Wojciech M. Kempa (auth.), Khalid Al-Begain, Simonetta's Analytical and Stochastic Modeling Techniques and PDF

By Wojciech M. Kempa (auth.), Khalid Al-Begain, Simonetta Balsamo, Dieter Fiems, Andrea Marin (eds.)

ISBN-10: 3642217133

ISBN-13: 9783642217135

This booklet constitutes the refereed court cases of the 18th foreign convention on Analytical and Stochastic Modeling concepts and purposes, ASMTA 2011, held in Venice, Italyin June 2011.

The 24 revised complete papers provided have been conscientiously reviewed and chosen from many submissions.The papers are equipped in topical sections on queueing thought, software program and desktops, information and inference, telecommunication networks, and function and performability.

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Extra resources for Analytical and Stochastic Modeling Techniques and Applications: 18th International Conference, ASMTA 2011, Venice, Italy, June 20-22, 2011. Proceedings

Sample text

In fact in [3] this expression has been derived for q(z), but a standard up-and down-crossing argument combined with PASTA [17] shows that the stationary number of customers at customer departure, at customer arrival and at arbitrary epochs are all the same. According to this q d (z) can be expressed as q d (z) = (1 − ρ)B(λ − λz) m(z) − f (z) . f −m B(λ − λz) − z (31) Furthermore the number of customers just before the customer departure epoch is one more than the number of customers just after that customer departure epoch.

E. 0 < λ < ∞, 0 < b < ∞, 0 < 1/μ < ∞ and 0 < h < ∞. 2 The arrival process, the customer service times, the sequence of vacation periods and the customer service times in the vacation periods are mutually independent. 3 The customers are served in First-In-First-Out (FIFO) order. We assume that the model is stable. Both the mean vacation time and the arrival rate are finite, thus only finite number of customers can be accumulated during the vacation period. Hence from the point of view of the stability only the service period has to be considered.

43) Applying (41), (42), and propositions 2 and 1 in (43) leads to q(z) = μbf (1 − ρ)z(1 − B(λ − λz)) m(z) − f (z) 1 + f (z). (44) 1 + μbf ρ(1 − z)(B(λ − λz) − z) f −m 1 + μbf Applying (9) and (10) results in the statement of the theorem. Corollary 1. Based on (40) the mean number of customers is q (1) = 5 2(1 + μb) + μλb(2) f + μb(1 + ρ)f (2) . 2(1 + μbf ) (45) The Stationary Waiting Time Let Wτ be the waiting time in the system at time τ . We define the distribution function of the stationary waiting time, W (t), as W (t) = lim P {Wτ ≤ t} .

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Analytical and Stochastic Modeling Techniques and Applications: 18th International Conference, ASMTA 2011, Venice, Italy, June 20-22, 2011. Proceedings by Wojciech M. Kempa (auth.), Khalid Al-Begain, Simonetta Balsamo, Dieter Fiems, Andrea Marin (eds.)


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