Introduction to Queueing Theory |
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Contents
Scope and Nature of Queueing Theory | 1 |
Review of Topics from the Theory of Probability | 9 |
BirthandDeath Queueing Models | 73 |
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analysis arbitrary customer arrival epoch arrival rate arriving customer arriving customer's distribution assume Bernoulli trials birth-and-death process blocked customers busy period calculate Chapter conditional probability consider customers arrive customers present customers waiting defined Equation Erlang delay system Erlang loss system example Exercise exponential service exponentially distributed finite follows formula geometric distribution given Hence interarrival interval iteration Laplace-Stieltjes transform length low-priority customer M/G/1 queue Markov chain Markov property mathematical mean number mean service method N-policy number of customers Observe obtain offered load order of arrival overflow group P₁ points Poisson distribution Poisson input Poisson process probability-generating function quasirandom input queue discipline queueing models queueing system queueing theory random variable Riemann-Stieltjes integral right-hand side servers busy service completion service-time distribution function Show simulation solution stationary policy statistical-equilibrium stochastic processes Takács test customer theorem tion traffic variance waiting customers waiting for service waiting positions X₁