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Scope and Nature of Queueing Theory
Review of Topics from the Theory of Probability
BirthandDeath Queueing Models
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analysis arbitrary customer arrival epoch arrival rate arriving customer arriving customer's distribution assume assumption Bernoulli trials birth-and-death process blocked customers busy period calculate Chapter conditional probability consider customers arrive customers present customers waiting defined equals Erlang delay system Erlang loss system example Exercise exponential service exponentially distributed finite follows formula geometric distribution given Hence interarrival iteration Laplace-Stieltjes transform low-priority customer M/G/l queue Markov chain Markov property mathematical mean number mean service method number of customers Observe obtain offered load order of arrival ordered server overflow group Pj(t points Poisson distribution Poisson input Poisson process probability-generating function quasirandom input queue discipline queueing models queueing theory random variable request for service Riemann-Stieltjes integral right-hand side servers busy service completion service-time distribution function simulation solution stationary policy statistical-equilibrium stochastic processes test customer theorem tion traffic variance waiting customers waiting for service waiting positions waiting-time distribution function