Non-derivative algorithm design for efficient routing over unreliable stochastic networks

We study the question of routing for minimum average drop rate over unreliable servers that are susceptible to random buffer failures, which arises in unreliable data or manufacturing networks. Interestingly, we first reveal that the traditional Join-the-Shortest-Queue (JSQ) or optimal Randomized Splitting (RS) strategies are consistently outperformed by the Constant Splitting Rule (CSR) where the incoming traffic is split with a constant fraction towards the available servers. inding motivates us to obtain the optimal splitting fraction under CSR. However, the objective function to be minimized depends on the mean queue length of the servers, whose closed-form expression is not available and often intractable for general arrival and service processes. Thus, we use non-derivative methods to solve this optimization problem by approximately evaluating the objective value at each iteration. To that end, we explicitly characterize the approximation error by utilizing the regenerating nature of unreliable buffers. By adaptively controlling the precision of this approximation, we show that our proposed algorithm converges to an optimal splitting decision in the almost sure sense. Yet, previous works on non-derivative methods assume continuous differentiability of the objective function, which is not the case in our setup. We relax this strong assumption to the case when the objective function is locally Lipschitz continuous, which is another contribution of this paper.