Introduction to Queueing Theory |
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Page 84
... distribution ( 3.3 ) is valid for an arbitrary service - time distribution function was conjectured by Erlang himself in 1917 , and proved by Sevast'yanov [ 1957 ] . Subsequently , many investigators studied this problem , and a variety ...
... distribution ( 3.3 ) is valid for an arbitrary service - time distribution function was conjectured by Erlang himself in 1917 , and proved by Sevast'yanov [ 1957 ] . Subsequently , many investigators studied this problem , and a variety ...
Page 216
... distribution generated by ( 8.12 ) depends on the particular choice of the service - time distribution function ; neverthe- less , as ( 8.32 ) shows , the probability III = Po does not . Thus , the probability that an arrival will find ...
... distribution generated by ( 8.12 ) depends on the particular choice of the service - time distribution function ; neverthe- less , as ( 8.32 ) shows , the probability III = Po does not . Thus , the probability that an arrival will find ...
Page 304
... service time of an arbitrary job , then X has distribution function P { X < x } = H ( x ) given by the Erlangian distribution function of order n : Η ( x ) = 1- Σ ( μx ) j ! j = 0 εμε › where n is the number of phases , each with mean μ ...
... service time of an arbitrary job , then X has distribution function P { X < x } = H ( x ) given by the Erlangian distribution function of order n : Η ( x ) = 1- Σ ( μx ) j ! j = 0 εμε › where n is the number of phases , each with mean μ ...
Contents
Scope and Nature of Queueing Theory | 1 |
Review of Topics from the Theory of Probability | 9 |
BirthandDeath Queueing Models | 73 |
Copyright | |
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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 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 Operations Research 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 simulation solution stationary policy statistical-equilibrium stochastic processes Takács test customer theorem tion traffic variance waiting customers waiting for service waiting positions X₁