By Winfried K. Grassmann (auth.), Winfried K. Grassmann (eds.)
Great advances were made in recent times within the box of computational chance. specifically, the cutting-edge - because it pertains to queuing structures, stochastic Petri-nets and structures facing reliability - has benefited considerably from those advances. the target of this publication is to make those issues available to researchers, graduate scholars, and practitioners. nice care used to be taken to make the exposition as transparent as attainable. each line within the ebook has been evaluated, and alterations were made at any time when it was once felt that the preliminary exposition was once now not transparent adequate for the meant readership.
The paintings of significant study students during this box contains the person chapters of Computational Probability. the 1st bankruptcy describes, in nonmathematical phrases, the demanding situations in computational chance. bankruptcy 2 describes the methodologies to be had for acquiring the transition matrices for Markov chains, with specific emphasis on stochastic Petri-nets. bankruptcy three discusses how to define brief possibilities and temporary rewards for those Markov chains. the following chapters point out how to define steady-state chances for Markov chains with a finite variety of states. either direct and iterative equipment are defined in bankruptcy four. info of those tools are given in bankruptcy five. Chapters 6 and seven take care of infinite-state Markov chains, which happen usually in queueing, simply because there are occasions one doesn't are looking to set a certain for all queues. bankruptcy eight offers with transforms, specifically Laplace transforms. The paintings of Ward Whitt and his collaborators, who've lately constructed a couple of numerical tools for Laplace rework inversions, is emphasised during this bankruptcy. ultimately, if one desires to optimize a procedure, a technique to do the optimization is thru Markov selection making, defined in bankruptcy nine. Markov modeling has stumbled on purposes in lots of components, 3 of that are defined intimately: bankruptcy 10 analyzes discrete-time queues, bankruptcy eleven describes networks of queues, and bankruptcy 12 offers with reliability theory.
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Extra resources for Computational Probability
Introduction to Stochastic Processes. PrenticeHall. , Bruell, S. , and Balbo, G. (1989). Alternative methods for incorporating non-exponential distributions into stochastic timed Petri nets. In Pmc. 3rd Int. Workshop on Petri Nets and Performance Models (PNPM'89), Kyoto, Japan. IEEE Compo Soc. Press. , and Haddad, S. (1993). Stochastic well-formed colored nets and symmetric modeling applications. IEEE Trans. , 42(11):1343-1360. , Kulkarni, V. , and Trivedi, K. S. (1994). Markov regenerative stochastic Petri nets.
In contrast to open Jackson networks, no arrivals are possible in a closed Jackson network. This makes the numerical solutions of closed networks somewhat more difficult than open networks. Generally, the product form is destroyed if the routing probabilities depend on the system state, or if the past history of the entities affects their behavior. For instance, the product form is no longer applicable if servers can be blocked, or if the routing may be changed to adapt to the present traffic. Other restrictions apply as shown in Chapter 11.
Chimento, P. F. , Muppala, J. , and Trivedi, K. S. (1993a). Automated generation and analysis of Markov reward models using Stochastic Reward Nets. In Meyer, C. , editors, Linear Algebra, Markov Chains, and Queueing Models, volume 48 of IMA Volumes in Mathematics and its Applications, pages 145-191. Springer-Verlag. , German, R, and Lindemann, C. (1993b). A characterization of the stochastic process underlying a stochastic Petri net. In 38 COMPUTATIONAL PROBABILITY Proc. 5th Int. Workshop on Petri Nets and Performance Models (PNPM'93), pages 170-179, Toulouse, France.