Computer Networks: 19th International Conference, CN 2012, by Miroslav Voznak, Lukas Kapicak, Martin Mikulec, Pavel Nevlud

By Miroslav Voznak, Lukas Kapicak, Martin Mikulec, Pavel Nevlud (auth.), Andrzej Kwiecień, Piotr Gaj, Piotr Stera (eds.)

This publication constitutes the refereed court cases of the nineteenth foreign convention on machine Networks, CN 2012, held in Szczyrk, Poland, in June 2012. The forty eight revised complete papers awarded have been conscientiously reviewed and chosen for inclusion within the booklet. The papers handle matters equivalent to new and rising applied sciences regarding networking fields; basics of computing device networks; web and internetworking; safety and security concerns; commercial machine networks; instant structures and sensor networks; the speculation of queues and queuing networks; purposes and machine networks usage.

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Service income versus different number of submitted offers for first price policy 30 J. Wrzuszczak-Noga and L. Borzemski Fig. 4. Service income versus different number of submitted offers for RFM pricing policy Fig. 5. Service income versus different number of submitted offers for auction based scheduling policy presented. In Figure 4 the RFM-based policy for auction scheduling and FIFO scheduling are presented. In Figure 5 three pricing mechanism are compared in auction based scheduling versus the number of offers.

Assume that x is fixed and equal to x . Let us define Lagrange function: M N S L1 (y, λ) = xmns τmns (x , y)+ m=0 n=1 s=1 L M N S λl + amnsl ymns xmns − Cl m=0 n=1 s=1 l=1 [λ1 , . . λL ]T where λ = is the vector of Lagrange multipliers. The Langrange function’s derivatives are as follows: ∂L1 (y, λ) = ∂ymns M N S xijk i=0 j=1 k=1 M N ∂τijk (x , y) ∂ymns L amnsl λl + xmns (4) l=1 S ∂L1 (y, λ) = amnsl xmns ymns − Cl . ∂λl m=0 n=1 s=1 (5) Equating above derivatives to 0 and solving the set of equations with respect to ymns and λl one can obtain the optimal solution of lower level problem (from KKT conditions [14], the only points where derivatives of convex function are zero coincide with the global optimum).

1) Compute τmns (ymns [t]) according to (9). (2) Receive τl from all links (routers) on the path to server s. Receive the value xmns l amnsl λl [t] from the network (routers). Update transmission rate ymns [t + 1] according to (13). If |ymns [t + 1] − ymns [t]| < then STOP. Increase t. Go to 2. Algorithm 2. Link algorithm for upper level subproblem The procedure below is executed in link l (routers’ software): 1. 2. 3. 4. 5. Let t = 0. e. m,n,s amnsl xmns ymns [t]. Update congestion signals λl [t + 1] according to (7).

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