Supplementary information for Efficient distributed edge computing for dependent delay-sensitive tasks in multi-operator multi-access networks

Article abstract

We study the problem of distributed computing in the multi-operator multi-access edge computing (MEC) network for dependent tasks. Every task comprises several sub-tasks which are executed based on logical precedence modelled as a directed acyclic graph. In the graph, each vertex is a sub-task, each edge – precedence constraint, such that a sub-task can only be started after all its preceding sub-tasks are completed. Tasks are executed by MEC servers with the assistance of nearby edge devices, so that the MEC network can be viewed as a distributed “primary-secondary node” system where each MEC server acts as a primary node (PN) deciding on sub-tasks assigned to its secondary nodes (SNs), i.e., nearby edge devices. The PN's decision problem is complex, as its SNs can be associated with other neighboring PNs. In this case, the available processing resources of SNs depend on the sub-task assignment decisions of all neighboring PNs. Since PNs are controlled by different operators, they do not coordinate their decisions, and each PN is uncertain about the sub-task assignments of its neighbors (and, thus, the available resources of its SNs). To address this problem, we propose a novel framework based on a graphical Bayesian game, where PNs play under uncertainty about their neighbors' decisions. We prove that the game has a perfect Bayesian equilibrium (PBE) yielding unique optimal values, and formulate new Bayesian reinforcement learning and Bayesian deep reinforcement learning algorithms enabling each PN to reach the PBE autonomously (without communicating with other PNs).

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