A few days ago, Sandy Johnston linked to a diagram of the single bus route in South Sioux City, Nebraska, a suburb of Sioux City, Iowa. While South Sioux City has a traditional main street in Dakota Avenue, the bus does not follow it; it meanders, hitting destinations on and off Dakota. Many destinations are on US Route 77, an arterial bypass around the built-up area, with recent auto-oriented retail and office uses, including a Wal-Mart (in small-town America often the biggest bus trip generator). The discussion around what to do with this region’s bus network made me realize a crucial concept in planning infrequent transit: getting route-length right. To start with, here is a map of the bus, numbered Route 9 within the Sioux City area:
Here is a PDF map of the entire network. It has 10 routes, using 12 buses running hourly, with a timed meet at the center of Sioux City (just off the above map) at :30 every hour. Most routes run as loops, with highly separated inbound and outbound legs. Route 9 above runs one-way southbound on Dakota Avenue in the northern and southern legs but then meanders to run southbound on Route 77; the Dakota Avenue leg in between the two major east-west runs is one-way northbound.
I asked, why need it be so complicated? The major destinations are all on Dakota or Route 77. It should be easy to run two distinct routes, one on each, right? Without the east-west meanders, there would be the same total service-hours, right?
But no. The route runs hourly. The scale of the map is small: from the bridge over the Missouri in the north to I-129 in the south it’s 4.1 km. There is so little traffic that in the evening rush Google Maps said it would be just 10 minutes by car from Downtown Sioux City to the southern edge of Dakota Avenue near I-129. The roundtrip time would be 25-30 minutes, so the bus would sit idle half the time due to the hourly pulse.
Getting route-length right
When designing regional rail schedules, as well as my take on night buses in Boston (since reduced to a single meandering route), I’ve taken great care to deal with roundtrip route length not always being an integer multiple of the headway. A train that comes every half hour had better have a roundtrip length that’s just less than an integer or half-integer number of hours, counting turnaround times, to minimize the time the train sits at the terminal rather than driving in revenue service. The same is true of buses, except that scheduling is less precise.
In Boston, the plan at the time was for hourly buses, and has since changed to half-hourly, but the principle remains. The roundtrip length of each leg of the night bus network, should it expand beyond one (double-ended) route, should be an integer or half-integer number of hours. In practice this means a one-way trip time of about 25-26 minutes, allowing for a little recovery time and for delays for passengers getting on or off; overnight there is no traffic and little ridership, so 25 minutes of driving time correspond to just less than 30 minutes of actual time.
Thus, on each corridor, the bus should extend about 25 minutes of one-way nighttime driving time from the connection point, and the choice of which routes to serve and where to end each route should be based on this schedule. Of course on some shorter routes 12 minutes (for a half-hour roundtrip) and on some long routes 38 minutes (for a 90-minute roundtrip) are feasible with half-hourly frequencies, but in Boston’s case the strong night bus routes in practice would all be 25.
Length and frequency
In the case of Sioux City, hourly buses meeting at the center should have a one-way trip time of 25 minutes. However, the city is so lightly populated that there is little traffic, and the average traffic speed is so high that 25 minutes puts one well outside the built-up area. The driving time from city center to the edge of the built-up area, around I-129, Lakefront Shopping Center, and the various Wal-Marts ringing the city, is around 10 minutes.
Moreover, a car travel time of 10 minutes corresponds to not much longer on a bus. Frequent commenter Zmapper notes that in small American cities, taking the driving time in traffic and multiplying by 1.2, or 1.3 with recovery time, is enough. A one-way driving time of 11-12 minutes involves a roundtrip bus time of half an hour.
With such a small urban extent, then, the bus frequency should be bumped to a bus every half hour, leveraging the fact that few important destinations lie more than 11-12 minutes outside city center. The question is then how to restructure the network to allow for doubling frequency without doubling operating expenses.
The importance of straight routes
Some of Sioux City’s bus routes go beyond the 12-minute limits, such as route 6 to the airport. But most stay within that limit, they’re just incredibly circuitous. Look at the map of route 9 again. It jumps between two main corridors, has multiple loops, and enters the parking lots of the Wal-Mart and other destinations on US 77.
The reason for the meanders is understandable. US 77 is a divided highway without sidewalks or crosswalks, and none of the destinations thereon fronts the road itself. From the wrong side of the road to Wal-Mart it’s 330 meters, and a few other retail locations are more than 100 meters off. Many agencies wince at making passengers walk this long.
However, understandable does not mean justifiable. Traversing even 330 meters takes only about 4 minutes, and even with a hefty walking penalty it’s much less than the inconvenience caused by hourly headways. The other routes in the Sioux City area have the same problem: not a single one runs straight between city center and its outer destination.
With straighter routes, the savings in service-hours would permit running every half hour. A single bus could run every half hour if the one-way car travel time were at most 11-12 minutes; up to 23 minutes, two buses would provide half-hourly service. With 12 buses, there is room to replace route 9 with two routes, one on Dakota and one on US 77 (possibly entering the Wal-Mart, since the route is so short it may be able to get closer to Wal-Mart while still staying under 12 minutes). The Lakeport Commons and Southern Hills Mall area could get buses at the entrance, as it is the logical end of the line (route 1, to Southern Hills).
Some pruning would still be required. Some low-density areas far from the main corridors would have to be stranded. Some circumferential lines would be pruned as well, such as route 10 (to the Commons) on US 75 and route 2 (on Pierce Jackson) to Wal-Mart. Circumferential lines at such a low frequency are not useful unless the transfers to the spokes are timed, which is impossible without breaking the city center interchange since the lines take different amounts of time to get between city center with the plausible connection point. Ultimately, replacing the hourly routes with half-hourly routes would guarantee better service to everyone who’d still get any service, which is nearly everyone.
It’s not just Sioux City
I focus on Sioux City because it’s a good toy model, at such scale that I could redesign the buses in maybe two weeks of part-time work. But it’s not the only place where I’ve seen needlessly circuitous routes wreck what should be a decent bus network for the city’s size and density. In 2014 Sandy wrote about the bus network in New Haven, which has okay trunks (I only needed to hitchhike because of a bus delay once – the other four or five times I took the bus it was fine) but splits into indescribably complex branches near its outer ends.
More recently, I looked at the network in Ann Arbor, partly out of prurient interest, partly out of having gone to two math conferences there and had to commute from the hotel to the university on the city’s most frequent bus, route 4. Zoomed out, the Ann Arbor map looks almost reasonable (though not quite – look at routes 5 and 6), but the downtown inset shows how route 4 reverse-branches. Ann Arbor is a car-oriented city; at my last math conference, in Basel, a professor complained that despite the city’s leftist politics, people at the math department were puzzled when the professor biked to campus. The buses are designed to hit every destination someone who’s too poor to own a car might go to, with speed, frequency, and reliability not the main concerns.
The underlying structure of bus networks in small American cities – radial buses converging on city center, often with a timed transfer – is solid. The problem is that the buses run every hour when cities should make an effort to run them every half hour, and the routes themselves are circuitous. In very small cities like Sioux City, increasing the base frequency is especially urgent, since their built-up extent is so compact a direct bus would reach the limit of the serviceable area in 10-12 minutes, perfect for a half-hourly schedule, and not the 25 minutes more typical of hourly schedules. Sometimes, scaling down requires maintaining higher frequency than the bare minimum, to avoid wasting drivers’ time with low-value meanders.