Download e-book for iPad: An Introduction to Queueing Theory: Modeling and Analysis in by U. Narayan Bhat

By U. Narayan Bhat

ISBN-10: 0817684212

ISBN-13: 9780817684211

This introductory textbook is designed for a one-semester path on queueing thought that doesn't require a direction in stochastic tactics as a prerequisite. by way of integrating the required historical past on stochastic techniques with the research of types, this e-book presents a foundational creation to the modeling and research of queueing platforms for a large 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 helpful as a self-study reference for purposes and extra study.

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

Example text

In queueing systems, and all systems that operate over time (or space or any other parameter), the model must be able to represent the system over time. That means we need a sequence or a family of random variables to represent such a phenomenon over time. Let T be the range of time of interest. Time can be continuous or discrete. We denote the time t T when it is continuous, and n T when it is discrete. Then the family of random variables {X(t), t T } or the sequence of random variables {Xn , n T } is known as a stochastic process.

Because of the complexity of the procedure and the final result, we do not provide it in this text. Interested readers may refer to Gross et al. (2008, pp. 98–101), where the results have been derived in detail. 2) (see Stewart 1994). 9)), we get pn = (1 − ρ)ρn where ρ = λ/μ < 1. ∞ 0 n = 1, 2, 3 . . 8) and n = 0, 1, 2, . . 4) 44 CHAPTER 4. SIMPLE MARKOVIAN QUEUEING SYSTEMS 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.

37) which is the same as the distribution of the inter-arrival 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. For a more exhaustive treatment of this problem see Burke (1956) who has considered this problem for the multiserver M/M/s queue. The important result coming out of this analysis states that the departure process of the M/M/1 queue in equilibrium is the same Poisson as the arrival 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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