## Queueing Networks with Discrete Time Scale: Explicit Expressions for the Steady State Behavior of Discrete Time Stochastic Networks (Google eBook)Building on classical queueing theory mainly dealing with single node queueing systems, networks of queues, or stochastic networks has been a field of intensive research over the last three decades. Whereas the first breakthrough in queueing network theory was initiated by problems and work in operations research, the second breakthrough, as well as subsequent major work in the area, was closely related to computer science, particularly to performance analysis of complex systems in computer and communication science. The text reports on recent research and development in the area. It is centered around explicit expressions for the steady behavior of discrete time queueing networks and gives a moderately positive answer to the question of whether there can be a product form calculus in discrete time. Originating from a course given by the author at Hamburg University, this book is ideally suited as a text for courses on discrete time stochastic networks. |

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according algorithms apply arrival at node arrival probabilities arrival process arrival stream Arrival Theorem arriving customer assume babilities batch movements behaviour Bernoulli arrival Bernoulli process busy positions Buzen's algorithm cells closed cycle compute consider Corollary customer of type customer's customers cycling customers on positions customers present Daduna denote departure candidates dependent Bernoulli server described in section different customer types discrete time queueing discrete time scale discrete time systems doubly stochastic nodes end-to-end-delay ergodic explicit exponential FCFS follows geometrical node geometrically distributed joint queue length Markov chain Markov property Markovian multiple events norming constant number of customers obtain open tandem permutation Petri nets positive recurrent Proceedings queue length process queueing networks queueing theory residual reversal routing section 5.3 sequence service probabilities single node single server slot stationary distribution stay-on customers stochastic networks stochastic process Subseries LNAI transition matrix transmission vector virtual channel