An Introduction to Queueing Networks |
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A₁ approximation arrival process arrival rate Arrival Theorem Assume average number bandit busy cycle calculate closed network Consider converges corresponds countable set customer of class defined Definition Denote discussed distributed with rate dynamic programming equal equations ergodic evolution Example exponentially distributed fact Figure finite follows formula function given implies independent Poisson processes interarrival invariant distribution irreducible Jackson network jump Little's result M/M/1 queue Markov chain Markov Property matrix Q minimize number of customers observed optimal policy overtake-free Phase-type distributions point process Poisson process probability problem process with rate product-form proof Proposition quasi-reversible queues queue length queueing system queues in tandem random variables rate matrix reversed S₁ second queue sequence service rate shows sojourn stationary stationary process stoch stochastic T₁ tion typical customer vector μ₁ μη μι