Approximating a ride-sourcing system with block matching

On-demand matching between waiting passengers and idle drivers is one of the most important components in a ride-sourcing system. A variety of matching mechanisms have been developed to meet different needs of ride-sourcing platforms, e.g. mitigating supply-demand imbalance, maximizing platform revenue. In this paper, we focus on a block matching system, a special type of matching mechanism, where the region of interest is partitioned into blocks, and on-demand matching is separately and simultaneously conducted in each block. Block matching can bring many benefits, such as limiting order assignment with long pick-up distance, simplifying the process of deployment, etc. However, it still remains a challenging yet interesting issue to determine the block size for the matching system, which is a key decision variable governing passengers' waiting time. To solve the problem, we model the ride-sourcing system with block matching via a M/M/c queue, in which the service rate is endogenous and partially determined by passengers' average pick-up time. Based on the model, we find that the average queueing time of passengers decreases with block size increasing, while the average pick-up time may increase instead. In addition, the average total waiting time (sum of average queueing and pick-up time) become nearly invariant to the change of block size when the block size is large, which we call plateau phenomenon. In the plateau, ride-sourcing platforms can choose the block size based on other standards while the average total waiting time is always maintained at the nearly lowest value. The findings are verified via an agent-based simulation study, demonstrating that the proposed model can be an effective tool to approximate block matching system.