Applications of Queueing TheoryThe literature on queueing theory is already very large. It contains more than a dozen books and about a thousand papers devoted exclusively to the subject; plus many other books on probability theory or operations research in which queueing theory is discussed. Despite this tremendous activity, queueing theory, as a tool for analysis of practical problems, remains in a primitive state; perhaps mostly because the theory has been motivated only superficially by its potential applications. People have devoted great efforts to solving the 'wrong problems. ' Queueing theory originated as a very practical subject. Much ofthe early work was motivated by problems concerning telephone traffic. Erlang, in particular, made many important contributions to the subject in the early part of this century. Telephone traffic remained one of the principle applications until about 1950. After World War II, activity in the fields of operations research and probability theory grew rapidly. Queueing theory became very popular, particularly in the late 1950s, but its popularity did not center so much around its applications as around its mathematical aspects. With the refine ment of some clever mathematical tricks, it became clear that exact solutions could be found for a large number of mathematical problems associated with models of queueing phenomena. The literature grew from 'solutions looking for a problem' rather than from 'problems looking for a solution. |
Contents
Introduction | 1 |
Deterministic fluid approximation single server | 25 |
Simple queueing systems | 53 |
Copyright | |
8 other sections not shown
Other editions - View all
Common terms and phrases
A(to A₁ arrival curve arrival process arrival rate arrivals and departures average behavior boundary conditions buses cars comparable cost cumulative arrivals cumulative number customer types customers arrive customers of type cycle D(to Da(t departure curve depend describe deterministic diffusion equation distribution function equilibrium distribution evaluate evolution example expected number exponentially distributed FIFO finite fluid approximation fo(l freeway geometric distribution graph headways integral interval k₁ m-channel maximum normal distribution number of arrivals number of customers observations obtained P₁ parameters passengers Poisson distribution Poisson process probability density problem properties queue discipline queue distribution queue length queue vanishes queueing models queueing systems queueing theory random variables represents rush hour s₂ Section served service rate single-channel server solution stationary stationary process statistically independent stochastic storage t₁ t₂ term time-dependent traffic signal typical variance vehicles wait