Synchronising Bus Bunching to the Spikes in Service Demand Reduces Commuters’ Waiting Time

Figure 1

Comparison of the average waiting time of passengers computed with analytical formulas and with a numerical simulation. The plot on the left considers the case of unlimited capacity described in Section 2, while the plot on the right considers a limited capacity of and uses the formulas from Section 3. The circles, triangles, and crosses represent the results from the simulation for the cases A, B, and C, respectively. Discrepancies are caused by simplified assumptions, discretisation of variables in the simulation, and limited running time. The percentage of mismatch in the legend is the median of the difference between the simulation and the analytical result across the range , rounded to the closest integer. As explained in Section 2.3, the hypothesis of perfectly staggered buses fails at high values of , as we see from the plot. In this example, there are two buses , the period of revolution is time units, the period of the spike is , and .