Queueing Modelling Fundamentals: With Applications in by Chee?Hock Ng, Boon?Hee Soong(auth.) PDF

By Chee?Hock Ng, Boon?Hee Soong(auth.)

ISBN-10: 0470519576

ISBN-13: 9780470519578

ISBN-10: 0470994673

ISBN-13: 9780470994672

Queueing research is an important device utilized in the overview of method functionality. purposes of queueing research conceal a large spectrum from financial institution automatic teller machines to transportation and communications facts networks.

absolutely revised, this moment version of a well-liked e-book comprises the numerous addition of a brand new bankruptcy on stream & Congestion keep an eye on and a piece on community Calculus between different new sections which have been additional to final chapters. An introductory textual content, Queueing Modelling Fundamentals makes a speciality of queueing modelling ideas and purposes of knowledge networks, interpreting the underlying ideas of remoted queueing platforms. This e-book introduces the advanced queueing concept in easy language/proofs to let the reader to fast decide up an outline to queueing thought with no using the varied valuable mathematical instruments. It encompasses a wealthy set of labored examples on its functions to verbal exchange networks.

beneficial properties contain:

  • Fully revised and up-to-date version with major new bankruptcy on circulation and Congestion keep an eye on as-well-as a brand new part on community Calculus
  • A accomplished textual content which highlights either the theoretical types and their functions via a wealthy set of labored examples, examples of purposes to information networks and function curves
  • Provides an perception into the underlying queuing ideas and contours step by step derivation of queueing effects
  • Written by means of skilled Professors within the box

Queueing Modelling Fundamentals is an introductory textual content for undergraduate or entry-level post-graduate scholars who're taking classes on community functionality research in addition to these working towards community directors who are looking to comprehend the necessities of community operations. The specific step by step derivation of queueing effects additionally makes it a great textual content for pro engineers.Content:
Chapter 1 Preliminaries (pages 1–41):
Chapter 2 advent to Queueing platforms (pages 43–70):
Chapter three Discrete and non-stop Markov methods (pages 71–102):
Chapter four Single?Queue Markovian structures (pages 103–140):
Chapter five Semi?Markovian Queueing structures (pages 141–168):
Chapter 6 Open Queueing Networks (pages 169–195):
Chapter 7 Closed Queueing Networks (pages 197–215):
Chapter eight Markov?Modulated Arrival method (pages 217–242):
Chapter nine circulation and Congestion keep an eye on (pages 243–257):

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Extra info for Queueing Modelling Fundamentals: With Applications in Communication Networks, Second Edition

Example text

11 This is a famous legendary puzzle. 6). During the move, a larger ring cannot be placed on top of a smaller one at the resting point. Determine the number of moves required if there are k rings in the pile. Solution To calculate the number of moves (mk) required, we first move the top (k − 1) rings to Point B and then move the last ring to Point C, and finally move the (k − 1) rings from Point B to Point C to complete the exercise. Denote its ∞ z-transform as M ( z ) = ∑ mk z k and m0 = 0, then from the above-mentioned k =0 recursive approach we have mk = mk −1 + 1 + mk −1 k ≥1 mk = 2 mk −1 + 1 Multiplying the equation by zk and summing it from zero to infinity, we have ∞ ∞ ∞ k =1 k =1 k =1 ∑ mk z k = 2∑ mk −1 z k + ∑ z k M ( z ) − m0 = 2 zM ( z ) + z 1− z and M (z) = z (1 − z )(1 − 2 z ) 27 z-TRANSFORMS – GENERATING FUNCTIONS To find the inverse of this expression, we do a partial fraction expansion: M (z) = 1 −1 + = (2 − 1) z + (22 − 1) z 2 + (23 − 1) z 3 + .

A coin is tossed an infinite number of times. Show that the probability that k heads are observed at the nth tossing but not earlier equals  n − 1 k n−k   p (1 − p) , where p = P{H}. k − 1 4. A coin with P{H} = p and P{T} = q = 1 − p is tossed n times. 5[1 + (q − p)n]. 5. Let A, B and C be the events that switches a, b and c are closed, respectively. Each switch may fail to close with probability q. 5. 6. 4, respectively. (a) What is the probability that two 1 s and three 0 s will occur in a 5-digit sequence.

L n−1 are eigenvectors of Ã−1. Moreover, any eigenvector of à is an eigenvector of Ã−1. (iv) à and ÃT do not necessarily have the same eigenvectors. However, if ÃTx˜ = lx˜ then x˜Tà = lx˜T, and the row vector x˜T is called a left eigenvector of Ã. It should be pointed out that eigenvalues are in general relatively difficult to compute, except for certain special cases. If the eigenvalues l1, l2, . . 62) where Λ˜ = diag(l1, l2, . . , ln), Ñ = [x˜1, x˜2, . . , x˜n] whose ith column is x˜i, Ñ −1 is the inverse of Ñ, and is given by 36 PRELIMINARIES π 1  π  2 N −1 =   …  π   n By induction, it can be shown that Ãk = ÑΛ˜kÑ−1.

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Queueing Modelling Fundamentals: With Applications in Communication Networks, Second Edition by Chee?Hock Ng, Boon?Hee Soong(auth.)

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