Modelling Crashes as Self-Exciting Point Process: A Study in Dhaka Metropolitan Area

Abstract

The thesis pertains to investigating whether the crashes occurring within the Dhaka Metropolitan Area exhibit properties of self-excitement and clustering. The motivation behind the study stems from the fact that a crash incites congestion in the traffic network, which increases the odds of more crashes in the system. A univariate exponentially decaying model following Hawkes Process is developed for the study of the crashes with four parameters: background intensity ?, parameter ? denoting an increase in crash intensity once a crash takes place, intensity decay rate ?, and the time of influence of a crash on the system ?. Using RStudio, the Most Likely Estimates of the parameters are determined, which are then used to compute the Goodness of Fit of the model along with the Stationary Condition, which gives an idea about the safety of the traffic network in the long run in terms of crash intensity. The result of the study shows that the crashes on a macroscopic level are not self-exciting, but there is evidence to prove that the crashes on a smaller scale indeed tend to be self-exciting. The values of the parameters obtained are large in magnitude, hinting that the road network becomes extremely unsafe once a crash occurs, making the traffic system prone to more crashes. It also implies that the road network becomes safe again quickly with a significant crash intensity decay rate. The effect of a crash in the crash intensity of the system tends to last longer, which might prove that the crashes are indeed self-exciting. Still, the combined impact of too many crashes in the influential timeframe ? tends to make the occurrence of crashes appear as randomly distributed.