Question

# Hi, I feel confused with this computer networking problem, it's like

a type of Dijkstra Algorithm problem, however, the constrains right here is the capacity of each links. Thus, it become something like maximum flow problem. But I'm not sure. Could you help me with this homework?

Thanks so much!

Lucas

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Traffic routing: Network operators vs. user's perspective 1. Algorithm overview The objective of this project is to find optimal control variables allocating traffic to various links connecting source S with destination D. We will consider two cases. In the first one the goal is to find an optimal solution for a network operator, in the second, an individual user's interest is the top priority. In both cases the traffic routing strategies are delay-related. We assume that an average delay experienced by a packet is d=1/(c-f) , where c denotes capacity of a link and f is intensity of traffic offered to this link. This formula results from the theory of stochastic service systems. 2. Optimal strategy for a network operator A packet can be routed from source S to destination D over one of two different links, whose capacities are c 1 and c 2 . A network operator makes a decision which link is selected for each incoming packet. What delay related quality criterion J n (a 1 ,a 2 ,c 1 ,c 2 ,A) is the best from the network operator's perspective? Find control variables a 1 and a 2 , resulting from optimization of J n , that allocate the total traffic A from S to D to both links f 1 =a 1 A and f 2 =a 2 A . What is the corresponding optimal value of the proposed quality criterion J n ? Assume A =10, c 1 =16, c 2 =4. Optimal strategy for an individual user The topology of our simple network is slightly modified, i.e. source S is connected with destination D with three different links (not two as in Section 2) of capacities c1 , c2 and c3 . Now every incoming packet (not the network operator) chooses for itself a path from S to D . What delay- related decision criterion Jp should be applied by each individual packet? Is this criterion identical to Jn ? Find the corresponding optimal traffic control variables a1 , a2 , a3 and the numerical value of Jp . Assume A =20, c1 =16, c2 =4, c3 =6.    