Throughput-Optimal Control of Distributed Computing Networks for Service DAGs

Executing service workflows with directed acyclic graph (DAG) dependencies over wireless distributed computing networks requires joint control of function placement, routing, and scheduling, together with synchronization of inputs from the same request at merge points. We study throughput-optimal control of these networks under stochastic request arrivals, time-varying wireless links, and interference constraints. We use a valid mapping abstraction that assigns each service function to a computation node and each DAG dependency to a routing path. Using this abstraction, we characterize the network capacity region to support service DAGs, and prove that synchronizing the packets of a request at merge points does not shrink the region. We develop Dynamic Computing Network Control for service DAGs (DCNC-DAG), a dynamic control policy that selects queue-aware valid mappings and schedules service DAG execution by nearest-to-origin (NTO) while enforcing input synchronization at merge points. With exact minimum-cost valid mappings, DCNC-DAG is throughput-optimal and ensures rate stability of the physical queues under bounded arrivals. These guarantees hold for any fixed finite interval between mapping updates, even when mapping decisions rely on boundedly stale queue length information. For larger service DAGs, we develop DCNC-DAG-H, which replaces exact mapping optimization with a queue-aware heuristic. Simulations show that DCNC-DAG supports $2.7\times$-$5.5\times$ the throughput of queue-blind baselines, while DCNC-DAG-H achieves up to $2.68\times$ those of the corresponding baselines on larger workflow and AI service DAGs.