Sepideh Pourazarm

Optimal Routing and Energy Allocation for Lifetime Maximization of Wireless Sensor Networks With Nonideal Batteries

An optimal control approach is used to solve the problem of routing in sensor networks where the goal is to maximize the networks lifetime. In our analysis, the energy sources (batteries) at nodes are not assumed to be “ideal” but rather behaving according to a dynamic energy consumption model, which captures the nonlinear behavior of actual batteries. We show that in a fixed topology case there exists an optimal policy consisting of time-invariant routing probabilities, which may be obtained by solving a set of relatively simple nonlinear programming (NLP) problems. We also show that this optimal policy is, under very mild conditions, robust with respect to the battery model used. Further, we consider a joint routing and initial energy allocation problem over the network nodes with the same network lifetime maximization objective. We prove that the solution to this problem is given by a policy that depletes all node energies at the same time and that the corresponding energy allocation and routing probabilities are obtained by solving an NLP problem. Numerical examples are included to illustrate the optimality of the time-invariant policy and its robustness with respect to the battery model used.

Energy-Aware Vehicle Routing in Networks with Charging Nodes

We study the problem of routing vehicles with energy constraints through a network where there are at least some charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations by determining routes as well as recharging amounts when the vehicles do not have adequate energy for the entire journey. For a single vehicle, we formulate a mixed-integer nonlinear programming (MINLP) problem and derive properties of the optimal solution allowing it to be decomposed into two simpler problems. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into subflows. We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.

Optimal routing of electric vehicles in networks with charging nodes: A dynamic programming approach

Motivated by the significant role of recharging in battery-powered vehicles, we study the routing problem for vehicles with limited energy through a network of charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We have studied the case of homogeneous charging nodes in [1] and generalized it to inhomogeneous charging nodes in [2] by formulating and solving a Mixed Integer Non-Linear Programming problem (MINLP) for a single-vehicle. In this paper, we solve the same problem using Dynamic Programming (DP), resulting in optimal solutions with lower computational complexity compared to [2]. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into “subflows” and propose a DP formulation. Our numerical results show that DP becomes prohibitively slow as the number of subflows increases. As in [1] and [2] we resort to an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss of accuracy.

Optimal routing of energy-aware vehicles in networks with inhomogeneous charging nodes

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dimensionality problem by exploiting properties of an optimal solution. We also obtain a Linear Programming (LP) formulation allowing us to decompose it into two simpler problems yielding near-optimal solutions. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into “subflows”. We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy.

The price of anarchy in transportation networks by estimating user cost functions from actual traffic data

We consider a large-scale road network in Eastern Massachusetts. Using real traffic data in the form of spatial average speeds and the flow capacity for each road segment of the network, we convert the speed data to flow data and estimate the origin-destination flow demand matrices for the network. Assuming that the observed traffic data correspond to user (Wardrop) equilibria for different times-of-the-day and days-of-the-week, we formulate appropriate inverse problems to recover the per-road cost (congestion) functions determining user route selection for each month and time-of-day period. Then, we formulate a system-optimum problem in order to find socially optimal flows for the network. We investigate the network performance, in terms of the total latency, under a user-optimal policy versus a system-optimal policy. The ratio of these two quantities is defined as the Price of Anarchy (POA) and quantifies the efficiency loss of selfish actions compared to socially optimal ones. Our findings contribute to efforts for a smarter and more efficient city.

Energy-Based Lifetime Maximization and Security of Wireless-Sensor Networks With General Nonideal Battery Models

We study the problem of maximizing the lifetime of a sensor network by means of routing and initial energy allocation over its nodes. We consider a general state space battery model and show that similar results to our previous work with simpler battery dynamics are still valid. In particular, we show that under this general dynamic battery model, there exists an optimal policy consisting of time-invariant routing probabilities in a fixed topology network and these can be obtained by solving a set of nonlinear programming (NLP) problems. Moreover, we show that the problem can be reformulated as a single NLP problem. In addition, we consider a joint routing and initial energy allocation problem over the network nodes with the same network lifetime maximization objective. We prove that the solution to this problem is given by a policy that depletes all node energies at the same time and that the corresponding energy allocation and routing probabilities are obtained by solving an NLP problem. Finally, we examine a networks performance under security threats, typified by faked-cost attacks, in terms of its lifetime and its normalized throughput. We illustrate how the optimal routing probabilities, as well as the network lifetime, are robust under such forms of routing attacks even though its normalized throughput can be significantly reduced.

Optimal Routing for Lifetime Maximization of Wireless-Sensor Networks With a Mobile Source Node

We study the problem of routing in sensor networks where the goal is to maximize the networks lifetime. Previous work has considered this problem for fixed-topology networks. Here, we add mobility to the source node, which requires a new definition of the network lifetime. In particular, we redefine lifetime to be the time until the source node depletes its energy. When the mobile nodes trajectory is unknown in advance, we formulate three versions of an optimal control problem aiming at this lifetime maximization. We show that in all cases, the solution can be reduced to a sequence of nonlinear programming roblems solved on line as the source-node trajectory evolves. When the mobile nodes trajectory is known in advance, we formulate an optimal control problem which, in this case, requires an explicit offline numerical solution. We include simulation examples to illustrate our results.

Lifetime maximization of wireless sensor networks with a mobile source node

We study the problem of routing in sensor networks where the goal is to maximize the networks lifetime. Previous work has considered this problem for fixed-topology networks. Here, we add mobility to the source node, which requires a new definition of the network lifetime. In particular, we redefine lifetime to be the time until the source node depletes its energy. When the mobile nodes trajectory is unknown in advance, we formulate three versions of an optimal control problem aiming at this lifetime maximization. We show that in all cases, the solution can be reduced to a sequence of Non-Linear Programming (NLP) problems solved on line as the source node trajectory evolves.

Optimal Routing of Energy-Aware Vehicles in Transportation Networks With Inhomogeneous Charging Nodes

We study the problem of routing for energy-aware battery-powered vehicles (BPVs) in networks with charging nodes. The objective is to minimize the total elapsed time, including travel and recharging time at charging stations, so that the vehicle reaches its destination without running out of energy. Relaxing the homogeneity of charging stations, and here, we investigate the routing problem for BPVs through a network of “inhomogeneous” charging nodes. We study two versions of the problem: the single-vehicle (user-centric) routing problem and the multiple-vehicle (system-centric) routing problem. For the former, we formulate a mixed-integer nonlinear programming (NLP)problem for obtaining an optimal path and charging policy simultaneously. We then reduce its computational complexity by decomposing it into two linear programming problems. For the latter, we use a similar approach by grouping vehicles into “subflows” and formulating the problem at a subflow-level with the inclusion of traffic congestion effects. We also propose an alternative NLP formulation obtaining near-optimal solutions with orders of magnitude reduction in the computation time. We have applied our optimal routing approach to a subnetwork of the eastern Massachusetts transportation network using actual traffic data provided by the Boston Region Metropolitan Planning Organization. Using these data, we estimate cost (congestion) functions and investigate the optimal solutions obtained under different charging station and energy-aware vehicle loads.

System-Centric Minimum-Time Paths for Battery-Powered Vehicles in Networks with Charging Nodes*

Abstract We study the routing problem for vehicle flows through a road network that includes both battery-powered Electric Vehicles (EVs) and Non-Electric Vehicles (NEVs). We seek to optimize a system-centric (as opposed to user-centric) objective aiming to minimize the total elapsed time for all vehicles to reach their destinations considering both traveling times and recharging times for EVs when the latter do not have adequate energy for the entire journey. Extending prior work where we considered only EVs entering the network, we formulate the problem by grouping all vehicles into a set of “subflows”and provide solutions based on both a Mixed Integer Non-Linear Programming (MINLP) approach and an alternative flow optimization problem. Since the problem size increases with the number of subflows, its proper selection is essential to render the problem manageable, thus reflecting a trade-off between proximity to optimality and computational effort needed to solve the problem. We propose a criterion and procedure leading to a “good” choice for the number of subflows.