Optimisation of stochastic networks with blocking: a functional-form approach
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Many stochastic networks encountered in practice exhibit some kind of blocking behaviour, where traffic is lost due to congestion. Examples include call dropping in cellular networks, difficulties with task migration in mobile cloud computing, and depleted stock points in spare parts supply chains. Blocking can be mitigated by increasing service capacity at congested stations, but purchasing these additional resources may be costly. Thus, finding the right resource allocation requires striking a careful balance between blocking and costs, a problem which is further complicated by the stochastic nature of the network. Although certain classes of queueing networks allow for a closed form optimisation problem to be formulated and solved, such results only exist for highly stylised networks, and in particularly do not allow for blocking. Another class of current solution methods is simulation-based optimisation, where the resource allocation is evaluated and updated using simulation. Although this works well for small instances, the associated computational costs are prohibitive for networks of real-life size. In this paper we propose a hybrid functional-form based approach that combines the strengths of the analytical and simulation-based approaches into a novel iterative algorithm. We do this by locally approximating the objective function through a functional form calibrated using simulation. In each iteration step we choose a new resource allocation based on this local approximation, which in turn gives rise to a new approximation. We implement this algorithm for a range of functional forms, computationally determine which work best, and provide an alternative formulation of the algorithm that does not rely on numerical solvers. Extensive experiments show that our functional-form approach has significantly lower computational costs compared to stochastic approximation.
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