Analytical and Stochastic Modeling Techniques and by Sofiane Ouazine, Karim Abbas (auth.), Alexander Dudin, Koen

By Sofiane Ouazine, Karim Abbas (auth.), Alexander Dudin, Koen De Turck (eds.)

This publication constitutes the refereed court cases of the twentieth foreign convention on Analytical and Stochastic Modelling and purposes, ASMTA 2013, held in Ghent, Belgium, in July 2013. The 32 papers offered have been rigorously reviewed and chosen from quite a few submissions. the focal point of the papers is at the following software subject matters: complicated structures; machine and knowledge platforms; conversation structures and networks; instant and cellular structures and networks; peer-to-peer program and companies; embedded platforms and sensor networks; workload modelling and characterization; highway site visitors and transportation; social networks; measurements and hybrid innovations; modeling of virtualization; energy-aware optimization; stochastic modeling for structures biology; biologically encouraged community design.

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Additional info for Analytical and Stochastic Modeling Techniques and Applications: 20th International Conference, ASMTA 2013, Ghent, Belgium, July 8-10, 2013. Proceedings

Example text

N −1 ri · r0 r1 i=k−1 . ri · r0 r1 r2 · · · i=k−1 .. rN −1 r0 r1 The proof of Theorem 1 is given in Appendix B. . rN −1 r0 r1 r2 .. ··· ⎤ ri ⎥ i=0 ⎥ N −2 ⎥ ri ⎥ ⎥ ⎥ i=1 ⎥ N −2 ri ⎥ ⎥ ⎥ i=2 ⎥ N −2 ⎥ ri ⎥ ⎥ i=3 ⎥ .. ⎥ ⎥ . ⎥ N −2 ⎥ ri ⎥ ⎥ i=k−1 ⎥ ⎥ .. ⎦ . 1 N −2 Average Delay Estimation in Discrete-Time Systems 45 Let us denote the maximum rejection probability as rmax max (r0 , r1 , . . r 0 1 N −1 . Then, the following theorem can be formulated. = = Theorem 2. The condition number cR of the matrix R satisfies the following inequality: N 1 + rmax 1 − rmax .

Algorithm NAMA example operation According to the algorithm NAMA, the probability of winning the competition depends only on the number of connected users and equals to pi = u1i . In real-world systems, the number of users typically varies in time due to their daily activity. Therefore, the proposed approach to delay analysis can be followed again. We denote the average number of connected users in the system as u. Hence, the equation (10) transforms into the following: d=u+ 1 N K−1 di,0 Δui . (17) i=0 Here, Δui = ui−1 −ui is a difference in the number of users between the adjacent slots.

RN −1 r3 r4 . . rN −1 r0 ⎢ ⎢ .. ⎢ ⎢ . ⎢ N −1 N −1 ⎢ ⎢ ri · r0 ⎢ i=k−1 ri i=k−1 ⎢ ⎢ .. ⎣ . rN −1 r0 rN −1 r0 r1 r0 r1 r2 ··· r1 r1 r2 ··· 1 r2 ··· 1 ··· .. .. N −1 ri · r0 r1 i=3 N −1 .. N −1 ri · r0 r1 i=k−1 . ri · r0 r1 r2 · · · i=k−1 .. rN −1 r0 r1 The proof of Theorem 1 is given in Appendix B. . rN −1 r0 r1 r2 .. ··· ⎤ ri ⎥ i=0 ⎥ N −2 ⎥ ri ⎥ ⎥ ⎥ i=1 ⎥ N −2 ri ⎥ ⎥ ⎥ i=2 ⎥ N −2 ⎥ ri ⎥ ⎥ i=3 ⎥ .. ⎥ ⎥ . ⎥ N −2 ⎥ ri ⎥ ⎥ i=k−1 ⎥ ⎥ .. ⎦ . 1 N −2 Average Delay Estimation in Discrete-Time Systems 45 Let us denote the maximum rejection probability as rmax max (r0 , r1 , .

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