Many stochastic networks encountered in practice exhibit some kind of blockingbehaviour, 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.
This paper introduces a class of stochastic networks with blocking, motivated by applications arising in cellular network planning, mobile cloud computing, and spare parts supply chains. Blocking results in lost revenue due to customers or jobs being permanently removed from the system. We are interested in striking a balance between mitigating blocking by increasing service capacity, and maintaining low costs for service capacity. This problem is further complicated by the stochastic nature of the system. Owing to the complexity of the system there are no analytical results available that formulate and solve the relevant optimization problem in closed form. Traditional simulation-based methods may work well for small instances, but the associated computational costs are prohibitive for networks of realistic size. We propose a hybrid functional-form based approach for finding the optimal resource allocation, combining the speed of an analytical approach with the accuracy of simulation-based optimisation. The key insight is to replace the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a single simulation run. We develop two implementations of this approach and conduct extensive computational experiments on complex examples to show that it is capable of substantially improving system performance. We also provide evidence that our approach has substantially lower computational costs compared to stochastic approximation.
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Many stochastic networks encountered in practice exhibit some kind of blockingbehaviour, where traffic is lost due to congestion. Examples include call dropping in cellular networks, difficulties with task migration in
This paper introduces a class of stochastic networks with blocking, motivated by applications arising in cellular network planning,
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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
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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
system. Owing to the complexity of the system there are no analytical results available that formulate and solve the relevant optimization problem in closed form. Traditional
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that combines the strengths of the analytical and
for finding the optimal resource allocation, combining the speed of an analytical approach with the accuracy of
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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
optimisation. The key insight is to replace the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a single simulation run. We develop two implementations of this approach and conduct extensive computational experiments on complex examples to show that it is capable of substantially improving system performance. We also provide evidence that our approach has substantially