Some Limit Theorems for Priority Queues |
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A₁ assumptions Chapter class 1 arrival class 1 customers CORME CORN CORNELL CORNELL CORNELL CORNELL CORNELL LIBRARY CORNELL CORNELL UNIVERSITY CORNELL FOUNDED CORNELL UNIVERSITY CORNELL customers who arrive d.f. B₁ define described in Theorem Dominated Convergence Theorem equation exp iw EZRA finite limiting distribution finite mean FOUNDED CORNELL GI/G/1 queue described head-of-the-line discipline Hence high priority arrivals high priority customers i.i.d. random variables inter-arrival Laplace transform Lemma LIBRARY CORNELL LIBRARY UNIVERSITY lim P t+ lim P t+00 limit theorems limits exist n₁ obtain P₁ Poisson process Prabhu 34 preemptive preemptive-resume discipline priority customers arrive priority queues Process W(t Proof queueing model renewal theory resume discipline server steady-state distribution stochastically bounded t+oo T₁ Takács Tauberian theorem Theorem A.2 Theorem follows theorems for Wo(t TN(t total uncompleted service traffic intensity UNIV CORNELL UNIVERSIT UNIVERSITY CORNELL CORNELL virtual waiting W₁(t αντ