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

A current trend in networking and cloud computing is to provide compute resources at widely distributed sites; 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. user-perceived response times can be reduced by offering services at nearby sites. But always assigning users to the nearest site can be a bad decision if this site is already highly utilised. This paper formalises two related decisions of allocating compute resources at different sites and assigning users to them with the goal of minimising the response times while the total number of resources to be allocated is limited – a non-linear capacitated Facility Location Problem with integrated queuing systems. To efficiently handle its non-linearity, we introduce five linear problem linearisations and adapt the currently best heuristic for a similar scenario 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 of distributions of available compute resources in the network on the response time: The time was halved for some configurations. The presented formulation techniques for our problem linearisations are applicable to a broader optimisation domain.