New PDF release: Analytical and Stochastic Modeling Techniques and

By Chesoong Kim, Olga Dudina, Alexander Dudin, Sergey Dudin (auth.), Khalid Al-Begain, Dieter Fiems, Jean-Marc Vincent (eds.)

ISBN-10: 3642307825

ISBN-13: 9783642307829

This booklet constitutes the refereed court cases of the nineteenth overseas convention on Analytical and Stochastic Modelling recommendations and functions, ASMTA 2012, held in Grenoble, France, in June 2012. The 20 revised complete papers offered have been conscientiously reviewed and chosen from various submissions. The papers are equipped in topical sections on queueing platforms; networking functions; Markov chains; stochastic modelling.

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Extra info for Analytical and Stochastic Modeling Techniques and Applications: 19th International Conference, ASMTA 2012, Grenoble, France, June 4-6, 2012. Proceedings

Example text

For negative values of γ, this implies that customers of both 1−β 1−γ classes alternate strongly; for positive values of γ, there may be very long sequences of customers of the same class. During such periods, the momentary load is either given by ρA λμA = 8λ or by ρB λμB = 2λ. 2, guarantees that ρB < 1, but not necessarily that ρA < 1. , the system is locally stable during B-sequences but not during A-sequences. In the latter case, labelled as the “compensated” equilibrium, (global) stability is assured because although the queue size builds up during A-sequences (because, on average, more work arrives than the server can perform), it decreases again during B-sequences (when much less work enters than the server can execute).

That the stability condition is fulfilled. , if and only if λE[c] < 1, with E[c] the average service time of an arbitrary customer. Expressed in the basic parameters of our system, this is equivalent to the condition λ(tA μA + tB μB ) < 1 , (12) Analysis of a Two-Class FCFS Queueing System with Interclass Correlation 37 where the quantities tA and tB are the steady-state probabilities of the arrival Markov chain (see Eqs. (5) and (6)). Assuming this condition fulfilled, we define the joint steady-state probabilities of the Markov chain {(tk , uk )} as pA (i) lim Prob[tk = A, uk = i] (13) lim Prob[tk = B, uk = i] , (14) k→∞ and pB (i) k→∞ for all i ≥ 0.

Pi,c−i ) (i = 0, 1, . . , c). In addition, let p = (p0 , p1 , . . , pc ) denote the stationary distribution of {C(t); t ≥ 0}, which is the unique solution of the following system of equations. pP = 0, pe = 1, where 0 and e denote a row and a column vector with an appropriate size with all zero and all one entries, respectively. The necessary and sufficient condition for the stability of {X(t); t ≥ 0} is given by pA+ e < pA− e, (31) according to [14]. Because the number of states of {C(t); t ≥ 0} is finite the stability condition presented by (31) itself is explicit.

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Analytical and Stochastic Modeling Techniques and Applications: 19th International Conference, ASMTA 2012, Grenoble, France, June 4-6, 2012. Proceedings by Chesoong Kim, Olga Dudina, Alexander Dudin, Sergey Dudin (auth.), Khalid Al-Begain, Dieter Fiems, Jean-Marc Vincent (eds.)


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