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TANDEM QUEUES WITH ARBITRARY ARRIVAL STREAM
OUTPUT OF AN M G11 QUEUE
2 other sections not shown
2.6 and Theorem ai+1 analyzed the queueing arbitrary arrival stream arrival epoch chain stationary chapter common distribution function constant server define denote departure epoch deterministic distinct elements distributed random variables effect of order entire system equation exactly i distinct exponential server fed by Poisson following theorem function of service Hence identically distributed random k e IN+ Ki<k kth customer leaves leaves first unit Lemma Let us consider M|G|1 queue Markov process n+1 _ NBU(UBN nonoverlapping service number of customers optimal order order of servers parallel channels peBi Poisson arrivals Poisson process Proof queueing system queues in tandem r=n+l require service result holds second server second unit sequence 1 sequence server has constant server is exponential service facility service time distribution stationary conditions stationary process tandem queues Theorem 2.7 theorem holds total waiting Unclassified