Spiral path simulation of pedestrian flow during Tawaf

Pedestrian agent performing Tawaf is modelled using the concept of parameterization of spiral. The agents are set at defined velocities on spiral trajectory, moving counter clockwise mode inward and outward for decreasing and increasing radii. We present a new trajectory path planning that simulates the movement of individual agents performing Tawaf. Our aim is to simulate complex scenarios involving multiple agents interacting with each other and avoiding collision within a defined path. The simulation was carried out for two proposed approaches; Spiral movement of agents for seven lapses in order of four inward and three outward (4in_3out) and undirected movement in circular pattern. An agent flow optimization comparison was carried out between the proposed methods for agents flow rate, average velocity, Tawaf duration and maximum densities of pedestrians. We found that the spiral movement 4in_3out presents better Tawaf ritual performance with durations of 38 minutes and average density of 4.2 agents per square meter.