Predicting a distribution of bus tardiness

I’m about to start digging into various real-time data feeds for American (bus) transit systems. For the most part right now I’m interested in finding a simple,  average distribution of lateness/earliness across all stops, the idea being that this could help riders predict, without live real-time feeds, when the bus is most likely to show up, by looking only at a fixed schedule.

Are buses more likely to be late than early? What percentage of buses are early, anyway? If it’s already five minutes late, is it very likely it’s coming in the next minute? Or should you start walking? What’s the difference in tardiness distributions between frequent and infrequent services? Are there types of places in a city which have consistently different distributions?

In the name of science, I’d like to make a prediction, ie. state my hypothesis, before I’ve collected any actual data. So here it is:

Predicted Bus TardinessI think that overall the distribution will have a strong late skew, a very short early tail, and a wide second hump around the time a second bus might start bunching up on the one in question. I’ll guess that between 10% and 20% of buses running on fixed schedules will be at least a few seconds early and that the median will be about 2 minutes late.

Now…anyone want to suggest a city with a real-time feed? I have my eye set on Portland at the moment but only because I’m have trouble finding decent APIs.

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Posted in: Analysis | Data
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Back Door Please

When you’re preparing to disembark the bus, please look ahead to your stop before the bus reaches it. Does it look like there people about to get on? If so, now is the time to leave through the back door.

Leaving through the front door when people are trying to get on slows down the bus for everyone still on board because the people boarding have to wait for you to clear the door before they can step in and make their payment. If you go out the back door, the bus can unload you at the same time it’s loading other passengers, and everyone can be on their way more quickly. This is particularly important at major stops like Government Square where I’ve seen thirty people take a whole minute to file out through the front door while thirty more people waited anxiously to board. What the hell, people?

Over time, if everyone does little things like this to keep out of the way, schedule planners can start to assume that less time will be spent at stops boarding passengers and they’ll build less padding into their timetables. Quicker buses, less delay, a few less seconds standing out in the cold…and all we have to do is go out the back door. They put it there for a reason ;-)

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Posted in: Tips & Tricks
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‘BRT’ – What is it?

I’ve heard a lot of talk about Bus Rapid Transit(BRT) lately, and I’m feeling the need to start unpacking some of it. Just what is BRT? I suspect many people have a fairly vague idea, but fortunately, I found this great slideshow on SORTA’s page about the topic that actually explains everything quite clearly. From the second slide:

“[BRT is] A flexible, high performance rapid transit mode that combines a variety of physical, operating, and system elements into a permanently integrated system with a quality image and unique identity.”

Sounds good so far, no?

On the next slide we learn that “BRT is tailored to each unique corridor” and “can be implemented incrementally“. There are a variety of “alternate BRT packages”. Awesome!

The fourth slide gives us a show of how many cities are supposedly planning BRT.

BRT popularity map

Sweeping the nation like a new boy band!

Then on the next two slides we go back to how flexible BRT is.

The infinite specturm of BRT

BRT will be your everything.

Now this is actually the second time this next slide appears in the document. They really don’t want us to miss the fact that BRT is plug and play.

parts of a so called BRT

Buy the expansion pack!

Let’s pause for a moment to get real: I’m sure Parsons Brinkerhoff does some decent work every once in a while, but this slideshow looks like it was put together by a first year planning student assigned to learn about BRT.

Carrying on again: From here on out, the document spends a few slides at a time highlighting certain features of BRT one at a time. Let’s pick them apart one by one.

“Stylish Vehicles”

BRT is stylish apparently

“Environmentally compatible”: You don’t have to install any proprietary codecs?

Let’s look closer at that one in the top right.

Damn, BRT. You fine.

Damn, BRT. You fine.

That’s pretty awesome. I’m not sure I’ve ever felt as excited about transportation as the emotions this picture conveys, but I have come close.

The big difference, as the next slide explains, between a BRT bus and a “regular”(?) bus is that the BRT is more “rail-like”. They even suggest retrofitting existing buses from the fleet with “front cones” and “wheel covers“.

But then of course if you don’t want any of that, BRT will be anything you want it to be. I mean, look at LA!

BRT will be anything for you

BRT is available in sizes XS -5XL

“Running Ways”

“BRT can operate in a wide variety of physical environments:
-On Street
-Bus Lane
-Bus Way…
-Guided or Non-guided
-Exclusive Lane or Mixed Traffic”

This is pretty neat. You mean to tell me it can go anywhere if we want it to? It could even have it’s own lanes?

buses frolicking in a feild

Buses frolicking in grass. Curiously, there is no sidewalk.

a variety of BRT lane types


Well, this is all well and good, but it amounts to little more than saying something like “Nate: with his two feet, he can go anywhere, climb stairs, even run! He’s found in the great outdoors, in bed, in coffee shops and many other physical environments. He could even fit in a hot-tub if you bought him one.” *wink, wink*

It’s simply a list of possibilities rather than requirements or standards. And it’s not unique to things called “BRT”. Trains could operate with essentially the same infrastructure. So could cars or bicycles or people or anything else that moves.

“BRT Stations”

We’re told that BRT “stations” can include such amenities as “artwork”, “customer information”, and “lighting”. That they can be “attractive and safe”, “permanent, substantial, and protected from weather”. It gives us a range of design possibilities, most of which look like nice bus shelters already do.

BRT station design

What’s this bus doing here? I thought this was the train station!

Most importantly, it tells us that a typical spacing between “stations” is 1/4 to 1 mile. This is the real meat of the difference between BRT and “local service”, and it’s taken us 3/4 of the presentation to get to it.


Basically, yes, you can still write all over the stations and vehicles. BRT is not made of Teflon so your logos will stick just like they always have.

branding options

BRT will strut for you.

“BRT Service Plans”

This pretty much lists everything transit can be– from omnipresent frequency to peak-only, stops spaced far apart or close together, local service or express.

things transit can do

You can have BRT where and when you want.

Closing Thoughts

BRT as I understand it in theory has one critical difference from most transit lines we have in Cincinnati. Higher average speed brought about by less frequent stops and a designated transit only right-of-way.

Any other differences are imagined or branded. Indeed, this whole slideshow has amounted to very little more than an enumeration of what is possible with any type of transit. I said earlier in the post it looked like it was put together by a student researching BRT. I take that back. It looks like it was put together by a student researching transit generally and presenting to an audience who hasn’t heard of such a thing before.

If clean, safe stops are a good thing to have, why should BRT lines be the only ones to have them? If level, multi-door boarding and off-board payment are good things to have, why shouldn’t any other line have them too? If running in an exclusive right-of-way can make transit faster, why should we limit such a boon to only certain lines?

And further, if the qualities of BRT that we’ve heard make it special, that differentiate it from other lines are so flexible as to be completely optional, to be implemented one at a time as we can afford them, why can’t similar incremental improvements be made to any line as the funds are available?

It seems then like “BRT” is a brand more than anything. It’s a look to be slapped on a transit service, like the Southbank Shuttle’s  self-conscious ‘trolley’.

southbank shuttle

It’s a forced distinction and ultimately an ambiguous, unnecessary and possibly confusing one. It’s already resulting in maps that, like the streetcar’s, completely ignore the rest of the transit system:

BRT stands in glorious isolation.

BRT stands in glorious isolation.

That sort of cartography is indicative of a line that will itself ignore much of what already exists. Indeed, SORTA has put out some specific suggestions for BRT line routing and they seem to almost completely overlap existing ‘local’ lines:

proposed Cincinnati brt alignments

In this case the #33, #17, #78, #43, #4 & #11 but with a very, very different stop spacing:

SORTA transit proposal

This map is uglier than even yo’ mamma, and just as decontextualized as that joke.

What this means is potentially more of the same sort of confusion I’ve written about regarding TANK’s stop locations in Downtown with the shuttle stop disjunction. Where does one go to wait for the next bus in such a case? It’s not totally clear(without checking multiple schedules) whether you’re better off waiting for the #4 or the faster bus that won’t pick you up if you’re at the wrong stop.

Further muddying the waters is the complete silence on possible frequency for the new services SORTA is proposing. Since these new lines would be almost completely redundant to the main high frequency corridors, they would work best in compliment to them. I’m going to go out on a limb and guess that SORTA doesn’t have the money to operate these new lines at anywhere close to the frequency of the lines they duplicate(if they did have extra, they would already be spending it. It’s annual operatin funds.). That would mean they could either make ‘BRT’ by taking buses from the existing heavily used lines to run them with limited stops, decreasing ‘local’ service, or they could operate a very low-frequency high-speed line over the still-high-frequency lower-speed line. In the former case, we would have very significant service changes ahead, and ones that people who don’t live near proposed BRT stops will not be at all happy with. In the later case, one would have to wait a reasonably long time for the higher speed line, making irrelevant much of it’s speed benefit. It’s been well demonstrated that, all else being equal, people would rather get a slow bus with little time waiting at the stop than wait a long time for a fast bus. I’ll call it the at-least-we’re-moving effect. Psychology is crazy.

But the point is that if the frequency of the ‘BRT’ service isn’t high enough(and it can’t be without sacrificing ‘local’ service somewhere) then the best option people will have in many of these transit corridors will still be to go out there and wait for the next bus. It might be a higher-speed limited-stop bus if they are near a stop, or a line like we have now. Whichever comes first will be the one they catch. I do this between Downtown and Northside. There are a number of lines I can take to get out there but the one I choose is always the one that happens to get to Government Square first.

Beyond the stops though, the other substantive difference with the idea of BRT is the designated, transit-only right-of-way that prevents cars and stop lights and squirrels from getting in the way. It’s not at all clear where if anywhere this would be found along these proposed routes. In fact, the City has been extremely reluctant to yield even an occasional parking lane for bikes. I doubt they would be friendlier to transit. It’s also not clear whether the vehicles would get priority at traffic signals. Without the assurance that they could avoid most car traffic between stops the potential for substantively higher speed is significantly diminished.

My suggestion would be to improve the high frequency lines that we have by eliminating some stops, assigning a designated right-of-way where possible, improving technology on most or all lines such as with the signal prioritization, and investing(as operating money is available) in higher frequencies and longer schedules. This would have the added benefit of keeping the maps and schedules simple. If a different line is added over the #4 for example, and I just want to get from Downtown to Norwood, I might now have to check two schedules rather than one. Or worse, a new rider may well not realize there are two lines and only check the schedule for one of them, leading to unnecessary wait.

In conclusion, I’ll point everyone to the last words in that slideshow:

don't oversell BRT

Don’t do it.

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Posted in: Definitions | Maps | modes | Technology Choices
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On Coverage vs. Expedience, or why the #24 is slow

By looking at the routing of a transit line, one can with a little study discern the motives of it’s establishment. I’ll take SORTA’s #24 as an example. The #24 is a relatively infrequent line, but one with trips evenly spanning most of the day.

The #24

The #24 goes from Anderson Township to Downtown through Mt. Lookout, Hyde Park, Walnut Hills, and Corryville.

It travels a fairly corrugated route, going, as the crow flies, only about 9 miles but taking a full 19 miles actually on the street to do it. It takes an average total time end-to-end of about 70-80 minutes, meaning an absolute end-to-end average speed of 7.2 MPH(as the crow flies) and as it actually travels on the street, closer to 15.2 MPH.

I take the #24 as an example particularly because of it’s illustrative zigzag in Mt. Washington.

#24 in Mt. Washington

The illustrative zigzag

This deviation from Beechmont Avenue takes an additional 2.8 miles over a hypothetical course that simply follows Beechmont through Mt. Washington.

possible #24 allignment

This doesn’t actually exist.

That means it accounts for about 15% percent of the surface distance of the trip. If we assume that the vehicle’s speed is roughly constant(its not getting on the highway or flying through the air at any point), we may fairly assume that the deviation also accounts for about 15% of the trip’s total travel time, 11.3 minutes, and a decrease in potential average speed(as the crow flies) of 1.65 MPH(8.9 MPH potential vs. 7.2 MPH actual).

This feature of the routing isn’t dictated by topography, nor by the necessity of of driving a large vehicle or any other purely mechanical matter. Indeed, Beechmont just carries right on and the bus seemingly can’t make up it’s mind as to whether it prefers main roads or side streets. The reason this zigzag exists it to provide access to transit. In another post I defined ‘access’ as the end goal of mobility. I also said that mobility tends, all things being equal, to enhance access. Thus the route deviates to pass directly in front of supposedly somewhat immobile people to provide them access to mobility itself and thereby access to many other things. But all things are rarely equal.

This zigzag itself introduces significant delay into the trip of anyone not stopping on one of the streets off of Beechmont to which the line deviates. That decreases their potential for mobility by substantially reducing the real distance they can travel in a given time. It also means, in a world of limited resources, that money spent here (gas, driver wages, maintenance) isn’t spent in some other part of the transit system.

Map of the #24 showing 10 minute travel distance

Here’s how much farther you can go with an extra somewhat-less-than 10 minutes.

schedule of the #24

Numerical proof of the above

For people living off of Beechmont who do have the ability to reasonably get to Beechmont, it may significantly add to travel time as well.

The zigzag, and it’s possible absence raise the question of who the line is designed to serve. In it’s current form, the line indicates a choice for closer access to transit itself for the people south of Beechmont in Mt. Washington over the expedience of those coming from or going to Anderson Township. This indicates that SORTA sees the line as serving people to whom the challenge of getting to a stop on Beechmont is greater than the cost of their time. This could include several general categories of people. People for whom the cost of traveling to a stop is high include the disabled, the elderly or people carrying small children or heavy bags. Then there are the unemployed and unattached, for whom time is of relatively little cost.

It assumes that there are people who can’t or won’t come to a stop on Beechmont and that coming to them instead is justified. This is transit as a social service. Providing easy mobility to these groups is a legitimate public goal(as is providing food to the hungry), and one among many goals that transit should strive to serve. The #24, at least by this segment then, does not as much intend to serve people to whom time is more of a cost than somewhat of a walk.

The #24 makes another important assumption. It assumes that people live where they do and will continue to do so, even if where they live comes to have minimal direct access to transit and that such access is critically important to them. It’s perfectly plausible that if the line were moved to our hypothetical Beechmont-only route that over time people who needed very close access to transit and who nonetheless want to live in Mt. Washington would move closer to Beechmont. This would give us the best of both worlds by allowing the line to directly serve people who need access to mobility and chopping about 11 minutes off the total trip time for everyone passing through. It would do so at the cost of people who need access and live somewhat far from Beechmont; they would either have to move or suffer from more limited access. However it’s important to note that the cost of delay from deviation is an ongoing one, and the cost of inducing people to relocate would be felt only once, though surely over the course of several years.

People not as well served by the #24 include able-bodied people with jobs, families and other significant time constraints, people who would rather walk a few extra blocks than wait 11.3 more minutes. SORTA seems to have recognized and compensated for this to some extent. Running an almost parallel overall course is the 30X, a rush hour only line going(mostly) toward Downtown in the morning, away in the evening.

SORTA 30X route map

Lines like this, of which there are more than a dozen in the current system almost exclusively serve people making trips to Downtown offices in the morning and home to the suburbs in the evening. The times the 30X operates, departing between 6 and 7 AM then again between 4 and 5:50PM, make it useless for almost any other type of trip.

The 30X also operates at a significantly higher speed, bypassing much of the course of the #24(including the off-Beechmont zigzag)and completing the same end-to-end distance in 30-36 minutes, less than half of the time the #24 takes to complete the same (insert lots of qualifiers…) trip. The combination of these two lines gives us a transit corridor with quite specialized, and actually bipolar goals. On the one hand, we have a service with a fairly high speed trip between Downtown and Mt. Washington(via Beechmont) and Anderson Township that almost exclusively serves downtown workers. On the other we have a slow, meandering line between the same points that seems to want to serve many people with low time costs and high travel costs, door to door with minimal walking.

Is there some middle ground? Is there some middle transit customer? Or could both goals, access to transportation and access generally for a broader group of people be met by some other configuration of transit service? More to come! And more to come even even on the subject of the #24. We didn’t even get to the unique connection with Uptown!

Sources: SORTA’s schedules and Google Map’s little ruler tool. Please check my math!

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Posted in: Access | Mobility | Simplicity
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Why rail is sexy

I have a theory that I don’t think is going to be very well liked: Rail transit is as popular as it is in large part because it tends to have simplified diagrammatic maps.

People in Cincinnati tend to make extremely sharp mental distinctions between buses and railcars. The two vehicles are almost always completely intertwined parts of the same transit system, but because this distinction is so important to so many people, agencies tend to separate transit lines by type of vehicle and even put them on completely separate maps.

Here’s what maps for buses tend look like:

Baltimore Transit Map

A transit map of Baltimore

Old Cincinnati Bus Map

SORTA’s last official transit map, circa 2011

SORTA downtown transit map

This is the way SORTA sees Downtown Cincinnati

What do you get from looking at these images? Not many specifics of any value certainly. What overall impression do you get? I see complexity. These maps do a tremendously good job of conveying a sense of overwhelming and unclassified complexity. It’s like something from a scary movie about a dystopian techno-future, oddly devoid of the futurist UI designers so characteristic of that kind of flick.

Here’s what maps for rail tend to look like:

New York City Subway Map

One of at least a dozen versions of an iconic map. I’ll be surprised if anyone doesn’t immediately know what city this is.

DC Metro Map

In DC, most apartment listings mention proximity to a rail station more prominently than the address of the building.

london tube map

The classic London Tubes


What are your impressions on looking at these? We quickly start to pick the maps apart, understanding and remembering how the system is laid out. It’s simplicity conveys an image of the city as ordered, if large and complex, collapsible into simple overlaid and overlapping corridors. The stops are iconic and identified, each with a name we are likely to recognize.

Rail ‘systems’ if such we can call things divorced from the rest of their body, their buses and other vehicles, lend themselves to simpler, diagrammatic maps. The rails themselves, always less prolific than bus lines cover less ground with little or no necessary surface detail, and so are easier to map. Bus systems, always more extensive(Subways can cost upwards of a billion dollars per mile these days) with few exceptions tend to run on the surface and stop more frequently. This often means that stops, even major ones can’t be highlighted for fear of leaving off minor ones, and that the details of topography tend to dominate over the simple lines of a connected network. In rail maps, the network defines and distorts topography. In bus maps, the topography defines and distorts the network.

This is a strong message to send with the primary medium with which we convey the essential structure of the transit system. Particularly in cities with both rail based and rubber-tire based transit vehicles, the first message sent by these maps is that rail and bus are essentially different and dissociated things. The second thing conveyed is the nature of this supposed distinction. We see that rail is able to convert the city into an easily discovered and sensible network of connected points and that bus makes a thorough mess of the city, indeed that it conveys nothing so effectively as it’s own complexity and encumbrance.

This is a big part of why we’re getting a streetcar. The confusion promoted by the night-and-day difference between rail and bus maps leads people to believe on an emotional level that rail transit is essentially different from and better than bus transit.

Here’s a quick local example:

Cincinnati Streetcar map

Map of the Cincinnati Streetcar provided by the City

My own version of the streetcar route map

Map of the streetcar in the context of other high frequency transit services. This is an honest attempt from when I was starting to work on the frequency map last year of a map of downtown transit line routing. I’ve just now added the streetcar in the same color as the map above. Can you find it?

Can you spot the difference now? Which one of these maps makes the streetcar seem like a primary, easy to understand and sensible service? Which one loses it among a dozen lines of equal weight and complexity? Which type of map is the city using to pitch the Streetcar? Do you think we’d have a streetcar if they had used the second map, putting the Streetcar in the context and syntax of buses?

The distinction people here make between rail based transit and rubber tire based transit is rooted, in a really fundamental way, on the types of maps that are used to convey two functionally almost identical services. There are a few other important and misleading distinctions other major cities have promulgated that lead to this misunderstanding, but more on that in another post. Also, just to be super clear, more on how rail and bus have very little in their essential natures that makes this distinction more than an academic one.

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Posted in: Design | Maps | modes | Talking about Transit | Technology Choices
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Rails: what it means to invest in ‘permanent’ infrastructure

I’ve heard a lot of talk around town that the Cincinnati Streetcar signifies an investment in permanent transit infrastructure, and that this permanence is the most significant feature of the project because it will stimulate economic development. It seems to be generally supposed that this couldn’t happen with any ‘less permanent’ technology than steel rails. This bothers me.

Permanence is indeed an important factor in deciding where to locate a home or business. We don’t live on clouds or ships after all, and to the extent that transit is important to someone’s regular functioning, locating near regular transit is important. If transit goes away one day, someone will be put off and some of their plans *ahem* derailed.

But while this talk about permanence is *cough* right on track, the connection between streetcar tracks and permanence is quite tenuous. Streetcar tracks aren’t the only way to signify a permanent commitment to a transit corridor and they most certainly are not the most efficient. A large new infrastructure investment isn’t necessary in many places for an equally significant private investment to occur, and streetcar tracks aren’t even all that permanent!

What do we mean when we talk about permanent infrastructure? Here in Cincy, it seems we’re trying to indicate that the city, or whatever relevant authority has put a foot down and said: “Here! Here we will have transit. Here on X street. Build your life here. We’ve spent $100,000,000 on rails and would be enormously peeved if we had to move them.” It’s a search for a symbolic commitment from authority rather than an assurance of necessity.

Does spending money on rail mean that transit service will continue to run on these rails no matter what? No it doesn’t. Cincinnati used to have an enormous amount of rail built into every major street. Every time construction workers tear up the pavement to do utility work you can see rail stuck beneath 4 inches of asphalt down there with the cobblestones and petrified horse manure. Permanent? Of course not! We have an extensive counterexample beneath our feet. There is nothing intrinsic in rail that makes transit service on them permanent. If there was, we would necessarily still have streetcars and a subway.

Cincinnati Subway

Where’s your subway now, Cincinnati?

But let us suppose for a second that rail does indicate that some level of service will perpetually exist. Does this mean that service would be frequent enough or late enough or fast enough to be of any value? Transit isn’t absolute. Just ‘having’ transit service doesn’t mean that you have good transit. King’s Island ‘has’ transit. It runs about twice a day and only in one direction at a time. Would you build your hipster art gallery out there? Or would you rather build it somewhere where there is service in both directions every 15 minutes throughout the day? The level of service is determined not by built infrastructure but by operating funds, something seemingly more fickle and prone to shrinking than my budget for shoes. Rail neither necessitates the presence of transit, nor a useful level of speed and frequency.

A lot of the discussion I’ve heard about all this seems to hinge on the idea that bus lines can change while rails lines cannot. This is misleading. First of all, this city has quite a few choke points created by the way it’s laid out as clusters of density among hills. We’re no Chicago or DC where any parallel street replaces another. The convening of transit lines at the intersection of Vine and McMicken in OTR is a great example. Could any transit line go up the northern hill of the basin without passing through the Vine-McMicken squeeze? There are no parallel streets, and so Vine-McMicken is for buses the most heavily travelled intersection in the region, seeing hundreds of buses each day. Cincinnati also has a great network of business districts surrounded by dense housing that have been established for more than a hundred years. Could any transit line reasonably pass through Clifton without going down Ludlow? The thought is absurd. Does Ludlow need rails for it’s people to invest in businesses serving transit users? Transit, as long as transit exists, will always serve the places like Ludlow where it works well. It will do so not only because it makes sense, but because it would be more difficult to do otherwise.

Transit routes don’t change on a whim, and there are certain places that are so situated that as long as there is transit, they will be served by it. The area to be served by the ‘permanence’ of the Streetcar is the perfect example. We seem to be spending tens of millions of dollars to make a symbolic commitment to transit serving Downtown. But how could transit not serve Downtown? Where the hell else would it go? Do people suppose that SORTA might move government square to Mason? People aren’t stupid and shouldn’t need a rail reminder to know that if they want to start a business that serves people who use transit, Downtown and OTR are good places to start looking. Do we need to ‘see rails in the ground’ to know fountain square is full of potential transit users, that there will ‘always’ be transit there? I think not.

More on this in another post, but rail isn’t the only way to visibly identify and symbolically invest in a very particular route. Buses on the west coast for example are more likely to run on permanent overhead electric wires and other cities have experimented with painting bright paths on the streets or giving buses a designated lane or separated right of way.

Mission Street Bus

Buses on Mission Street in San Fransisco are attached to overhead electric wires, and come by every few minutes throughout the day.


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Posted in: Investments | modes | Priorities | Technology Choices
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