The waiting time paradox: why is my bus always late? (2018)

The further behind the previous bus a bus is, the more people will arrive at the bus stop. The more people there are at the stop, the longer the bus has to spend picking them all up and selling them tickets etc. Therefore the delayed bus will tend to experience more delay. The bus behind them will have less people to pick up, so it will spend a shorter time at stops and tend to catch up with the first bus, so the two busses are dragged towards each other.

In my country, apart from an app/ online, you can buy a ticket pretty much anywhere. I guess someone worked out that bus drivers with money are a potential theft risk, and also that selling tickets on the bus takes time and makes busses late(r than they would be).

I can link my payment method, and purchase tickets in seconds whenever I’m ready.

Compare:

https://www.lubus.info/images/stories/taborbus/5122-57.jpg vs https://www.chicagobus.org/system/photos/250/large/DSC00925....

That's double the boarding time at every stop right there.

The schedule is also designed in such a way that the bus is usually ~1 minute ahead of time and can wait for the proper time to depart from each bus stop - zeroing the randomness on each stop. If it gets too delayed on one part of the route it can catch up on next few bus stops.

On intercity routes there's fewer bus stops so usually there's just 1 door and the driver sells the tickets.

It's not worth it to make every stop optional because then the routes become too unpredictable and scheduling is hard. Usually there's like 5-10% of optional bus stops on each route - only in the places where very few people get in/out.

Most people that drive often just have monthly tickets so they don't have to do anything - just get in/out of the bus.

Drivers are banned from selling tickets - they only do the driving. And nobody checks if you bought a ticket on every ride - there's a random check every now and then and if you're caught you pay a high fine. But you have maybe 1% chance of being checked at any given ride.

I think most people complaining about buses in this thread just live in a city where public transport isn't a priority so it barely works :/

The city buses I've seen in USA have 1 or 2 doors. It's already wrong - it makes the boarding time unnecessarily long. Then there's the tickets - drivers shouldn't be selling or checking the tickets. You should buy tickets in a ticket machine or on your smartphone. And they shouldn't be checked every time - it takes too long. Have a group of people who board random buses and check the tickets there while the bus is driving so as not to waste anybody's time.

Bus schedules and routes should be designed with randomness in mind. There should be a small buffer (1 minute is enough if boarding is quick) to zero the randomness on each bus stop. Most bus stops should be mandatory so that 3 consecutive bus stops without passangers don't wreck the whole schedule (and then it spreads to other buses because you have to wait for 5 minutes at a bus stop for your departure time and you block entrance for other buses' passangers which makes boarding longer).

If you just put an intercity bus (that can work with 1 door and driver selling the tickets) and use it as a city bus that stops every 1-5 minutes - it won't work.

City buses should be optimized for latency not throughput.

This is how it works in every big city in Poland, it's working great. More cities started to use this system over time, because it improves the scheduling so much.

The point of city buses is that they drive in traffic anyway - they rarely drive over 50 km/h and they stop every 5 minutes. How regular they are is MUCH more important than how fast they drive.

If you skip 3 stops because nobody waited there - you get to the 4th bus stop 5 minutes too early and wait for 5 minutes there - potentially blocking the bus stop for others and wrecking havoc with the scheduling. Much better to split these 5 minutes between the bus stops where nobody is blocked.

It's like in gamedev - you don't want to optimize happy case cause you're making the situation WORSE. If your fastest frame takes 5 ms instead of 10 ms it changes nothing at best (and makes for more jerky movement at worst). If your longest frame takes 15 ms instead of 18 ms - it means you can keep consistent 60 FPS now - and that's a HUGE win.

If you buy a transit pass or use their app you can get significant discounts.

For express busses, stops are far enough in between and all major locations, so you may as well stop at all of them.

For milkrun busses, where the frequency is so high, scheduling errors are only really a problem if the busses bunch up and create excessive gaps.

If a bus trip takes 45 minutes when a car takes 15, more people drive and then traffic gets bad. But busses with dedicated lanes and coordinated light-timing can go much faster than traffic, when they aren't stopping for passengers!

I think you and I must live in cities with very differently-run transit companies!

If nobody is waiting and nobody asks to get off they don’t stop. If nobody asks to get off and there’s a second bus right behind, drivers skip the stop.

Way too many transit operators choose extremely slow. Having bus stops every 100m is popular because it offers almost door to door service. But when every single person separately boards it results in the vehicle being stopped 1/3 of its running time! People generally prefer faster bus routes (average 20 MPH) even if it requires them to walk a block to the stop versus a service that stops every block but averages 6 MPH (bicycle speed).

https://humantransit.org/2011/04/basics-walking-distance-to-...

Do you not have schedules at bus stops? If you skip almost all the bus stops you'll be like 10 minute early at the first non-empty bus stop, so you'll have to wait for these 10 minutes there (or you depart early which makes people miss their bus).

Potentially you'll be blocking the bus stop for these 10 minutes for other buses.

Why not split these 10 minutes between the empty bus stops instead?

And yes, the drivers would coordinate. (I've sometimes seen it done with a brief honk for attention followed by a hand wave.)

[1]: [A self-coördinating bus route to resist bus bunching](https://doi.org/10.1016%2Fj.trb.2011.11.001)

[2]: [NAU’s new bus system makes for shorter wait times for riders](https://news.nau.edu/nau-bus-schedules/)

> the Keoride app matches customers who are travelling in the same direction and calculates an optimised flexible route to pick up and drop off customers close to their destination, you can even track the vehicle and get updated on your ETA in real time.

> If a bus is indicating ( min 5 secs ) and is pulling out from a bus stop they have right of way. Failure to Give Way is worth a $362 fine and [demerit] 3 points.

what is right is a compromise but everx block is too much

The Oyster system in London is a classic example of this - originally you needed to load money onto a separate card, now you can do it with your bank card instead, but it still all works the same. I believe it's also the cheapest option - the daily and weekly caps are cheaper than their paper ticket equivalents. You can probably get better deals in specific cases, but generally the Oyster system is the way to go. I know they're slowly bringing that concept in in other cities in the UK as well, and there are schemes around Europe that use an app with GPS as the "tap on, tap off" mechanism.

Looking at the second link, it seems they implement it by having the buses pause at certain points. Does it do that with riders onboard? That seems like it could be a deterioration in experience for those riders that are on the bus pausing.

It's 12 km on foot one way and probably like 20 km in the bus the other way (it can't drive on the pedestrian/bike path along the river). I walk these 12 km in 2 hours and the bus takes 40 minutes to take me back. There's 25 bus stops on the route I take (and a few more later). There's 2 optional bus stops but they are past the point where I get off the bus.

So that's 1.5 minutes between bus stops (including the stops themselves which take around 5-15 seconds usually).

What's wrong with walking being competetive with buses BTW? The point is that it's better than driving in a car.

There's nothing all that bad about driving a car, so public trasport has to be at least better than walking to be better than driving.

For example, looking at some of the commutes my family does (I work fully remotely), one has to spend 45 minutes to travel ~12km via subway, which would be 20 minutes via car, or 2 hours if walking. Another has to spend 2 hours to travel ~50km via subway and bus (all still within the city) or 30 minutes via car, with the equivalent walk apparently taking 7 hours.

So, in the first case, that's an extra hour and a half they're losing per day to just transport, and in the second case that's 3 hours per day being lost to transport. Now add in time spent taking kids places, and basically you end up spending most of your life outside of work just getting around instead of actually doing stuff.

Seriously, Translink runs on a 28-hour day for bus service. If you want someone to test every single system, especially someone that knows how a system should work vs how it does work vs how it failed on this particular bus, you already have an employee for the job; one that's doing customer service and working around any shortcomings at the same time.

I would not count on bus drivers being replaced by AI any time soon.

But otherwise, they have a bunch of optimizations to spread the pauses out so they aren't too jarring. They also display the timer prominently so that riders are aware of what's going on.

In practice, riders seem happy with the tradeoff, since it has resulted in overall lower times to get from point A to point B.

The surprising results:

- According to the results of the traffic modelling, the on-demand scenario wasn't substantially more successful in attracting additional passengers than the "classic buses running every 10 minutes" scenario (i.e. in both cases predicted passenger counts increased, but by approximately the same amount). This was because on-demand public transport has quite a bit of time-wise overhead, too: You need to order a vehicle instead of simply showing up at the bus stop, it takes a while for the next vehicle to arrive, due to ride sharing some detours might be incurred compared to a direct route, and the unpredictable journey time variation due to these factors is very disadvantageous when connecting to fixed-route fixed-timetable public transport, such as the remaining three bus routes, or railway services.

- The overhead of operating a large fleet of on-demand vehicles was high enough that even with driverless operation the on-demand scenario was more expensive to operate than the expanded every-ten-minutes bus service with drivers

At least in London it stops there, i.e. the automatic capping doesn't do longer than weekly capping. Also the weekly capping only runs on a fixed Monday to Sunday period, whereas an individually bought weekly travelcard can start on any day of the week.

SF recently acquired 33 new buses for $1.7 million apiece. Throw in maintenance and fuel costs and it’s easy to see that amortizing over a driver making $40/hr plus benefits is just not that big a deal, especially if you’re now adding a suite of sensors, electronics, and computing hardware.

In practice I see buses slowing down or stopping to keep their ordering, and I don't understand why.

(Of course that doesn't work for trains which can't overtake)

It's a good plan but you have to make sure fairness is ensured. It's the same feeling as, if I go get a burger & fries, the guy behind me orders identically, burger and fries, and somehow gets served first. The instinct is to say, "what the heck, why does HE get fast service than me in a straightforwardly unfair manner?!?"

So you'd need the empty bus and full bus to hit the same spot at the same time, fill the empty bus as the full one unloads. But which bus leaves first? If the former empty bus leaves first, you're being unfair QoS to the people who are seated on the full bus (which, to their perspective, at their prior stop, was the first-in-order-on bus so therefore should be the first-in-order-off bus. On the other hand, if the full bus leaves first, why did you make incoming passengers board the empty one? They should have boarded the full one to get to their destination faster.

The solution, which we see in practice, is to have the empty bus wait 5 or 10 minutes and let the full one get ahead. If we are seeing rounded fairness to all parties as the priority.

In a network metaphor, you do not halt all other TCP connection on a system because one TCP connection was stalled by a lost packet, in the name of fairness. No one would ever want that.

The people on the full bus can easily see that they are not moving because they are still unloading. Who would see another empty bus passing by and thinking "those people should be made to wait"?

In my experience on the subway, a train will start SKIPPING STATIONS when they are bunched together, forcing me to get off and wait for another train entirely. So I don't think fairness is the reasons buses keep their order.