Mathematical Proceedings of the Cambridge Philosophical Society · 1976 · 20 citations · 14 references
BusinessComputer ScienceProbability TheoryQueuing TheoryStochastic ProcessesQueueing AnalysisQueueing ProcessesQueueing SystemsQueueing TheorySingle-server QueuesWaiting Time AnalysisAsymptotic Analysis Of QueuesEquilibriumInfinite DivisibilityM/g/1 QueuesPerformance Bounds In QueuesQueue Length Tail ProbabilitiesSingle-server Queue AsymptoticsTraffic Intensity
Various elegant properties have been found for the waiting time distribution G for the queue GI /G/ 1 in statistical equilibrium, such as infinite divisibility ((1), p. 282) and that of having an exponential tail ((11), (2), p. 411, (1), p. 324). Here we derive another property which holds quite generally, provided the traffic intensity ρ < 1, and which is extremely simple, fitting in with the above results as well as yielding some useful properties in the form of upper and lower stochastic bounds for G which augment the bounds obtained by Kingman (5), (6), (8) and by Ross (10).
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