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 A -> B -> C -> D; Flow 2: A, F, C, D; Flow 3: E,F,C,G

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.

Explanation / Answer

Time Complexity: Time complexity of the above algorithm is O(max_flow * E). We run a loop while there is an augmenting path. In worst case, we may add 1 unit flow in every iteration. Therefore 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

Here the optimal path is flow1

Network throughput refers to the average data rate of successful data or message delivery over a specific communications link. Network throughput is measured in bits per second (bps). A common misconception on measuring network throughput is that measuring the time it takes to upload or download a large file is the maximum throughput of a network.

nitions

Throughput: As defined in the usual way, the time average

of the number of bits that can be transmitted by each node to

its destination is called the per-node throughput. The sum of

per-node throughput over all the nodes in a network is called

the throughput of the network.

Feasible Throughput: We say that a per-node throughput,

denoted by (n), is feasible if there exists a spatial and

temporal scheduling scheme that yields a per-node throughput

of (n) bits/sec.

Per-node Throughput Capacity: We say that the per-node

throughput capacity in the network ( [12]) is of order O(f(n))

bits per second if there is a deterministic constant 0 < c1 <

+ such that

lim inf

n+ Prob((n) = c1f(n) is feasible) < 1,

and is of order (f(n)) bits per second if there are determin-

istic constants 0 < c2 < c3 < + such that

lim inf

n+ Prob((n) = c2f(n) is feasible)=1,

lim inf

n+ Prob((n) = c3f(n) is feasible) < 1.

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