Game-theoretic routing of GPS-assisted vehicles for energy efficiency

Abstract

Congestion on roads and highways is an issue that leads to reductions in the energy-efficiency of travel. Current GPS navigation devices include features which provide turn-byturn directions to vehicles based on real-time traffic conditions, and these features provide an opportunity to improve average fuel consumption. Routing strategies in these devices optimize individual travel times, but theoretical (e.g., Braess's paradox) and empirical results show that this can actually increase congestion and average travel times. We model traffic routing in the game-theoretic framework of Stackelberg games, which is a simplification of the true information patterns, and then use this model to provide an algorithm for turn-by-turn directions. One advantage of our algorithm is that it can be easily incorporated into existing GPS devices by modifying the traffic information sent to them. Our framework is used to qualitatively study the effectiveness of traffic routing on a specific road network topology. If roughly 60% of users follow GPS directions implementing our strategy, then the average delay will be close to the optimal average delay for the road network. This poses social and technological challenges for reduction in congestion through routing. The situation is not hopeless though, because our qualitative results indicate that having a small percentage of compliant users may still lead to large reductions in congestion.

Duality Approach to Bilevel Programs with a Convex Lower Level

“…A common class of routing games consists of a directed graph with multiple edges between vertices, convex delay functions for each edge, and a listing of inflows and outflows of traffic [1]- [5]. The Stackelberg strategy is a situation where a leader controls an α fraction of the flow, the remaining flow is routed according to a Nash equilibrium given the flow of the leader, and the leader routes their flow to minimize the average delay in the network.…”

Statistical Watermarking for Networked Control Systems

“…Next observe the upper block triangle of (19) is correct by construction of Q I,J,k i,j and by definition of the e i , and so we only have to prove that the lower-right block is correct. In particular, note that E((C j δ i,n − z n )(C j δ i,n − z n ) T ) = E((C j δ i,n )(C j δ i,n ) T )+Σ Z,I since z i,n is independent of δ i,n by (11).…”

“…This implies that we have that as-lim n E((C j δ i,n − z n )(C j δ i,n − z n ) T ) = C j D i C T j + Σ Z,I . This result means that asymptotically the summation S i,j = 1 n+ n+1 ψ n,i,j ψ T n,i,j with ≥ (m i +q i ) has a Wishart distribution with degrees of freedom and a scale matrix that matches (19), and we use this to define a statistical test. In particular, we check if the negative log-likelihood…”

Finding Significant Stress Episodes in a Discontinuous Time Series of Rapidly Varying Mobile Sensor Data

“…Another example is [53] that proposed a system where earpieces (to monitor chewing and swallowing), augmented-reality glasses (for capturing food consumed) and a physiological sensor (for heart rate) are connected to a mobile-phone application that processes the data and gives feedback to the user. Sensor-triggered JITIs have also been proposed for preventive maintenance of a plant (see a review in [11]) and for GPS-based vehicle navigation [2, 4]. But, none of these methods can be used directly to mine the time series of stress to find significant stress episodes.…”