5. (25 pts) An AIMD-based video rate adaptation system (discussed in class) can be represented as...

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5. (25 pts) An AIMD-based video rate adaptation system (discussed in class) can be represented as a computational function of the form: L = net (1), where \ > 0 and L > 0. Internal details of net(...) to compute L for an input are not known to the network system programmer, i.e., net(X) appears as a black-box taking as input and returning L as output. But the programmer has a high-level view how the net(...) behaves when changes, as given by the relationship: net ( + A) > net(\) > net(\ A) for A > 0. The main control program invokes the net(A) function in the following ways: Suppose Xo is an initial input for which net(o) returns a value Lo > Sh, where Sh> 0. In that case, the program reduces in multiple steps of (B x L) decrements to a value A such that net () < , where > 0 and 0 < d < Sh. Thereupon, the program increases A in multiple steps of a increments to a value X, such that net() > Sh, where a > 0. Thereafter, the decrease procedure kicks in again. It is thus a repetitive cycle of decrease and increase of X. The computation steps in the program interacting with net(...) are shown in Figure 2-(a) as a pseudo- code in a C-like language. Figure 2-(b) shows the empirical behavior of program with respect to the time-steps i = 1,2,,3,.. for certain base values 3 = 3' and a = a'. A: B: C: (a) State the truth or otherwise of the following mathematical properties exhibited by the L = net(X) function i.e., a characterization of how L increases with respect to an increase in X): i) Monotonically convex increase; ii) Monotonically concave increase; iii) Linear increase; iv) No changes, i.e., constant. Give reasons for your choice. Video source Input Show an empirical graph of how (L, A) varies with respect to i for each of the cases: i) B > B', a = a'; ii) B = ', a > a'; iii) > ', a > a'; and iv) < ', a < a'. Can you reason about the convergence property of AIMD algorithm ?? t Nf 0 Sh 81 0 output L L=net(2) C-like description of the increase-decrease phases of input to the function "L=net(2)" based on observed output L Network path Interfering cross-traffic data video data flow Lo 1 Video receiver increase phase Input-output behavior of computational function: L=net(2) 3 4 5 6 3 increase int i=0; L = net(2); //2=-20, L=Lo: where Lo > Sh repeat if (L> 8h) while (L 81) =-BL; L = net(); i++; if (L <81) while (L 8h) = + ; L = net(2); i++; until (true == false). decrease phase decrease 10 Ami:200 Computational iteration #: i a, are constants For base values: B-', -a' 15 (b) 20 22 Figure 2: Behavior of program that embodies a black-box view of L net() function 5. (25 pts) An AIMD-based video rate adaptation system (discussed in class) can be represented as a computational function of the form: L = net (1), where \ > 0 and L > 0. Internal details of net(...) to compute L for an input are not known to the network system programmer, i.e., net(X) appears as a black-box taking as input and returning L as output. But the programmer has a high-level view how the net(...) behaves when changes, as given by the relationship: net ( + A) > net(\) > net(\ A) for A > 0. The main control program invokes the net(A) function in the following ways: Suppose Xo is an initial input for which net(o) returns a value Lo > Sh, where Sh> 0. In that case, the program reduces in multiple steps of (B x L) decrements to a value A such that net () < , where > 0 and 0 < d < Sh. Thereupon, the program increases A in multiple steps of a increments to a value X, such that net() > Sh, where a > 0. Thereafter, the decrease procedure kicks in again. It is thus a repetitive cycle of decrease and increase of X. The computation steps in the program interacting with net(...) are shown in Figure 2-(a) as a pseudo- code in a C-like language. Figure 2-(b) shows the empirical behavior of program with respect to the time-steps i = 1,2,,3,.. for certain base values 3 = 3' and a = a'. A: B: C: (a) State the truth or otherwise of the following mathematical properties exhibited by the L = net(X) function i.e., a characterization of how L increases with respect to an increase in X): i) Monotonically convex increase; ii) Monotonically concave increase; iii) Linear increase; iv) No changes, i.e., constant. Give reasons for your choice. Video source Input Show an empirical graph of how (L, A) varies with respect to i for each of the cases: i) B > B', a = a'; ii) B = ', a > a'; iii) > ', a > a'; and iv) < ', a < a'. Can you reason about the convergence property of AIMD algorithm ?? t Nf 0 Sh 81 0 output L L=net(2) C-like description of the increase-decrease phases of input to the function "L=net(2)" based on observed output L Network path Interfering cross-traffic data video data flow Lo 1 Video receiver increase phase Input-output behavior of computational function: L=net(2) 3 4 5 6 3 increase int i=0; L = net(2); //2=-20, L=Lo: where Lo > Sh repeat if (L> 8h) while (L 81) =-BL; L = net(); i++; if (L <81) while (L 8h) = + ; L = net(2); i++; until (true == false). decrease phase decrease 10 Ami:200 Computational iteration #: i a, are constants For base values: B-', -a' 15 (b) 20 22 Figure 2: Behavior of program that embodies a black-box view of L net() function