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Simple queueing systems
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analysis apply approximately normal arrival curve arrival process arrival rate arrivals and departures average number behavior binomial binomial distribution boundary conditions central limit theorem constant cost of delay cumulative arrival cumulative number curve A(t customer types customers arrive customers in service customers of type departure curve departure process depend differential equation diffusion equation distribution function equilibrium distribution evaluate example exponentially distributed FIFO Figure finite fluctuations fluid approximation geometric distribution graph homogeneous Poisson process increases integral interpretation interval mathematical mean queue normal distribution number in service number of arrivals number of customers observe obtained optimal parameters partial differential equations passengers Poisson distribution postulates quasi-stationary distribution queue discipline queue distribution queue length queue vanishes queueing systems queueing theory random variables rush hour Section served service facility service rate solution specified stationary stationary process statistically independent strategy sufficiently large Suppose total delay traffic intensity type 1 customers typical variance zero