## Some limit theorems for priority queues |

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### Contents

Preliminaries | 5 |

The Case of Poisson Arrivals | 9 |

Low Priority Arrivals General | 35 |

4 other sections not shown

### Common terms and phrases

arrivals are Poisson assume assumptions busy cycles busy period initiated Chapter class 1 arrival class 1 customers customers who arrive decreases at unit define described in Theorem distribution of WQ(t Dominated Convergence Theorem families of random finite limiting distribution finite mean Gaver GI/G/1 queue described head-of-the-line discipline Hence high priority arrivals high priority customers i.i.d. random variables inter-arrival Jensen's Inequality Laplace transform last inequality following Lemma lim P{J(t limit theorems limits exist low priority customers M/G/l queue non-lattice Poisson arrivals Poisson process portion of 0,t preemptive preemptive-resume discipline priority customers arrive priority queues process W(t queueing model renewal theory resume discipline Section 2.1 service load service time distributions steady-state distribution stochastically bounded sufficiently large Takacs Tauberian theorem Theorem A.2 Theorem follows theorems for WQ(t theory tN(t total uncompleted service variances virtual waiting VQ(t waiting time process weak convergence Whitt 49 Wj(t zero