  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.
