An Introduction to Queueing Theory: Modeling and Analysis in by U. Narayan Bhat

By U. Narayan Bhat

This introductory textbook is designed for a one-semester direction on queueing concept that doesn't require a path in stochastic tactics as a prerequisite. through integrating the mandatory heritage on stochastic procedures with the research of types, the paintings offers a valid foundational advent to the modeling and research of queueing structures for a large interdisciplinary viewers of scholars in arithmetic, information, and utilized disciplines akin to desktop technological know-how, operations examine, and engineering.

Key features:

* An introductory bankruptcy together with a historic account of the expansion of queueing thought within the final a hundred years.

* A modeling-based process with emphasis on identity of types utilizing issues equivalent to number of info and checks for stationarity and independence of observations.

* Rigorous therapy of the principles of simple types normal in purposes with applicable references for complex topics.

* A bankruptcy on modeling and research utilizing computational tools.

* A complete remedy of statistical inference for queueing systems.

* A dialogue of operational and selection problems.

* Modeling routines as a motivational software, and assessment routines overlaying historical past fabric on statistical distributions.

An creation to Queueing Theory can be used as a textbook by way of first-year graduate scholars in fields akin to laptop technology, operations learn, commercial and platforms engineering, in addition to similar fields comparable to production and communications engineering. Upper-level undergraduate scholars in arithmetic, facts, and engineering can also use the ebook in an non-obligatory introductory path on queueing idea. With its rigorous insurance of simple fabric and huge bibliography of the queueing literature, the paintings can also be worthy to utilized scientists and practitioners as a self-study reference for purposes and extra research.

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Additional info for An Introduction to Queueing Theory: Modeling and Analysis in Applications

Sample text

3) follows by letting t → 0. 3) should be solved along with the initial condition Pi (0) = 1, Pn (0) = 0 for n = i. ) Unfortunately, even in simple cases such as λn = λ and µn = µ, n = 0, 1, 2, 3, . . , that is when the arrivals are Poisson and service times are exponential (M/M/1 queue), deriving Pn (t) explicitly is an arduous process. Furthermore in most of the applications the need for knowing the time-dependent behavior is not all that critical. 3) by letting t → ∞. A general result on Markov processes is given below.

7) period (m, r) is Pik now follows by multiplying these two probabilities and summing over all values of k ∈ S. 10). The stochastic processes underlying queueing systems considered in this book primarily belong to two classes: discrete-state and -parameter spaces (case (i) above) and discrete-state space and continuous-parameter space (case (ii) above). 8) can be used in their analysis here and in Appendix B. Case (i): Discrete-state and -parameter space. Let {Xn , n = 0, 1, 2, . . } be a timehomogeneous Markov chain.

Random variables. If there are reasons to make such assumptions, statistical tests can be used for verification. Some of the tests that can be used to verify independence of a sequence of observations are tests for serial independence in point processes, described in Lewis (1972), and various tests for trend analysis and renewal processes, given by Cox and Lewis (1966). To verify the assumption of independence between interarrival and service times, nonparametric tests seem appropriate. Spearman’s rho and Kendall’s tau (Conover (1971), Randles and Wolfe (1979)) are used to test for the correlation between two sequences of random variables, whereas Cramer–von Mises-type statistics (see Koziol and Nemec (1979) and references cited therein) are used to test for bivariate independence directly from the definition of independence applied to random variables.

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