For the network in the figure, apply the max-min flow control algorithm to assig

Question

For the network in the figure, apply the max-min flow control algorithm to assign sessions for the following network. Three different flows each with offering Poisson arrivals streams are sharing the links in this network. The link capacities (equivalent with the transmission rates for each transmission line) are marked in the figure. The service times for a transmission line are assumed to be exponentially distributed.

The session flow 1 has the path Aà B à C à D; Flow 2: A, F, C, D; Flow 3: Eà FàCàG. Link capacities: CD=6; AB=8; BC=5; EF=10; FC = 5; CG=9;AF=10;

Assign maximum allowable throughputs for each session according to the max-min flow control algorithm, such as the time delay in each queue (including service time) for a transmission line should not exceed T = 4 seconds.

Please Note: I don't need a program code for this. I need answers as numbers and equations.

Explanation / Answer

Algorithm time complexity is O(max_flow * E). If there is a augmenting path then we can run a loop. In worst case, we may add 1 unit flow in each iteration. So that the time complexity becomes O(max_flow * E).

For minimum flow: n (n-1)/2

Flow1:8+5+6=19

Flow2:10+5+6=21

Flow 3:10+5+9=24

So that the optimal path is flow1

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