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arriving customer assume average number behavior birth-death process busy period calculate Chapman-Kolmogorov equation Chapter Cn+1 coefficients condition consider constant convolution customers arrive define definition denote density function departure derivative discrete-time equal equilibrium probability ergodic Erlangian evaluate example exponentially distributed expression factor finite flow geometric distribution given in Eq gives hippie imbedded Markov chain independent instants integral interarrival interval invert Laplace transform last equation limit linear M/M/l queue M/M/l system Markov process matrix memoryless method node notation number of arrivals number of customers obtain parameter permit Pk(t Poisson arrival Poisson process probability vector queueing system queueing theory random variables random walk reader referred renewal theory result semi-Markov processes sequence server service facility service-time shown in Figure solution solve state-transition-rate diagram stochastic processes theorem transition probabilities vector waiting z-transform zero