ON G/G/1 QUEUES WITH LIFO-P SERVICE DISCIPLINE

Jeyaveerasingam George Shanthikumar · Ushio Sumita

21 citations0/0 files storedJournal of the Operations Research Society of Japan

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

Abstract

We consider a single server queueing system G/G/1 having general interarrival times (not necessarily i.i.d), i.i.d. service times, and LIFO-P (preemptive last in first out, but not restricted to resumption) service disciplines. Furthermore a customer finding n other customers in system upon his arrival joins the system with probability p(n) and immediately leaves the system with probability 1 - p(n), where 0 ≤ p(n) ≤ 1. The relations among various ergodic probabilities of the number of customers in system are established via sample path arguments. Sufficient conditions are given for the customer average ergodic probability distribution to be geometric, thereby extending recent results of Fakinos (1981) and Yamazaki (1982, 1984). Key words: G/G/1 queues, preemptive last in first out service discipline, geometric distribution, stochastic ordering.

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References

1984Matrix-Geometric Solutions to Stochastic Models 1987Convex ordering of sojourn times in single-server queues: extremal properties of FIFO and LIFO service disciplines 1981The G/G/1 Queueing System with a Particular Queue Discipline

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1987The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline 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 2001NOTE ON THE GI/GI/ 1 QUEUE WITH LCFS-PR OBSERVED AT ARBITRARY TIMES

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