Out of the box Mathematics of bus routes
I wish to explain the mathematics behind trunk services. 

In Singapore, a trunk service has an average of 50 stops and takes 100 minutes to complete a journey (one way). Suppose the trunk service is broken into 4 shorter services of 12 stops each. Does it improve the efficiency of the bus system?

Certain stops along the route are busy at certain times of the day, for example schools or large workplaces. To avoid overcrowding or long waiting time, more buses have to be deployed on the service to cater for the busy stops. 

As the bus is crowded only for these stops, the bus becomes relatively empty after these stops. It is likely that the average occupancy of the buses for the service is 30% (say).

If the trunk service is broken into several shorter services, more buses can be run for the busy segments and less buses for the other segments. This may allow the average occupancy to increase to 60%, say. This would improve the efficiency by 100% and free up half of the buses, without affecting the service level.

One disadvantage of shorter routes is that the passenger has to make more transfers. On average, the passenger may have to make 2 transfers, compared to a trunk service that aims to a direct service to the destination. In practice, it is convenient to make the transfer, as it is done at the same stop. 

The waiting time for a short service is shorter, compared to a trunk service. The total waiting time, including the transfers, may be the same. 

It is more efficient to have a bus system that have more services, each with fewer stops, than a network of trunk services with more stops. 

Tan Kin Lian 

 

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