# Optimising capacity allocation in networks of stochastic loss systems: A functional-form approach

## TL;DR

This paper presents a hybrid analytical-simulation method for efficiently optimizing capacity allocation in complex networks of stochastic loss systems, balancing congestion mitigation and cost.

## Contribution

It introduces a novel iterative algorithm that combines analytical approximations with minimal simulation, significantly reducing computational effort while achieving near-optimal solutions.

## Key findings

- Achieves near-optimal solutions comparable to advanced optimization methods.
- Requires substantially less computational time than traditional simulation-based approaches.
- Effective for complex networks with high computational efficiency.

## Abstract

Motivated by a wide variety of applications, this paper introduces a general class of networks of stochastic loss systems in which congestion renders lost revenue due to customers or jobs being permanently removed from the system. We seek to balance the trade-off between mitigating congestion by increasing service capacity and maintaining low costs for the service capacity provided. Given the lack of analytical results and the computational burden of simulation-based methods, we propose a hybrid functional-form approach for finding the optimal resource allocation in general networks of stochastic loss systems that combines the speed of an analytical approach with the accuracy of simulation-based optimisation. The key insight is a core iterative algorithm that replaces the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a simple simulation run. Extensive computational experiments on complex networks show that our approach renders near-optimal solutions with objective function values that are comparable to those obtained using stochastic approximation, surrogate optimisation and Bayesian optimisation methods while requiring significantly less computational effort.