The Dynamic Priority Queueing System |
Common terms and phrases
basic relations Bell Laboratories bounds chapter class 0 customers class 1 virtual class i arriving compound Poisson process constant between successive converges in distribution Cornell University Corollary customer arriving customer of class customers present distribution function dynamic priority discipline dynamic priority queue e-suE[e equation ew t,u ew(t first-come-first-served given by Lemma given by Theorem head-of-the-line discipline independent input process joint variation Laplace transform let W(t n₁ n₁w(t n₂ n₂w(t obtain owo(t,u Poisson input pre-emptive resume priority class priority function priority queue discipline PROOF random variables range of W(t result follows resume and head-of-the-line server queueing system service time distribution single server queueing static priority discipline successive jumps SUEL T+(w Tauberian Theorem Theorem 2.2 gives Theorem 2.5 thesis two-fold dependence urgency number V₁(t virtual waiting w]du W₁(t W₁(t+u,u W₁(u waiting time Wo(t,u workload W(t x]dt x]du dt X₁(t X₁(t+u αντ ᎾᎳ