Abstract
Minimum cost of multicast is the process of finding the node transmission cost such that the total cost of bandwidth used for sending messages from source to any destination nodes is minimized. The Network Coding Algorithm(NCA) was developed using linear programming framework by considering packets delay as the only key performance metrics. This research work is based on Shannon Hartley channel capacity theorem aimed at interpreting the cost of bandwidth within the channel and this was achieved by considering more performance metrics that affect the channel. Loss and delay of packetare collectively considered and later delay, loss and rejection packet are also considered on the Network Coding Algorithm. The problem was formulated as optimization problem using mixed integer linear programming problem. Simulation results showed that the average cost of bandwidth decrease as more performance metrics are collectively considered. When two performance metrics of delay and loss are considered collectively, there was a reduction in the average cost of bandwidth used during multicast by 27%, 28.7%, 29.5%, 20.9% 18.5%, 23.8%, 21.6% and 20.9% for 20, 30, 40, 50, 60 and 70 randomly generated nodes multicasting to groups of receivers when compared with the benchmark algorithm of delay only. Similarly, considering three performance metrics (delay, loss and rejection) achieved a reduction in the average cost of bandwidth by 37.07%, 37.6%, 41.15, 29%, 30% and 35.3% for 20, 30, 40, 50, 60 and 70 randomly generated nodes multicasting to various groups of receivers as compared with benchmark algorithm. Equally, results also showed that the average cost of bandwidth for NCA with three performances parameters decreases for 12.7%, 13.6%, 16.6%, 11.1%, 16.3% and 15.1% for all the number of randomly generated nodes as compared to a situation when two performance metrics are considered. From the results obtained, it can be observed that the cost of bandwidth with 40 randomly generated nodes recorded the highest decrease in the average cost of bandwidth because the cost of multicast for NCA, INCA with two and three performance metrics tends to be linear and increase as the number of receivers increases.From these results, it could be concluded that the more performance metrics considered in the NCA, the better the true picture of the channel is represented. When interpreting the cost of bandwidth using Shannon-Hartley channel capacity theorem, the study established that the cost of bandwidth within the channel was under estimated as more performance metrics are considered.
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