Conventional Optimization Technique Based Methodology to Estimate Gap Acceptance Functions
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ORIGINAL ARTICLE
Conventional Optimization Technique Based Methodology to Estimate Gap Acceptance Functions Durgesh Vikram1 Received: 24 April 2019 / Accepted: 20 June 2020 © Springer Nature Switzerland AG 2020
Abstract The definition of a critical gap in literature supports that it not only varies from driver to driver but also for (over) rejected gaps by a driver. In this light, multinomial probit (MNP) models were proposed in the past as gap acceptance functions. There are few methodologies available in the literature to estimate these functions. These methodologies are either computationally expensive or involve sophisticated mathematics. This is possibly one of the reasons due to which MNP models are not explored extensively as a tool to model critical gaps. Further, estimation of such gap acceptance functions always leads to maximization of likelihood functions. This paper proposes a methodology based on a conventional optimization technique for the first time to estimate the parameters of a class of gap acceptance functions. It is also shown that the estimation results match with those from another method, namely CHOMP. The proposed method turns out to be a simple yet effective one. Keywords Gap acceptance function · Multinomial probit model · Optimization · Unsignalized intersection
Introduction Conflicting movements do arise at unsignalized intersections. A schematic of a typical T-intersection is presented in Fig. 1. The T-intersection is formed due to intersection of a major and a minor roads. At such an intersection there are many combination of movements from the two roads which conflict with each other. One such conflicting pair is shown in the figure using arrows. As often is the case that a major road movement (like East–West movement in Fig. 1) has priority over a minor road movement (like South-East movement in Fig. 1) whenever a conflict arises. Considering the description, whenever a vehicle belonging to South-East movement arrives at the intersection, and it needs to find a suitable gap between vehicles belonging to East-West movement to complete its maneuver. In this study, “gap” is always referred to the time interval between arrival times of vehicles from East-West movement at the intersection. Let T be the critical gap for a driver from SouthEast movement. As per the description of critical gap in * Durgesh Vikram [email protected] 1
Department of Civil Engineering, Birla Institute of Technology and Science Pilani, Pilani, Rajasthan 333031, India
literature (for example, see [9]), any gap less than T will be rejected by the driver, and this driver will accept the first gap greater than T. Interestingly, the matter of estimating critical gap is not yet settled, and researchers are still working on it (see [11, 17]). Further, gap acceptance function is the function that relates the duration of the gap to its probability of acceptance. It may also be noted that the literature (see [1, 2, 6]) discusses that the value of T varies from driver to driver; and, it also changes for th
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