Read e-book online An Introduction to Queueing Theory: Modeling and Analysis in PDF

By U. Narayan Bhat

ISBN-10: 0817647244

ISBN-13: 9780817647247

This introductory textbook is designed for a one-semester direction on queueing thought that doesn't require a path in stochastic methods as a prerequisite. by way of integrating the mandatory history on stochastic tactics with the research of types, the paintings presents a valid foundational creation to the modeling and research of queueing structures for a huge interdisciplinary viewers of scholars in arithmetic, records, and utilized disciplines equivalent to desktop technology, operations examine, and engineering.

Key features:

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

* A modeling-based strategy with emphasis on id of types utilizing themes reminiscent of choice of information and exams for stationarity and independence of observations.

* Rigorous remedy of the principles of uncomplicated types primary in purposes with acceptable references for complex topics.

* A bankruptcy on modeling and research utilizing computational tools.

* A finished remedy of statistical inference for queueing systems.

* A dialogue of operational and selection problems.

* Modeling routines as a motivational device, and evaluation workouts masking historical past fabric on statistical distributions.

An creation to Queueing Theory can be used as a textbook via first-year graduate scholars in fields comparable to laptop technology, operations learn, commercial and platforms engineering, in addition to comparable fields reminiscent of production and communications engineering. Upper-level undergraduate scholars in arithmetic, records, and engineering can also use the booklet in an non-compulsory introductory path on queueing conception. With its rigorous assurance of simple fabric and large bibliography of the queueing literature, the paintings can also be worthy to utilized scientists and practitioners as a self-study reference for purposes and additional research.

Show description

Read or Download An Introduction to Queueing Theory: Modeling and Analysis in Applications PDF

Similar linear programming books

Download e-book for iPad: Linear Programming and its Applications by Horst A. Eiselt, Carl-Louis Sandblom

Within the pages of this article readers will locate not anything under a unified remedy of linear programming. with out sacrificing mathematical rigor, the most emphasis of the publication is on types and purposes. crucial periods of difficulties are surveyed and offered through mathematical formulations, by way of answer tools and a dialogue of quite a few "what-if" situations.

Download e-book for kindle: Sequential Approximate Multiobjective Optimization Using by Hirotaka Nakayama

This ebook highlights a brand new path of multiobjective optimzation, which hasn't ever been taken care of in prior courses. whilst the functionality type of goal features isn't identified explicitly as encountered in lots of sensible difficulties, sequential approximate optimization in keeping with metamodels is an efficient instrument from a realistic perspective.

Introduction to Applied Optimization - download pdf or read online

This ebook offers a view of optimization autonomous of any self-discipline. This new version includes new chapters, one on worldwide optimization and one in all a real-world case examine that makes use of the rules from every one bankruptcy within the publication.

Download e-book for iPad: Evolutionary Algorithms and Agricultural Systems by David G. Mayer

Evolutionary Algorithms and Agricultural structures offers with the sensible software of evolutionary algorithms to the research and administration of agricultural structures. the reason of structures learn technique is brought, and examples indexed of real-world functions. it's the integration of those agricultural platforms types with optimization recommendations, essentially genetic algorithms, which kinds the focal point of this publication.

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

Sample text

33) can be solved by noting that F (x) d ln F0 (x) = 0 = −λ. dx F0 (x) Hence ln F0 (x) = −λx + C. 33) can be obtained by induction. Let Fn−1 (x) = pn−1 e−λx , n = 1, 2, . . 33), we get Fn (x) + (λ + µ)Fn (x) = λpn−1 e−λx . 34). We get 42 4 Simple Markovian Queueing Systems Fn (x) = pn e−λx , n = 1, 2, 3, . . 37) which is the same as the distribution of the interarrival times. 36) also confirms the independence of the distribution of T from the queue length distribution at departure points. Note that here we are talking about the independence of distribution of two random variables and not any relationship between their specific values.

9)), we get pn = (1 − ρ)ρ n , n = 0, 1, 2, . . 4) where ρ = λ/µ < 1. The probability that the server is busy is a performance measure for the system. Clearly, this utilization factor = 1−p0 = ρ = traffic intensity in this case. Recall that we have defined Q(t) as the number of customers in the system. Write Q(∞) = Q and let Qq be the number in the queue, excluding the one in service. Now we may define two mean values, L = E(Q) and Lq = E(Qq ). 4), we get 36 4 Simple Markovian Queueing Systems ∞ L= n(1 − ρ)ρ n = n=1 ρ , 1−ρ which can also be written as = λ .

As the fraction of time that the process occupies state n in the long run. 3. Having started from state i, let Nij (t) be the time spent by the Markov process in state j during (0, t]. Then lim t→∞ Nij (t) − pj >∈ = 0. t The general birth-and-death queueing model encompasses a wide array of special cases. Some of the widely used models are discussed in the following sections. 2 The Queue M/M/1 The M/M/1 queue is the simplest of the queueing models used in practice. The arrivals are assumed to occur in a Poisson process with rate λ.

Download PDF sample

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

by Charles

Rated 4.06 of 5 – based on 9 votes