## The dynamic priority queueing system |

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### Contents

A SINGLE SERVER QUEUEING SYSTEM WITH THE DYNAMIC | 7 |

THE BEHAVIOR OF THE VIRTUAL WAITING TIMES | 24 |

BOUNDS AND SUGGESTIONS FOR FURTHER WORK | 44 |

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### Common terms and phrases

00 in Theorem basic relations Bell Laboratories chapter class 0 customers class 1 virtual class i arriving compound Poisson process conjectures constant between successive continuous-time converges in distribution Cornell University Corollary customer arriving customer of class customers present discrete-time dynamic priority discipline dynamic priority queue e"aT e"SUE[e equation ew t,u EW(t EWQ(t,u fixed t _ given by Lemma given by Theorem gives EW head-of-the-line discipline independent inf{t input process joint variation Laplace transform limit behavior mean waiting nature to W(t obtain Poisson input pre-emptive resume priority queue discipline PROOF random variable range of W(t residual workload process result follows resume and head-of-the-line server queueing system service time distribution single server queueing static priority discipline successive jumps successive service system busy period t+u,u Tauberian Theorem gives Theorem 2.2 gives Theorem 2.5 thesis Tt(w two-fold dependence u]du urgency number virtual waiting w]du waiting times WQ(t,u Wt(u x]dt x]du dt XQ(t