Demand Sensitive Scheduling for Public Transport

Routing and scheduling in public transportation is a well-studied problem, and very relevant today in the face of rampant traffic congestion in most big cities across the globe. The routes and schedules need to be planned by transit agencies so as to successfully cater to the public demand, maintaining the revenue earned and operational cost incurred. The traditional schedules are built to increase revenue or improve utilization. On the other end, when commuter satisfaction is more of a focus the schedules are tuned to decrease waiting times of commuters by providing high frequency services. However, this could result in underutilization of the resources (buses).

So the question is, can public transit schedules balance these seemingly orthogonal goals to increase commuter satisfaction, without compromising on revenue or costs? Here are two case studies that show that this is indeed possible.

Improving Bus Commuter satisfaction in Latin America

In the first case study, we consider a Bus Rapid Transport (BRT) network in a city in Latin America. The BRT corridor consists of 35 stations and three terminals served with 300 buses. Corridor stretches for 26km and served around 0.7 million passengers a day. The bus stops are provided with gated enclosures with contactless card to access it. The fare is deducted when the card is swiped every time a passenger enters the bus enclosure. A constant fare is deducted for every travel trip irrespective of the distance travelled.

Objective: The operations of the buses in the corridor was inefficient and as a result, there was a lot of dissatisfaction within the commuters. The commuters faced long waiting times and often had to board crowded buses. The transit agency wanted to improve commuter satisfaction and at the same time increasing utilization of buses.

Data: The data available was the ticket swipes recorded for commuters using the transit network. There was three months ticketing data available through the ticketing solution provided by Conduent to the transit agency. Apart from this, the existing schedules, information on number of buses and the capacity of bus were also provided.

Methodology: We develop a mathematical framework that uses the patterns of mobility inferred from the ticketing data to build a schedule that is sensitive to the demand patterns and minimizes the waiting time of commuters. We use an objective function that models the percentage of commuters waiting for more than five minutes at any stop in the network. We then search for a schedule that would decrease this objective function with the constraints that the schedule should not use more buses than are available and the number of passengers accommodated in the bus cannot exceed the capacity of the bus. We also impose a constraint that the bus utilization as measured by the number of people per km of travel is within reasonable range of values. By finding the schedule that maximizes the objective without breaking any of the constraints, we ensure that the number of commuters waiting for more than 5 minutes is minimized without compromising on the utilization of buses in the transit operation.

The mathematical framework developed takes as input the demand at each bus stop at different times of the day. The objective function is optimized to output a schedule that is sensitive to the demand observed during a month. The schedule produced in the case study is related to minimizing waiting times, but it can be replaced with an objective that is of interest to a particular transit agency. It could be maximizing revenue, minimizing cost of operations etc.

Results: The schedule is first built based on the demand pattern observed during a month. The schedule is then simulated using the demand pattern deduced from the following months. The waiting times and the utilization of the buses are measured compared with that of the existing schedules. Different schedules are built based on different objectives. Metrics for different schedules are shown in table 1. Table 1 shows the comparison of different schedules built to improve different objectives. The first row represents the current schedule which can be seen to have around 36% of commuters who wait for more than five minutes. The cost of operating the current schedule is given by the number of trips which are being run, in this case, 356. In schedule A, we try to decrease the percentage of commuters who wait for more than five minutes while maintain the same cost (number of trips) as the current schedule. We can see from the table we can decrease the number of commuters who experience significant waiting times by about 6%. Alternatively, schedules B and C are cases where with additional trips, the commuter satisfaction can be improved. Finally, schedule D is the case where the cost (number of trips) is decreased keeping the commuter satisfaction unchanged.