The steady-state appearance of the M / G /1 queue under the discipline of shortest remaining processing time

R. Schaßberger

27 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

For the queue M/G/ 1 under the discipline SRPT (shortest remaining processing time) the system state is taken to be the counting measure N which assigns to each Borel set A of R + the number N ( A ) of customers present with residual service times taking values in A . A steady-state analysis is given for the corresponding Laplace functional. As a corollary, the steady-state number in queue is obtained in terms of its generating function.

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References

1983The Single Server Queue 1968Letter to the Editor—A Proof of the Optimality of the Shortest Remaining Processing Time Discipline 1966The Queue M/G/1 with the Shortest Remaining Processing Time Discipline 1987Palm Probabilities and Stationary Queues 1973Warteschlangen 1984A new approach to the M / G /1 processor-sharing queue

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2004Quantifying the properties of SRPT scheduling 1993The M/G/1 processor-sharing model: transient behavior 2015Diffusion limits for shortest remaining processing time queues under nonstandard spatial scaling 2005Revisiting unfairness in Web server scheduling

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