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The fluid limit of a heavily loaded processor sharing queue

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References

1995On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models886 cited
1970Multiple channel queues in heavy traffic. I438 cited
1998State space collapse with application to heavy traffic limits for multiclass queueing networks309 cited
1998Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse264 cited
1994Instability of FIFO Queueing Networks263 cited
1987Processor-sharing queues: Some progress in analysis189 cited
2001Real-time queues in heavy traffic with earliest-deadline-first queue discipline146 cited
1996Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks135 cited
1996Convergence to equilibria for fluid models of FIFO queueing networks133 cited

Cited by

2004Diffusion approximation for a processor sharing queue in heavy traffic83 cited
2009Fluid Limits for Shortest Remaining Processing Time Queues71 cited
2008Steady state approximations of limited processor sharing queues in heavy traffic56 cited
2004Diffusion approximation for a processor sharing queue in heavy traffic51 cited
2009Law of Large Number Limits of Limited Processor-Sharing Queues

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2008Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime45 cited

2012Fluid models of many-server queues with abandonment41 cited

2008A functional central limit theorem for the M/GI/∞ queue34 cited

2005AnRG-Factorization Approach for a BMAP/M/1 Generalized Processor-Sharing Queue32 cited

2011Fluid models of many-server queues with abandonment32 cited

2013On queues with impatience: stability, and the optimality of Earliest Deadline First30 cited

2011Diffusion limits of limited processor sharing queues25 cited

2006The Fluid Limit of an Overloaded Processor Sharing Queue25 cited

2009Dynamics of New Product Introduction in Closed Rental Systems24 cited

2006The impact of reneging in processor sharing queues24 cited

2005Balancing Queues by Mean Field Interaction23 cited