Journal of Applied Probability · 1974 · 87 citations · 4 references
BusinessComputer ScienceProbability TheoryQueuing TheoryStochastic ProcessesQueueing AnalysisQueueing NetworksQueueing ProcessesQueueing SystemsQueueing TheoryQueuing AnalysisAsymptotic Analysis Of QueuesG/g/1 QueuesG/g/c QueueMartingale InequalitiesMartingale TheoryPerformance Bounds In QueuesQueue Length Tail ProbabilitiesQueueing Delay Bounds
Bounds are obtained for the limiting distribution of the delay in queue for a GI/G/ 1 system via Martingale theory. These bounds are somewhat stronger than similar bounds recently obtained by Kingman. Simplifications of the bounds are obtained in the special cases where the service distribution is either IFR, DFR, NBU or NWU.
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