Optimisation of stochastic networks with blocking: a functional-form approach

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

Performance of merging lines with uneven buffer capacity allocation: the effects of unreliability under different inventory-related costs

This simulation study investigates whether machine efficiency, mean time to failure (MTTF) and mean time to repair (MTTR) significantly affect the performance of uneven buffer capacity allocation patterns for merging lines. Also studied is the trade-off between increasing throughput via bigger buffers and their associated inventory-related costs, since previous studies have shown that higher overall buffer capacity and higher average inventory content result in higher throughput. Results suggest that an ascending buffer allocation pattern (concentrating buffer capacity towards the end of the line) produces higher throughput in shorter, more unreliable lines; whereas the balanced pattern shows better performance in longer, more reliable lines. Increasing average buffer capacity per station and/or having higher average buffer content was found to be more cost-effective in lines with lower machine inefficiency, shorter MTTF and MTTR, and longer lines. Results differed between reliable and unreliable lines since reliable lines were particularly penalised by buffer capacity investiment/maintenance costs due to a relatively low increase in throughput resulting from the addition of extra buffer capacity