Optimal sub-graph selection over coded networks with delay and limited-size buffering

The authors consider the problem of finding a minimum cost multicast sub-graph based on network coding, where delay values associated with each link, limited buffer-size of the intermediate nodes and link capacity variations over time are taken into account. The authors consider static multicast (where membership of the multicast group remains constant for the duration of the connection) in lossless wireline networks. For such networks, first the continuous-time (asynchronous packet transmissions) model is formulated. Subsequently, the discrete-time model for the synchronous packet transmissions scenario is derived. Then, by using an auxiliary time-expanded network, a decentralised algorithm in the presence of link delays, limited buffer-size and time-varying link capacity is proposed. The proposed algorithm when coupled with decentralised code construction schemes results in a fully decentralised approach for achieving minimum-cost in such multicast networks. Also, how adding buffering capability at intermediate nodes reduces the overall cost of the optimal sub-graph is discussed in this study. In addition, as will be shown, inclusion of buffering capacity at intermediate nodes makes it possible to find minimum multicast solution in scenarios that such solutions do not exist otherwise.