Response-Time-Optimised Service Deployment: MILP Formulations of Piece-wise Linear Functions Approximating Non-linear Bivariate Mixed-integer Functions

TL;DR

This paper develops and compares MILP formulations to optimize resource deployment and user assignment in wide-area networks, reducing response times by approximating non-linear functions and outperforming heuristics.

Contribution

Introduces five linear approximations and adapts a heuristic to solve a complex non-linear resource allocation problem in networking.

Findings

Best MILP formulation outperforms heuristic in time and quality

Resource distribution significantly impacts response times

Proposed models applicable to broader optimization problems

Abstract

A current trend in networking and cloud computing is to provide compute resources at widely dispersed places; this is exemplified by developments such as Network Function Virtualisation. This paves the way for wide-area service deployments with improved service quality: e.g, a nearby server can reduce the user-perceived response times. But always using the nearest server can be a bad decision if that server is already highly utilised. This paper formalises the two related problems of allocating resources at different locations and assigning users to them with the goal of minimising the response times for a given number of resources to use -- a non-linear capacitated facility location problem with integrated queuing systems. To efficiently handle the non-linearity, we introduce five linear problem approximations and adapt the currently best heuristic for a similar problem to our scenario. All six approaches are compared in experiments for solution quality and solving time. Surprisingly, our best optimisation formulation outperforms the heuristic in both time and quality. Additionally, we evaluate the influence ot resource distributions in the network on the response time: Cut by half for some configurations. The presented formulations are applicable to a broader optimisation domain.