MDS Coded Task Offloading in Stochastic Wireless Edge Computing Networks

Coded computation has attracted great interests as a promising technique to cope with straggling computing nodes in mobile edge computing (MEC) networks. Contrary to the existing coded computation schemes developed with a fixed network topology, this paper studies a MDS coded computation for random networks. Specifically, we put forth maximum distance separable (MDS) coded task offloading and investigate its MDS coded computing gain by deriving the average successful retrieval probability with stochastic geometry in random wireless edge computing networks, where it encodes the original task into multiple equal and small sized MDS coded sub-tasks and offloads their subset to edge computing nodes for computation. We also identify a tradeoff between the latency in processing a sub-task at an edge node and the minimal number of edge nodes required to retrieve the original task output, according to the size of MDS coded sub-tasks. To efficiently control the tradeoff, we determine the desirable size of MDS coded sub-tasks in a semi-closed form to maximize the average successful retrieval probability for regime 1 and regime 2 networks, which correspond to the cases that communication latency is negligible compared to computation latency and that computation latency is negligible compared to communication latency, respectively, and develop an efficient algorithm with low search complexity for a general environment. Our numerical results reveal that the proposed scheme outperforms the other conventional task offloading schemes such as partial task offloading and replication task offloading in terms of average successful retrieval probability.