If you love mathematics, there are plenty of mathematical studies of transit planning that you can explore. In fact, there’s a whole area of research that seeks a perfect mathematical model that would let computers do transit planning, putting experts like me out to pasture.
But most real-world transit decisions are made by people who don’t love math all that much. So I’ve steered away from equations in this book, and tried to explain the concepts in other ways.
Still, there’s one equation I can’t avoid. If you’re going to form coherent views about transit, you have to understand what transit service costs to operate. There are four parts to this cost:
- Time-based costs vary based on how many transit vehicles are operating and for how long. The dominant time-based cost is the wages and benefits of the driver and any other on-board employees, which we pay for by the hour.
- Distance-based costs vary with the odometer reading of the transit vehicle. As in cars, most of transit’s maintenance and fuel costs are distance-based.
- Fleet-based costs vary with the number of transit vehicles owned. Fleet size is based on the number of vehicles needed to run the most intensive part of the service day, typically the commute period which transit planners call the peak. Fleet size drives some maintenance cost, but it main impact is the cost of the vehicles themselves, and of the facilities needed to store and maintain them.
- Finally, there may be some administrative costs unrelated to any of these, though in fact most administration costs are roughly proportional to the other measures of size.
The mixture of these costs varies, but in the high-wage developed world, you can go far by focusing on just one element: the time-based costs.
It's All About Labor
Driver labor, and related time-based costs, are the dominant element – often 70% or more -- of transit operating budgets in the developed world. The only exception is a fully automated driverless service, such as Vancouver’s SkyTrain.
Most transit vehicles require one transit employee on them to operate, whom I’ll call the driver. This person’s job description varies quite a bit based on the technology and operations style of the service. Obviously, driving a train is a different job from driving a bus, and you may or may not be interacting with passengers and dealing with fares. If you’re the employee sitting at the front end of an automated San Francisco Bay Area BART train, you’re not really driving so much as watching for trouble. Many North American transit agencies prefer to call the on-board employee the operator, but that term is too vague to be useful here. So regardless of their exact job description, I’ll call a single on-board employee a driver.
For these one-employee-per-vehicle systems, then, we can understand the basics of operating cost by focusing on how many vehicles are in operation, and for how many hours. You may sometimes may hear a transit planner say “if we do this, we’ll save a bus.” What the planner really means, though, is that we’ll save a driver. In the high-wage developed world, the driver, not the transit vehicle, is the basis of operating cost.
This is the main reason why transit agencies don’t save much money running small buses rather than large ones, as advocates of small buses often assume. If an agency does talk about small buses as being much cheaper to operate, they’re probably referring to a difference in driver wages. Often, some mixture of labor contracts and licensing requirements can allow small-bus drivers to be paid less than large-bus drivers. In that case, the smaller vehicle is cheaper to operate only because of the pay scale, not because of any feature of the vehicle itself.
So how many service hours does it take to run a line? This is the one equation that we can’t avoid. Let’s ease into it.
Service Hours = Span x Vehicles (and drivers) Required.
If a line requires five vehicles in service to cycle the line, and it runs for twelve hours, that will be 60 service hours, 5 x 12. Easy. But how do know how many vehicles we need? Here’s the crucial equation:
Vehicles (and drivers) Required = ROUNDUP (Cycle Time / Headway)
Suppose a line takes 20 minutes to run, in service, from one end to the other, including break time for the driver. That’s 40 minutes round trip, so the cycle time is 40 minutes. Every 40 minutes, a vehicle has completed a cycle of the line and is ready to start another.
So if we only wanted service once every 40 minutes, or longer, we’d just need one vehicle to drive the line. That elapsed time between consecutive trips on a line is called the headway, and it’s the main measure of frequency. (Remember that high frequency means a low headway.)
Now suppose we want service to come at a 10-minute headway – that is, service every 10 minutes. We’d need four vehicles and drivers to drive the 40-minute cycle. Do you want service every 5 minutes? That will be eight vehicles, and drivers. If you double the frequency (by halving the headway) you’ve doubled the operating cost.
Now, suppose we want service on our 40-minute cycle to come every 30 minutes. We’ll need two vehicles and drivers to do that: the cycle time is 40 minutes, the desired headway is 30 minutes and 40/30 rounded up is two. But in this case, the cost of running a 30-minute headway is the same as that of running a 20-minute headway.
In short, transit’s operating cost is lumpy. You can't add a fraction of a bus or train to a line -- or, what we really mean here, is that we can't add a fraction of a driver if we need an entire bus or train to be driven. So at low frequencies, you often end up with inefficient patterns due to the relationship between headway and cycle time. If we run a 20-minute headway on our route that cycles in 40 minutes, we’ll need two vehicles. If we run a 30-minute headway, we’ll still need two vehicles, which means we’re really paying the drivers for a 60-minute cycle. In that case, the drivers will have 20 minutes of extra break time every hour. Drivers may like these shifts, but transit managers don’t.
Lumpiness has important consequences when designing lower-frequency networks, such as local bus routes in low-density suburbs. In these cases, good planning designs routes to be of a certain length, so that they will run an efficient cycle. If our network of local routes is meant to all run every 30 minutes, for example, we try to design routes that cycle in 29 or 59 minutes, but not 31 or 61.
A small deterioration in speed can cause sudden big changes in operating cost. If we’re running 30-minute frequencies on a route that cycles in 29 minutes, that will require one vehicle. But if for some reason the line slows down just a little, so that it now cycles in 31 minutes, we have to add a whole additional vehicle and driver, doubling the cost of running the line. A mere 7% increase in the cycle time has become a 100% increase in operating cost. In that case, a planner may try to redesign the route to make it shorter.
Lumpiness is an important reason that route design and scheduling need to be done together – especially in low-frequency networks such as those of small cities, outer suburbs, or in the middle of the night in big cities. Some transit agencies try to think in separate, rigid, non-repeated steps: First, planners design the route. Second, we drive it and establish the running times. Third, schedulers write the schedules. Thinking that way makes it impossible to optimize the efficiency of schedules and connections. The three tasks have to work together, or at least in several cycles of revision so that planners can revise their structures in light of the apparent running times.
The Elements of Cycle Time
Finally, let’s take cycle time apart. It has three parts:
- The length of the line, in km or miles, round trip.
- The average speed at which the service can operate, including passenger stops. This speed, times the length of the line, is the running time.
- Added factors called layover and recovery. Technically, layover means driver break time, which is usually specified in labor agreements, while recovery means time added to the schedule so that a late vehicle has a chance to catch up to the schedule. In practice, these two kinds of time are usually added together as one factor. For example, an agency policy or labor contract might require adding 10% to running time, for layover and recovery, to generate the cycle time.
The One Equation
So here’s how it all fits together. Operating cost varies mostly with service hours (technically called revenue hours in North America), and these hours are figured like this (click to enlarge and sharpen):
- Every increase in frequency is an increase in service hours, and thus in operating cost. If you want to increase service on a line from every 30 minutes to every 15 minutes, that will double the cost of running the line. This is why most transit agencies would like their service to be more frequent, but have trouble affording that frequency. We explore frequency in Chapter 7.
- Every increase in average speed is a savings in service hours, and thus in operating cost. If we can cut the cycle time of a line by 25%, that cuts its operating cost by 25%. This is why transit agencies are always trying to control delay (Chapter 8).
- At low frequencies, operating cost is lumpy. Because you can’t run a fraction of a driver, small differences in speed or frequency can create large differences in operating cost, if the overall frequency is low.
Frequency and speed are both great things for the customer. But for the transit operating company, frequency costs money, while speed saves money. When discussing the hard choices surrounding frequency and speed – choices that really pervade every part of this book – it’s essential to keep that in mind. Frequency costs; speed saves.