The effect of passenger boarding on bus services

We all know the saying "you wait ages for a bus, and them 3 arrive at once". But why is this?

The basic reason is simple: once a bus starts to run late, there are likely to be more passengers waiting at stops, slowing it down. Because it's running late, the bus behind it has fewer passengers waiting when it gets to stops, and catches it up. There's a strong feedback loop that drives well-separated buses further apart, and closely separated buses get pushed together.

As a passenger, I noted the characteristics of a number of journeys I took over the summer. These were during the day, so avoid the rush hour.

Very roughly, what I see is that on a 24 minute journey between home and the centre of Cambridge, we spend typically:

• 12 min actually moving
• 6 minutes boarding
• 5 minutes stopped due to traffic/lights
• 1 minute unboarding

This doesn't account for the unboarding at my destination stop (terminus).

The boarding is much higher than unboarding for the simple reason that you just get off. When you board, you have to pay, show your ticket, or may have queries.

What was also true was that the distribution of boarding times isn't simple. The majority of passengers board quickly in the 10-20s range (there are two peaks, those who've prepaid and are just showing their card or ticket, and a somewhat slower group who have to pay). However, there's a long tail: a small number of passengers have much longer than average boarding times. I've seen some take several minutes - maybe they don't know where they're going, they don't have the right change, they don't understand the system.

The traffic lights are also rather variable. If you get caught by the lights, you can get a wait of several minutes. (The junction at the Catholic church in Cambridge in particular can cause large delays.)

Unlike a train, which pulls into a station, opens its doors for a fixed time, and then goes, a bus stops as long as necessary to let its passengers on or off. This, coupled with the traffic delays, means that wait times are highly variable.

This also means that the predicted arrival times as shown on bus stops by the real time traffic displays simply can't be terribly accurate.




I knocked up a quick model of my bus journey with the observed distribution of boarding and wait times, and (as expected) it comes back with results that aren't dissimilar to the characteristics of actual journeys:

• Just allowing for the fact that the number of passengers on the journey is random gives a variance of +/- 3 minutes
• Allowing for the feedback of delays early in the journey causing longer queues later gives a variance of +/- 4 minutes
• Allowing for the previous bus as well gives a variance of +/- 5 minutes

Given this variability, it's hardly surprising that adherence to the bus timetable is notional at best.

One way to deal with this is to add waits to bring the bus back in line with the timetable. (You have to add waits, you can't remove time unless you have a time machine.) And my 24-minute journey is allowed 30 minutes, so we routinely stop 2 or 3 places along the route. But having to build in this extra wait time is pure waste.

What you can also see is that if the bus were to be full (in other words, taking on 60 people) then it's not entirely unreasonable to require 15 minutes for everyone to board. Those who have stood in a queue in the city centre on a busy evening or a Saturday afternoon will have seen the buses stationary at the stop for this sort of time. Even with the slop in the schedule, it's almost impossible to keep to the timetable if the bus is full. (Especially as those tend to be times when the roads are more congested.)

What if you could reduce boarding time? This gives you a double win: less boarding time makes the journey quicker, but also gives less variability, so you need to build in less slop. It's better for passengers, who get quicker and more reliable journeys, and it's better for the bus operators who make much better utilization of their buses and drivers.

Looking at my journey just to be specific, optimization of loading could almost halve journey times and double efficiency. At busy times on short routes having a second staff member check tickets - rather than forcing the driver to do so - is obviously a win. (This doesn't have to be a conductor, who would check or sell tickets while the bus is moving after everyone has boarded. It could be an inspector at certain stops who validates tickets of those in the queue. When I was living in Toronto some of the busier bus stops were closed interchanges, you paid as you entered the system and didn't need to be checked at the point of boarding at all.)

Eliminating charges entirely would have a similar effect. People just walk on without having to stop. Again, the system is far more efficient as a result.

One of the other minor issues with buses in Cambridge is only having one door. Those wishing to board have to wait for everyone who wants to get off to do so; many other systems have separate doors allowing boarding and unboarding to operate in parallel.

The actual process of issuing tickets has improved, I think. Smart cards and contactless payments are much quicker than the old cash and paper tickets.

But what's interesting here is that improving the efficiency with which passengers board a bus does have the potential to significantly improve journey times, reliability, and the efficiency of the bus system.