Understanding single-file movement with ant experiments and a multi-grid CA model

Single-file traffic is a simple and fundamental phenomenon that can be observed in vehicle transportation, pedestrian flow, animal movement and many others. In this paper, the fundamental diagram of single-file movement is studied by ant experiments and modeling. For ant, single-file traffic is a very important activity. From single-file movement experiments, ant follows the one in front can be observed. It is also observed that the critical density, i.e. the density corresponding to the maximum flow, is larger than 0.5. The flow-density curve present as an asymmetrical arch, which is different to those of traffic flow and pedestrian flow. In order to get insight of the phenomenon, we introduce a multi-grid NaSch (MG-NS) model, based on multi-grid cellular automata model and traditional NaSch (NS) model, to understand the single-file ant trails. The multi-grid method is convenient to refine the time and space, therefore one agent (ant) can occupy multiple grid sites and its movement can be calculated in detail. Based on the model, we get the theoretical relationship between flow and density with varying delay time tj. It is different from that of traditional NS model and agrees well with the simulation results. In addition, MG-NS model can match the result of ants experiment well with tj=0.25 (n=4). The smaller the delay time tj (larger n) is, the larger the flow, speed and the critical density are. Through stability analysis, the smaller delay time tj means agents react faster and can keep the flow in steady state easier. It is also indicated that in the traditional NS model, because the size of grid equals to agent size, the delay time is always equal to or greater than one time step. But for the agent with sensitive response, the traditional NS model will be no more applicable. The MG-NS model proposed overcomes the disadvantages and thus is an improvement to the traditional one, thus can be used to reveal detailed mechanisms of traffic.