Large-scale workflow placement in serverless computing using integer nonlinear programming

Large-scale workflow placement in serverless computing is primarily addressed by formulating the scheduling problem as an Integer Linear Programming (ILP) or Mixed Integer Linear Programming (MILP) optimization model, rather than nonlinear programming, to minimize completion time and monetary cost.

• HEFTLess is a key orchestration service that formulates the scheduling problem as a Binary Integer Linear Programming model, accounting for workflow constraints and compute continuum resource limitations.
• Due to the high computational resolution required for optimal ILP formulations, researchers often employ lightweight scheduling heuristics or Deep Reinforcement Learning (DRL) techniques, such as Dueling Double Deep Q-Networks (D3QN), to make real-time scheduling decisions in dynamic edge environments.
• Other approaches, like NEPTUNE, utilize MILP to strategically place latency-sensitive functions on edge nodes based on user proximity and GPU availability, while GenDoc offers approximation algorithms for dependent task placement with on-demand function configuration.

This paper addresses large-scale workflow placement in serverless edge computing, where user workflows are executed as collections of dependent tasks or functions across a heterogeneous pool of cloud servers and edge devices. The central problem is to decide where to place each workflow component so that the system can serve many workloads efficiently while respecting task dependencies, resource capacities, network conditions, and service-level constraints. Because serverless abstraction hides infrastructure management from users, the placement decision becomes especially important: it directly affects both the user’s monetary cost and the total time required to evaluate the workflow.

The key contribution is a formal integer nonlinear programming formulation for this placement problem. Integer variables model discrete placement decisions, such as assigning a task to a particular server or edge device, while nonlinear terms capture realistic dependencies among resource selection, execution time, communication latency, and pricing. This modeling approach is useful because workflow performance and cost in serverless edge systems are not simply linear functions of resource allocation; they depend on heterogeneous device capabilities, workload size, task ordering, and network topology. By expressing the problem as an INLP model, the paper makes the cost–latency tradeoff explicit and provides a structured basis for optimization-based placement.

The work matters because serverless edge computing is increasingly used for latency-sensitive and cost-sensitive applications, but large-scale placement across many devices is combinatorially difficult and highly sensitive to resource heterogeneity. A principled optimization framework can help operators and users balance monetary cost against workflow completion time, improve resource utilization, and support deadline-aware or budget-aware scheduling. Even if the formulation itself is not a complete scalable solver, it provides an important modeling foundation for designing heuristics, approximation methods, or specialized solvers for real-world serverless edge platforms.