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Basic Tools of Probabilistic Modelling
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achievable performance vectors active jobs analysis arrival rate assume average number average queue length average response balance equations behaviour boundary class r jobs coefficient of variation computer systems conservation law Coxian distribution defined degree of multiprogramming denote departure device diffusion approximation distribution function equal exponentially distributed external arrivals g-jobs given independent inner system instants interarrival interval Jackson network job classes job of class jobs at node k-th lifetime function Little's theorem M/G/1 queue M/M/1 system main memory Markov chain Markov process matrix minimise mixing strategy node non-pre-emptive number of class number of customers number of jobs obtained page faults paging drum parameters Poisson arrivals Poisson process probability distribution queue with server queueing network queueing system queueing theory random variables required service sample path satisfies scheduling strategies server of walking service time distributions solution station stationary queue length steady-state distribution stochastic process subset throughput walking type