Benes's formula for M/G/1–FIFO ‘explained' by preemptive-resume LIFO

Robert B. Cooper · Shun‐Chen Niu

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

Abstract

We provide a term-by-term interpretation of Beneš's well-known but mysterious inversion of the Pollaczek–Khintchine formula. The strategy is to recognize the equality of waiting time in M/G/1–FIFO with remaining work in M/G/1–LIFO–preemptive resume. In the process, we give a new and simple derivation of some known results for M/G/1–LIFO–preemptive resume.

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References

1977Fundamentals of Queueing Theory.1982Poisson Arrivals See Time Averages 1985Fundamentals of queueing theory (2nd ed.).1983Introduction to Queueing Theory (2nd ed.).1984The sojourn-time distribution in the M/G/1 queue by processor sharing 1957On Queues with Poisson Arrivals 1981Insensitivity in queueing systems 1980Insensitivity in queueing systems

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1989Duality and Other Results for M/G/1 and GI/M/1 Queues, Via a New Ballot Theorem 1988Representing workloads in GI/G/1 queues through the preemptive-resume LIFO queue discipline 1988Analysis of theGI/GI/1 Queue and its Variations via the LCFS Preemptive Resume Discipline and Its Random Walk Interpretation 2001NOTE ON THE GI/GI/ 1 QUEUE WITH LCFS-PR OBSERVED AT ARBITRARY TIMES

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