On the Complexity of Reachability Properties in Serverless Function Scheduling

TL;DR

This paper investigates the computational complexity of verifying reachability properties in serverless function scheduling, revealing that affinity-aware policies significantly increase the complexity to PSpace, impacting verification feasibility.

Contribution

It introduces a formal semantics for an affinity-aware serverless scheduling language and analyzes the complexity of verifying reachability properties within it.

Findings

Reachability checking without affinity is linear in complexity.

Affinity-aware policies make reachability verification PSpace-complete.

Formal semantics for aAPP facilitate complexity analysis.

Abstract

Functions-as-a-Service (FaaS) is a Serverless Cloud paradigm where a platform manages the execution scheduling (e.g., resource allocation, runtime environments) of stateless functions. Recent developments demonstrate the benefits of using domain-specific languages to express per-function scheduling policies, e.g., enforcing the allocation of functions on nodes that enjoy low data-access latencies thanks to proximity and connection pooling. We present aAPP, an affinity-aware extension of a platform-agnostic function scheduling language. We formalise its scheduling semantics and then study the complexity of statically checking reachability properties, e.g., useful to verify that trusted and untrusted functions cannot be co-located. Analysing different fragments of aAPP, we show that checking reachability of policies without affinity has linear complexity, while affinity makes the problem PSpace.