A 2-Dimensional Cellular Automaton for Agents Moving from Origins to Destinations

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise ($p$) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter $"\mu"$ is also introduced to control the probability that the movement of all agents involved to the same site (conflict) is denied at one time step. This model displays two states; namely the freely moving and the jamming state. If $\mu$ is large and $p$ is low, the system is in the jamming state even if the density is low. However, if $\mu$ is large and $p$ is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if $\mu$ is large and $p$ is low (jamming state); but long travel times are suppressed if $p$ becomes large (freely moving state).