Dynamic Programming-based Pedestrian Hotspot Identification Approach

Network screening techniques are widely used by state agencies to identify locations with high collision concentration, also referred to as hotspots. However, most of the research in this regard has focused on identifying highway segments that are of concern to automobile collisions. A major difference between pedestrian and automobile hotspots is that pedestrian-based conflicts are more likely to arise in localized regions, such as near intersections, mid-blocks, and/or other crossings, as opposed to along long stretches of roadway. Hence, in order to address this issue, a dynamic programming-based hotspot identification approach is proposed which provides efficient hotspot definitions for pedestrian crashes. The proposed approach is compared with the sliding window method and the results reveal that the dynamic programming method generates more hotspots with a higher number of crashes, while covering fewer miles. TRB 2015 Annual Meeting Paper revised from original submittal. Medury and Grembek 2 INTRODUCTION Pedestrians, along with bicyclists, represent some of the most vulnerable users of the transportation system. In a comparison of all the crashes to have taken place in the state of California between 2005 and 2009, Grembek (1) found that pedestrians were 53 times more likely to get injured in a crash with a passenger vehicle, than the travelers in the vehicle itself. The relative vulnerability of pedestrians in traffic conflicts becomes even more worrisome given the recent trends in pedestrian fatalities. Between 2009 and 2012, the relative share, as well as the overall number, of pedestrian fatalities in the United States has consistently increased, even as the total number of all traffic fatalities exhibited a non-monotonic trend in the same time period (2). Such a trend is disconcerting as it seems to indicate that the safety concerns of pedestrians are not being adequately addressed. One of the ways to suggest potential safety improvements to the transportation infrastructure is to identify the locations where pedestrians are most at-risk. However, individual crashes can be spatially dispersed due to natural variation in crash locations. Hence, in order to identify potentially hazardous segments of the road network, it is common practice, especially in state departments for the purpose of on-site investigation, to aggregate individual crashes to identify “hotspots” or high collisions concentration locations. The highway traffic safety literature discusses a wide variety of frameworks to identify hotspots, also referred to as network screening techniques. The objective of network screening, especially in the context of highway segments, is to identify the appropriate start and end points for hotspots along a road segment containing homogeneous traffic and similar built environment attributes. A popular network screening technique among transportation agencies is the sliding window (SW) approach (3, 4, 5, 6), wherein a window of fixed length is moved along the road network in small increments until a pre-specified hotspot selection criteria, such as a critical crash count/rate threshold, is satisfied. The peak searching (PS) method involves dividing entire network into a finite number of windows of fixed length, and testing for the statistical significance of the crash count/rate within these segments by estimating the coefficient of variation (3). Chung et al. (7) developed a continuous risk profile (CRP) method to empirically determine hotspot segments based on collision data. Herein, a risk profile is generated for the entire road segment by computing a weighted moving average of collisions taking place around each location of the road segment. The resulting smoothened risk profile is compared against a baseline risk threshold, and the regions of the curve lying above this threshold are identified as the hotspots. However, since the aforementioned techniques were primarily developed for automobile collision-based hotspots, their efficacy vis-a-vis identifying pedestrian hotspots has not been investigated in the literature yet. A major difference between pedestrian and automobile hotspots is that pedestrian-based conflicts are more likely to arise in localized regions, such as near intersections, mid-blocks, and/or other crossings, as opposed to along long stretches of roadway. For instance, if a mid-block or an intersection is an at-risk location for pedestrians, it is unlikely that a moving segment of 0.2 miles can provide a meaningful hotspot specification under such a scenario. As a result, pedestrian hotspots are more likely to be shorter and more dense in nature. Hence, the objective of this paper is to develop a new network screening approach which can provide denser hotspot definitions for pedestrian crashes. Prior to providing a detailed description of the proposed network screening method, the next section first discusses the sliding window approach, so as to highlight the limitation of this approach for pedestrians, and consequently, better inform the formulation of the proposed framework. TRB 2015 Annual Meeting Paper revised from original submittal. Medury and Grembek 3 SLIDING WINDOW APPROACH The first step towards hotspot identification is to select the input parameters which define a hotspot. In the sliding window method, there are two parameters of interest which are required to be defined by the user: the hotspot window length and the minimum number of crashes per hotspot. The hotspot window length is a fixed road segment length which is used to aggregate pedestrian crashes. It is assumed that The hotspot window will have homogeneous pedestrian and road infrastructure elements so that all the crashes covered by that road segment can be expected to have occurred under similar conditions. The minimum number of crashes per hotspot defines a critical threshold which determines whether a road segment should be a hotspot or not. While frequency-based identification of hotspots does not account for the pedestrian volumes at a location, crash rates associated with any given road segment were harder to quantify since pedestrian exposure data was not available for the entire state highway system. Once the inputs are defined, the sliding window method works as follows: a window of fixed length is moved across the entire road network so as to identify locations which meet the critical crash threshold criterion. In a slightly modified version of the traditional implementation of the sliding window approach, the window can also be moved in a manner that the starting location of a potential hotspot window is always a crash. The rationale for such an implementation is that a pedestrian hotspot should be as dense as possible. Hence any empty space, either at the start or at the end of a hotspot is excessive. Once a hotspot satisfying critical crash threshold is identified, the search for other hotspots continues from the next available crash that does not overlap with any hotspot. The limitations of the sliding window approach, as described above, are two-fold. Firstly, owing to the fixed window length assumption, even if the hotspot is forced to be begin with a crash, it cannot be guaranteed that the hotspot definition will end with a crash as well. Consequently, there may be an arbitrary length of road segment at the end of the hotspot definition which does not cover any collision. The second limitation of the sliding window method, which has not been well documented in the literature, is that it selects hotspots on a first-come-first-serve basis. In other words, the method selects the first segment along the highway which matches the selection criteria. Such an assumption may impact the selection of more/better hotspots further downstream of that location. For instance, an overlapping hotspot which can be observed after sliding the window slightly further downstream may include more crashes. In order to address these issues, it is important to relax the fixed window length assumption, and subsequently identify an overarching objective to guide the selection of hotspots. In the subsequent section, a dynamic programming-based algorithm is proposed which relaxes the assumption of a fixed window length, and instead interprets it as the maximum possible window length. DYNAMIC PROGRAMMING Dynamic programming (DP) is a decision-making framework used to solve problems involving multiple, sequential sub-problems (8). It involves generating and storing the solutions of each intermittent sub-problem before identifying the overall optimal solution. In the case of the sliding window method, the sub-problems are generated when a window of fixed length is moved from one crash to another as a starting point. In proposing a dynamic programming-based hotspot identification algorithm, it is necessary to define an overarching goal for hotspot selection. In this paper, the objective of the proposed hotspot identification approach is defined to maximize the total number of crashes covered by the TRB 2015 Annual Meeting Paper revised from original submittal. Medury and Grembek 4 hotspots which are eventually chosen based on the minimum number of crashes per hotspot criterion. In addition, the proposed approach also relaxes the fixed window length assumption, and instead imposes a constraint that the size of each hotspot should be no bigger than the maximum window length prescribed by the user. An outcome of relaxing the fixed hotspot length assumption is that a hotspot can begin and end with a crash. In other words, the crashes can now be defined to be as dense as possible. The dynamic programming approach breaks down the task of optimally identifying the hotspots across the entire road network into smaller sub-problems of identifying whether a crash i (at postmile di) should form an end point of a hotspot or not. In terms of the mathematical notation, let the maximum hotspot window length be defined as w, and let the