U. Narayan Bhat's An Introduction to Queueing Theory: Modeling and Analysis in PDF

By U. Narayan Bhat

ISBN-10: 0817684212

ISBN-13: 9780817684211

This introductory textbook is designed for a one-semester path on queueing idea that doesn't require a direction in stochastic tactics as a prerequisite. by means of integrating the mandatory heritage on stochastic approaches with the research of types, this ebook presents a foundational creation to the modeling and research of queueing platforms for a wide interdisciplinary viewers of scholars. Containing routines and examples, this quantity can be used as a textbook by way of first-year graduate and upper-level undergraduate scholars. The paintings can also be invaluable as a self-study reference for functions and extra learn.

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Additional resources for An Introduction to Queueing Theory: Modeling and Analysis in Applications (2nd Edition)

Example text

Then the process is identified as a marked point process. Regenerative Process Consider a stochastic process {X(t), t T } and a discrete set of points t1 < t2 < . . < tn T . Suppose the distribution properties of the process from ti onwards is the same for all i = 1, 2, . . , n. Then we can consider the process regenerating itself at these points. Renewal Process Consider a discrete set of points (t0 , t1 , t2 , . ) at which a specified event occurs and let ti − ti−1 = Zi (i = 1, 2, . d) random variables.

In addition to the treatment of data on the occurrence of events as a time series and the determination of second-order properties of the counting processes, they consider statistical problems related to renewal processes and provide tests of significance in some general, as well as some specific cases. Lewis (1972) updates this study and considers topics such as trend analysis of nonhomogeneous Poisson processes. In many queueing systems (such as airport and telephone traffic), the nonstationarity of the arrival process leads to a periodic behavior.

Ym be the number of arrivals during the second interval for m periods (usually m = n). If F and G represent the distributions of the X s and Y s, respectively, then the hypothesis to be tested is F = G against the alternative F = G, for which the Mann–Whitney–Wilcoxon statistic can be used. Using this test, successive stationary periods can be delineated and the system can be studied in detail within such periods (see Moore (1975), who gives an algorithm for the procedure). To analyze cyclic trends of the type discussed above, we may also use the periodogram method described by Lewis (1972) for the specific case of a nonhomogeneous Poisson process.

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An Introduction to Queueing Theory: Modeling and Analysis in Applications (2nd Edition) by U. Narayan Bhat

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