Optimal Paths in Large Deviations of Symmetric Reflected Brownian Motion in the Octant

We study the variational problem that arises from consideration of large deviations for semimartingale reflected Brownian motion (SRBM) in the positive octant. Due to the difficulty of the general problem, we consider the case in which the SRBM has rotationally symmetric parameters. In this case, we are able to obtain conditions under which the optimal solutions to the variational problem are paths that are gradual (moving through faces of strictly increasing dimension) or that spiral around the boundary of the octant. Furthermore, these results allow us to provide an example for which it can be verified that a spiral path is optimal. For rotationally symmetric SRBM's, our results facilitate the simplification of computational methods for determining optimal solutions to variational problems and give insight into large deviations behavior of these processes

A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane

We present a stochastic programming model for informing the deployment of temporary flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.Comment: 35 pages, 12 figure

Relay-Assisted User Scheduling in Wireless Networks with Hybrid-ARQ

This paper studies the problem of relay-assisted user scheduling for downlink wireless transmission. The base station or access point employs hybrid automatic-repeat-request (HARQ) with the assistance of a set of fixed relays to serve a set of mobile users. By minimizing a cost function of the queue lengths at the base station and the number of retransmissions of the head-of-line packet for each user, the base station can schedule an appropriate user in each time slot and an appropriate transmitter to serve it. It is shown that a priority-index policy is optimal for a linear cost function with packets arriving according to a Poisson process and for an increasing convex cost function where packets must be drained from the queues at the base station.Comment: 14 pages, 5 figures, submitted to the IEEE Transactions on Vehicular Technology in October 2008, revised in March 2009 and May 200

Two-stage models for flood mitigation of electrical substations

We compare stochastic programming and robust optimization decision models for informing the deployment of temporary flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce novel adaptations of the DC and LPAC power flow approximation models that feature relatively complete recourse by way of a blackout indicator variable and relaxed model of power generation. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful whereas the choice of power flow model is of little to no consequence