Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.Comment: 10 pages, 2 figures, submitted to ECC 201

Comparison between Static and Dynamic Modeling Approaches for Heterogeneous Cellular Networks

In order to accommodate growing traffic demands, next generation cellular networks must become highly heterogeneous to achieve capacity gains. Heterogeneous cellular networks composed of macro base stations and low-power base stations of different types are able to improve spectral efficiency per unit area, and to eliminate coverage holes. In such networks, intelligent user association and resource allocation schemes are needed to achieve gains in performance. We focus on heterogeneous cellular networks that consist of macro and pico BSs, and study the interplay between user association and resource allocation using two modeling approaches, namely a static modeling approach and a dynamic modeling approach. Our first study focuses on modeling heterogeneous cellular networks with a static approach. We propose a unified static framework to study the interplay of user association and resource allocation under a well-defined set of assumptions. This framework allows us to compare the performance of three resource allocation strategies: partially Shared deployment, orthogonal deployment, and co-channel deployment when the user association is optimized. We have formulated joint optimization problems that are non-linear integer programs which are NP-hard. We have, therefore, developed techniques to obtain upper bounds on the system's performance. We also propose a simple association rule that performs much better than all existing user association rules. We have used these upper bounds as benchmarks to provide many engineering insights, and to quantify how well different combinations of user association rules and resource allocation schemes perform. Our second study focuses on modeling heterogeneous cellular networks with a dynamic modeling approach. We propose a unified framework to study the interplay of user association, resource allocation, user arrival, and delay. We select three different performance metrics: the highest possible arrival rate, the network average delay, and the delay-constrained maximum throughput, and formulate three different optimal user association problems to optimize our performance metrics. The proposed problems are non-linear integer programs which are hard to solve efficiently. We have developed numerical techniques to compute either the exact solutions or tight lower bounds to these problems. We have used these lower bounds and the exact solutions as benchmarks to provide many engineering insights, and to quantify how well different user association rules and resource allocation schemes perform. Finally, using our numerical results, we compare the static and dynamic modeling approaches to study the robustness of our results. Our numerical results show that engineering insights on the resource allocation schemes drawn out the static study are valid in a dynamic context, and vice versa. However, the engineering insights on user association rules drawn out of the static study are not always consistent with the insights drawn out of the dynamic study.4 month

Data-Driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method. Comment: 10 pages, 2 figures, submitted to ECC 201