  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 $\nu=1$.
