Intelligent Buses in a Loop Service: Emergence of No-Boarding and Holding Strategies

Abstract

We study how N intelligent buses serving a loop of M bus stops learn a no-boarding strategy and a holding strategy by reinforcement learning. The no-boarding and holding strategies emerge from the actions of stay or leave when a bus is at a bus stop and everyone who wishes to alight has done so. A reward that encourages the buses to strive towards a staggered phase difference amongst them whilst picking up passengers allows the reinforcement learning process to converge to an optimal Q-table within a reasonable amount of simulation time. It is remarkable that this emergent behaviour of intelligent buses turns out to minimise the average waiting time of commuters, in various setups where buses move with the same speed or different speeds, during busy as well as lull periods. Cooperative actions are also observed, e.g., the buses learn to unbunch.

Mitigating bus bunching with real-time crowding information

“…Boarding limits implemented as a sole (isolated) measure were also found to be effective in reducing headway variability and improving travel times (Zhao et al 2016;Enayatollahi et al 2019). Saw et al (2019) conclude that noboarding policies perform favorably in mitigating the bus bunching when compared against holding strategies in busy periods, but contrarily-backfire during low-demand periods (by imposing excessive waiting times) when holding is a more advantageous solution.…”

“…Imposing boarding limits or a no-boarding policy implies that when specific (in)stability criteria are met, the PT operator constrains the number of passengers allowed to board a PT vehicle, forcing the remaining ones to wait at the stop for a later departure. In the context of reversing the bus bunching mechanism, while holding strategies aim at 'slowing down' the second bus that moves ahead of schedule, the objective of no-boarding strategies is to 'speed up' the first bus that is otherwise increasingly delayed (Saw et al 2019). Delgado et al (2012) estimate that boarding limits can foster the benefits of holding strategies when applied simultaneously, particularly in the case of highfrequency and high-demand services, requiring fewer and shorter holding times to restore service regularity and travel comfort.…”

Chaotic semi-express buses in a loop

“…This erratic behaviour emerges completely in the absence of any noise. To enforce regular bus arrival times at bus stops, active intervention strategies like holding [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]40], no-boarding [34][35][36][37][38][39][40], stop-skipping [23,[41][42][43][44][45], deadheading [42,[45][46][47][48] which are adaptive real-time or when the phase difference goes beyond some prescribed bound, would seem necessary to maintain stable anti-bunched configurations of buses in a loop [14]. Nevertheless, semi-express buses do not actively interfere with prescribed bus services to the various origin bus stops.…”

Analysis and Simulation of Intervention Strategies against Bus Bunching by means of an Empirical Agent‐Based Model

“…Similar findings were reported in ref. [43] where there was an improvement in waiting time due to holding the faster bus to match the slower bus, albeit at the expense of an increase in average total travelling time.…”

“…Unlike the s-holding strategy, the result of c-holding strategy in Table 5 shows a marginal improvement in the efficiency, with a 14% reduction in waiting time, which is consistent with similar works found in ref. [14,26,43].…”