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Download e-book for kindle: Analytical and Stochastic Modeling Techniques and by Wojciech M. Kempa (auth.), Khalid Al-Begain, Simonetta

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

ISBN-10: 3642217133

ISBN-13: 9783642217135

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

The 24 revised complete papers offered have been rigorously reviewed and chosen from many submissions.The papers are equipped in topical sections on queueing idea, software program and desktops, facts and inference, telecommunication networks, and function and performability.

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Read or Download Analytical and Stochastic Modeling Techniques and Applications: 18th International Conference, ASMTA 2011, Venice, Italy, June 20-22, 2011. Proceedings PDF

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

Example text

42) σ + 1/μ It follows from the theorem of total probability that q(z) = pb q b (z) + pv q v (z). (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 .

This ensures the applicability of the distributional Little’s law [2]. Furthermore the time in the system of an arbitrary customer is the sum of its waiting time and its service time, which are independent due to the model assumptions. Taking it also into account the distributional Little’s law can be given to our model as q(z) = w (λ − λz) B (λ − λz) . Substituting z = 1 − s λ (47) into (47) and rearranging yields w (s) = q(1 − λs ) B (s) . (48) The statement comes from (48) and (40). d From (48) the mean waiting time, E(W ) = − ds w (s) |s=0 , is E(W ) = q (1) − b, λ (49) which is the regular Little law obtained from the distributional Little law.

Analysis of a GI/M/1 queue with multiple working vacations. Operation Research Letters 33, 201–209 (2005) 2. : The distributional Little’s law and its application. Operations Research 43, 298–310 (1995) 3. : Polling models with and without switchover times. Operations Research 45, 536–543 (1997) 4. : Queueing systems with vacations - a survey. Queueing Systems 1, 29–66 (1986) 5. : Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations. Operations Research 33, 1117–1129 (1985) 6.

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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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