Deadline-Aware Task Offloading With Concurrency in Serverless Edge Computing

Serverless edge computing enables low-latency Internet of Things (IoT) services but faces scalability challenges due to complex concurrency and resource management. While existing approaches address function initialization and edge-cloud offloading, they often overlook the joint optimization of serverless concurrency and physical-layer resources, leading to potential service degradation and increased costs. To tackle this, we propose OPLA, a novel cross-layer framework for joint latency and concurrency optimization, designed to minimize end-to-end latency while optimizing concurrent serverless functions. OPLA models interactions between physical-layer resources (e.g., bandwidth, transmission power, offloading ratios) and application-layer concurrency decisions. The formulated problem is a highly non-convex mixed-integer nonlinear program (MINLP), which we prove to be at least NP-complete in certain cases. To approximate its optimal solution efficiently, we propose an iterative exploration-exploitation procedure (EEP). The exploration phase, which is embarrassingly parallelizable, balances solution quality and efficiency with single parameter tuning. The exploitation phase is just a simple successive convex approximation to OPLA. Moreover, we also develop a presolve-postsolve heuristic with deterministic rounding to ensure feasibility for OPLA. Numerical results demonstrate that EEP consistently achieves solutions within a 6% optimality gap relative to a global solver across a wide range of network scales and workloads, confirming its effectiveness and scalability for real-world serverless edge deployments.