Stochastic decomposition (SD) has been a computationally effective approach to solve large-scale stochastic programming (SP) problems arising in practical applications. By using incremental sampling, this approach is designed to discover an appropriate sample size for a given SP instance, thus precluding the need for either scenario reduction or arbitrary sample sizes to create sample average approximations (SAA). When compared with the solutions obtained using the SAA procedure, SD provides solutions of similar quality in far less computational time using ordinarily available computational resources. However, previous versions of SD were not applicable to problems with randomness in second-stage cost coefficients. In this paper, we extend its capabilities by relaxing this assumption on cost coefficients in the second stage. In addition to the algorithmic enhancements necessary to achieve this, we also present the details of implementing these extensions, which preserve the computational edge of SD. Finally, we illustrate the computational results obtained from the latest implementation of SD on a variety of test instances generated for problems from the literature. We compare these results with those obtained from the regularized L-shaped method applied to the SAA function of these problems with different sample sizes.

We formulate and solve the problem of optimal channel coding and flow-rate control for serving deadline-constrained traffic with average delivery ratio requirements (typical of multimedia streaming and interactive real-time applications) over time-varying channels. To that end, we first characterize the largest set of arrival processes (rather than rates) whose deadline and delivery ratio requirements can be satisfied. Then, we propose a dynamic (channel) coding algorithm that provably satisfies the requirements of any arrival process in this region. This optimal dynamic algorithm evolves through simple iterations to utilize a combination of pricing and finite-horizon dynamic programming operations. Next, we proposed two low-complexity approximations of the algorithm that has provable performance. We also extend the setup to allow for a flow controller that adjusts the incoming flow rates to satisfy their delivery ratio constraints when the arrival process is unknown but controllable. We propose a joint dynamic coding and a rate control algorithm to solve this problem, and prove its stability under the stochastic system operation. We also apply these general results to an important wireless down-link broadcast scenario with and without random network coding capabilities. Our theoretical work is supported by extensive numerical studies, which also reveal that our dynamic coding strategy outperforms any static coding strategy by opportunistically exploiting the statistical variations in the arrival and channel processes.

We study the problem of optimal dynamic coding and rate-control for broadcasting deadline-constrained traffic with average delivery ratio constraints over time-varying wireless channels. In particular, we propose and analyze a novel policy that utilizes a combination of pricing and finite-horizon dynamic programming strategies to jointly optimize the operation of the following two components: (i) a dynamic rate allocation policy, which manages the incoming traffic flow rates so as to maximize their weighted sum; (ii) and a dynamic coding window selection policy, which satisfies the flows' individual delivery ratio requirements. Our heuristic fluid analysis of the resulting stochastic network operation indicates that our joint policy maximizes the weighted sum of the deadline-constrained flow throughput subject to heterogeneous delivery ratio requirements imposed on them. We also apply these general results to an important cellular downlink scenario with and without network coding capabilities to study its behavior under various conditions. Our simulations reveal that the dynamic coding strategy outperforms the optimal static coding strategy by opportunistically exploiting the statistical variations in the arrival and channel processes.