Developing an Optimal Sensing Strategy for Accurate Freeway Travel Time Estimation and Traveler Information

Accurate freeway travel time estimates are critical for transportation management and traveler information—both infrastructure-based and in-vehicle. Infrastructure managers are interested in estimating optimal freeway sensor density for new construction and retrofits. This paper describes a concept developed from first principles of traffic flow for establishing optimal sensor density based on the magnitude of underand overprediction of travel time during shock passages when using the midpoint method. A suggested aggregate measure developed from vehicle hours traveled (VHT) is described for a reasonable range of detector densities. Extensions of the method to account for both recurring and nonrecurring congestion are included. Finally some suggestions for future research are described. INTRODUCTION Accurate travel time estimation is important for transportation situational awareness and management. In the U.S., freeways account for 3% of the national highway mileage, but accommodate more than 30% of the vehicle-miles traveled (VMT). The alleviation of congestion on urban freeways is receiving heightened attention, and transportation agencies are applying improved management strategies to reduce congestion and improve travel time reliability. Even to the extent that congestion cannot be reduced markedly, there is benefit in accurate predictions of travel time that enable better informed traveler decisions. Incident management and traveler information systems can be implemented at relatively low cost. However, such systems rely upon accurate measurement of traffic parameters such as flow, speed, travel time, and delay. Usually these data are measured by fixed sensors (loop detectors, video cameras, radar sensors, etc.) or by mobile data sources such as automatic vehicle identification (AVI) toll tags or automatic vehicle location (AVL) probe vehicles and in the future by such technologies as vehicular ad hoc networks. In order to answer the question “how much detection is needed,” this paper focuses on the common use of fixed sensors (such as loop detectors) as a basis for formulating an optimal detector placement strategy. Figure 1 illustrates a hypothetical space-time (x-t) plane of length λ and time interval t1. A set of vehicle trajectories is shown (in grey) with that of vehicle i being highlighted in black. If equipped with AVL or any other data logging system, vehicle i’s trajectory could be plotted and all information necessary to completely describe its path would be known, including its actual travel time and its speed (slope of trajectory) at any point. If one assumes a free flow speed, the free flow travel time can be computed and the delay (actual minus free flow travel time) for vehicle i is known. In practice it is more common to use sensors at fixed points (such as point x1) to measure speed and subsequently extrapolate that speed over a segment. In Figure 1 one can observe how a speed measured at x1 is TR x1 Measured Speed i Actual Travel Time tf = Free Flow Travel Time Free Flow Speed vf Extrapolated Travel Time λ = S eg m en t L en gt h x t Extrapolated Speed Overprediction t1 = Time Interval Delay FIGURE 1 Segment travel time features. B 2008 Annual Meeting CD-ROM Paper revised from original submittal. Bertini and Lovell 3 extrapolated over a segment of length λ resulting in the calculation of the extrapolated travel time. As shown, the estimate does not perfectly match the actual travel time. The magnitude of this difference, as a function of detector density, is the topic of interest in this paper. Ignoring sensing errors, the passage of a shock represents the “worst case scenario” for travel time prediction, so the methods presented in this paper can be interpreted as a form of robust decision analysis about sensor spacing. TRAVEL TIME ESTIMATION FRAMEWORK A fundamental traffic flow relation is assumed, as shown in Figure 2. In particular, the triangular shape is used – this is common in the literature when broad questions need to be addressed with a minimum of complications. A congested state C (flow qc and speed vc) and uncongested states A, B, and D (flows qA, qB, qD, speed vf) are shown. Below the flow-density (q-k) diagram is an x-t plane showing a bottleneck (either recurrent or nonrecurrent) at location bn. We will assume, for the sake of simplicity, that the bottleneck state is binary; i.e., it is either active, with some reduced capacity captured by state C, or it is inactive, in which case the nominal roadway capacity can be permitted. Following the rules of standard first-order macroscopic traffic dynamics, and assuming the nominal traffic state was A, there is a transition between uncongested state A and congested state C, defined by a shock of velocity vAC. Figure 2 shows that for an arbitrary highway segment (separated by the two dashed lines) transition AC is bounded by a rectangle as the shock passes. If this were an active bottleneck that was deactivated at time tdeact, then transition CD would occur, from congested state C to uncongested state D, marked by a backward-moving recovery wave of velocity vCD. Transition DA (the return to nominal conditions) is separated by a forward-moving recovery wave of velocity vf. We do not assume that these three transitions always occur in this configuration or order, and the computations later in the paper assess each type of state transition separately. The overall pattern of Figure 2 is simply convenient because all of the interesting possible transitions are shown.