time Queues
Mathematics of Operations Research
Law of Large Number Limits of Limited Processor-Sharing Queues
Mathematics of Operations Research
Population effects in multiclass processor sharing queues
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Computer Networks: The International Journal of Computer and Telecommunications Networking
Content dynamics in P2P networks from queueing and fluid perspectives
Proceedings of the 24th International Teletraffic Congress
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This paper primarily concerns strictly supercritical fluid models, which arise as functional law of large numbers approximations for overloaded processor sharing queues. Analogous results for critical fluid models associated with heavily loaded processor sharing queues are contained in Gromoll et al. (2002) and Puha and Williams (2004). An important distinction between critical and strictly supercritical fluid models is that the total mass for a solution that starts from zero grows with time for the latter, but it is identically equal to zero for the former. For strictly supercritical fluid models, this paper contains descriptions of each of the following: the distribution of the mass as it builds up from zero, the set of stationary solutions, and the limiting behavior of an arbitrary solution as time tends to infinity. In addition, a fluid limit result is proved that justifies strictly supercritical fluid models as first order approximations to overloaded processor sharing queues.