Biham-Middleton-Levine Traffic Model With Origin-Destination Trips
  We extended the Biham-Middleton-Levine model to incorporate the origin and destination effect of drivers trips on the traffic in cities. The destination sites are randomly chosen from some origin-destination distances probability distribution "ODDPD". We use three different distributions: exponential, uniform and power-law. We consider two variants of the model. In conserved particles model (Model A), drivers continue their travelling even if they reached their destinations. In non-conserved particles model (Model B), a driver which reaches its destination disappears with rate $\beta$. It is found that the traffic dynamics in model A and the evacuation processes in model B are greatly influenced by the ODDPD. On one hand, we found that we can adjust the ODDPD to enhance the road capacity of the city and to minimize the arrival times of drivers in particles conserved system and to optimize the evacuation time of drivers in non-conserved case. On the other hand, we find that, independently on the ODDPD, the evacuation time $T$ of drivers diverges in the form of a power law $T \propto \beta^{-\nu}$, with $\nu=1$. 
Najem Moussa