SPARQ: An Optimization Framework for the Distribution of AI-Intensive Applications under Non-Linear Delay Constraints

Next-generation real-time compute-intensive applications, such as extended reality, multi-user gaming, and autonomous transportation, are increasingly composed of heterogeneous AI-intensive functions with diverse resource requirements and stringent latency constraints. While recent advances have enabled very efficient algorithms for joint service placement, routing, and resource allocation for increasingly complex applications, current models fail to capture the non-linear relationship between delay and resource usage that becomes especially relevant in AI-intensive workloads. In this paper, we extend the cloud network flow optimization framework to support queuing-delay-aware orchestration of distributed AI applications over edge-cloud infrastructures. We introduce two execution models, Guaranteed-Resource (GR) and Shared-Resource (SR), that more accurately capture how computation and communication delays emerge from system-level resource constraints. These models incorporate M/M/1 and M/G/1 queue dynamics to represent dedicated and shared resource usage, respectively. The resulting optimization problem is non-convex due to the non-linear delay terms. To overcome this, we develop SPARQ, an iterative approximation algorithm that decomposes the problem into two convex sub-problems, enabling joint optimization of service placement, routing, and resource allocation under nonlinear delay constraints. Simulation results demonstrate that the SPARQ not only offers a more faithful representation of system delays, but also substantially improves resource efficiency and the overall cost-delay tradeoff compared to existing state-of-the-art methods.