Second-order stochastic properties in queueing systems

Article Abstract:

It is difficult to establish second-order stochastic properties for queueing systems even in the simplest cases in which closed-form results exist. The convexity-concavity of the throughput function of a closed Jackson network is one such difficult case. Traditional algebraic and analytical techniques are often ineffective or inappropriate tools for this research, but probabilistic tools have been developed and applied with much success. These techniques are based on building and comparing sample paths of the stochastic processes being studied. Past research in this area has been concerned only with two processes being compared at a time for establishing monotonicity properties. New approaches are developed for studying second-order stochastic properties that allow more than two processes to be built and compared at one time. Some new notions of convexity and concavity have also been developed.

Network analyzers, LAN Monitor, Optimization, Mathematics of Computing, Scientific Research, Stochastic Model, Probability, Queuing Networks, Models of Computation, technical

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Petri nets: properties, analysis and applications

Article Abstract:

Petri nets are useful graphical and mathematical tools for modeling and analyzing complex information processing systems that may be concurrent, distributed or parallel, nondeterministic, asynchronous, and-or stochastic. The mathematical nature of Petri nets enables the solution of complex systems through the use of equations and other mathematical models. The graphic qualities of Petri nets enable them to be used as communication tools for systems analysis, as well as simulation tools for system activities. The primary rule of Petri net theory is the rule for transition enabling and firing, transitions being changes (events) in system states. Modeling examples, behavioral properties of Petri net models, the three primary analysis methods, and subclasses of and modified Petri nets are extensively described.

Algorithms, Algorithm, Modeling, Data modeling software, Petri nets, Applications, Analysis

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