Efficient Distributed Edge Computing for Dependent Delay-Sensitive Tasks in Multi-Operator Multi-Access Networks

We study the problem of distributed computing in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multi-operator multi-access edge computing</i> (MEC) network for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dependent tasks</i>. Every task comprises several <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub-tasks</i> which are executed based on logical precedence modelled as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">directed acyclic graph</i>. 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributed</i> “<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">primary-secondary node</i>” system where each MEC server acts as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">primary node</i> (PN) deciding on sub-tasks assigned to its <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">secondary nodes</i> (SNs), i.e., nearby edge devices. The PN's decision problem is complex, as its SNs can be associated with other <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">neighboring</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">graphical Bayesian game</i>, where PNs play under uncertainty about their neighbors’ decisions. We prove that the game has a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">perfect Bayesian equilibrium</i> (PBE) yielding <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unique optimal values</i>, and formulate new <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Bayesian reinforcement learning</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Bayesian deep reinforcement learning</i> algorithms enabling each PN to reach the PBE autonomously (without communicating with other PNs).