A One-Track Mind

While at this point, we are almost assuredly beating a dead horse, until the Green Line Extension (Southwest LRT) is actually under construction, there remains the possibility it can be improved. While the best improvement (given the existence of an LRT to fourth ring Southwest suburbs) would be to route it along a path where people actually live, if we cannot maximize benefits, surely we should minimize costs.
I speak of course of the tunnel under the park.

Kenilworth Sections

Kenilworth Sections

The stated reason is the right-of-way is insufficiently wide to accommodate two tracks of LRT, one track of freight rail serving about 3 trains a day, a bike path, and the buildings that were built where it would have been convenient to run some more track.
There are two obvious solutions to this problem which have not been given serious consideration as far as I can tell.

First, the freight and LRT can share the track at different times. The experience with Northstar certainly demonstrates why having a few passenger trains on a freight railroad can create lots of passenger delay, but this is different; it would be a freight train on a passenger track owned by the public.

Everyone says “But, FRA”. I realize there are institutional barriers which need to be overcome. Perhaps those are more expensive to overcome than $130 million, or whatever the difference in the surface solution and what the tunnel will cost.

Second, if one-track is good enough for freight, why is it not good enough for LRT for a short section? (This is an idea previously considered by Matt Steele at streets.mn.) This of course is a tight fit, and may require waivers from appropriate regulatory authorities, but is physically possible from the drawing I have seen.

Section B-B existing, a pinch point

Section B-B existing, a pinch point


For the sake of argument, let’s assume we want to single track 1.5 miles, with trains going up 45 miles per hour (say an average speed of 30 mph to make the math easy). This would take 3 minutes. The trains are on 10 minute headways in each direction, or one train every 5 minutes through the bottleneck. (Note, Matt assumed 2 minutes, and higher speeds. I am using conservative assumptions).

If timing were perfect, there could be zero delay from this scenario. This is a deterministic case. That is the assumption underlying Matt’s post.

However, as we know, timing is rarely perfect, so we need to look at stochastic delay. Stochastic is engineering jargon for random. Random is engineering jargon for a case where multiple outcomes have an equal likelihood of being chosen (or some are more likely than others, but we cannot be sure that would be the case).

Even when things are random, that doesn’t mean we cannot ascertain the average of the distribution.

Let’s suppose we  have an arrival rate of 1 train every 5 minutes (our arrival rate lambda=0.2 trains per minute), and a server rate of 1 train every 3 minutes (mu=0.33 trains per minute). If the systems is completely random (and we certainly hope it is better than that), we can use stochastic queueing theory to estimate the delay.

Worst case (aside from someone actively and maliciously controlling the trains so they do arrive at the same time (which implies that deterministic solutions with zero delay are possible), we can model this as an M/M/1  queue (meaning, as wikipedia says: arrivals follow a Poisson process and job service times have an exponential distribution) . This assumes Markovian (random) arrival and departure processes and a single channel.

The utilization rate (rho = lambda/mu) is 0.6, meaning the server is busy 60% of the time.

Math gives us a formula for the average queue size:

Average queue size = rho/(1 – rho) = 1.5

Math gives us a formula for the average wait time :

E(w) = lambda / mu(mu-lambda) = 0.2/(0.333(0.333-0.2))=4.5 minutes

At 1 million passengers per month (12 million per year) for 30 years, this is 360 million people delayed 4.5 minutes=1.6 billion minutes of delay. At $20/hour, this is $533 million.

Clearly this value is larger than the cost of the tunnel.

On the other hand, perhaps we only need to single track for 0.5 miles.

In that case, the server time is 1 minute, so mu=1. Capacity utilization is 20% (i.e. rho is 0.2). Average queue size is 0.25 trains. The average wait time is 0.25 minutes.

Our 360 million people are delayed 0.25 minutes at $20/hour is $30 million. This is considerably less than the cost of the tunnel.

The train speeds could be adjusted so no-one would know they were delayed (i.e. trains would slow down approaching the switch, or be held at the previous station, as needed. And remember this is worst case, delay should be less than this with any competent schedule adherence. With perfect schedule adherence, they are indeed zero (our deterministic solution).

Single-tracking is a solution to high capital costs. It is not optimal. It has delay costs  that depend on the length of the stretch, headways, how much control Metro Transit has over running times, and so on.

Everything involves trade-offs.

There is of course a concern about running LRT next to (near) freight trains, carrying lots of explosive ethanol. I say, don’t do it. Run them at different times, even if on different tracks. If freight trains are only permitted at night, or in a mid-day window when an LRT is held upstream of the pinch-point for a few minutes, or ideally in a scheduled break, there should be zero chance of collision. There is always a chance of derailment – that doesn’t change, but derailment is less hazardous than collision for what I hope are obvious reasons.

In the long run, maybe freight will go away (e.g. once people stop using ethanol), go somewhere else, or another solution will be found. At that time, the line can be double-tracked if needed.

In the short term, the money saved could be used to temporarily relocate the trail to quiet residential streets nearby, compensate the neighborhood, give money to the Park Board, or any number of other socially worthwhile goals.


32 thoughts on “A One-Track Mind

    1. David LevinsonDavid Levinson Post author

      In the absence of the freight railway, there was enough room for two tracks at grade. Given the tracks are the same gauge, there must be enough room for 1 track with the freight railway. Some land near buildings might be taken, but not the building themselves.

    2. David LevinsonDavid Levinson Post author

      In the absence of the freight railway, there was enough room for two tracks at grade. Given the tracks are the same gauge, there must be enough room for 1 track with the freight railway. Some land near buildings might be taken, but not the building themselves.

      1. Matt SteeleMatt Steele

        It’s interesting how the Kenilworth neighbors changed their tune over the course of the planning. The anti-colocation sentiment was rather strong the whole time, but at first they were fine with a freight reroute with hundreds of LRT trains on dual tracks as an accepted replacement. Later on, it seems like some of them thought through what that meant, and instead preferred the idea of a handful of slow, if noisy, freights at grade in the corridor.

        Which leads me to my main premise… this should be completely doable politically. It solves the water table BS that MPRB is wasting my our tax dollars on. It keeps a double track profile at grade, which the neighbors already consented to. It saves us PILES of cash. It’s a no brainer.

        The only issue, which David alludes to, is that the FRA or FTA may balk at a freight track to LRT track centerline to centerline that would otherwise be fine for double track freight or double track LRT. I know private railroads have fought this on safety grounds in other states, but I think that was primarily to avoid the hassle of having new passenger service in their existing freight corridor. Well, HCRRA owns this track, so it’s not an issue of ownership. And if FRA or FTA had a separation issue, we could easily come up with some sort of compromise… maybe time separation of LRT and the most volatile freight loads in the same corridor. Or maybe a reduced LRT speed limit at times when a freight train is present in the corridor. These things can be overcome with a little compromise, common sense, and eagerness to solution.

  1. Monte Castleman

    I do like this idea. It gets even better when you use $16.00 / hour for a lost person-hour (the recommended Mn/DOT figure.) And good point that we might not be using ethanol for the 100 year life of a major structure. Battery car technology is completely inadequate for my (and judging by the sales evidently most) people’s needs right now, but in 100 years could get a lot better (or we could even go to fuel cells or Mr. Fusion or something not even dreamed of right now.)

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  3. Joe D

    Here’s a crazy idea. Make the 2 trails (biking and walking) into a shared use 10-12 foot trail. That opens up enough right of way to punch through two LRT lines.

    LRT lines with 12.5′ center to center, and center to edge of right-of-way = 37.5′

    10′ shared trail = 10′

    Total used rightofway = 47.5′ with the remaining 1.5′ construct a retaining wall between the trail and lrt?

      1. Alex CecchiniAlex Cecchini

        That’s basically what would have to happen to have 1 freight and 1 LRT track running through here with the trail remaining. I’m not sure that this configuration is really any better than simply having the connection from Midtown Greenway to Kenilworth use Cedar Lake Ave/Dean Parkway instead.

        I guess I really sympathize with the argument of this trail connection as-is being highly valuable. Certainly cycling doesn’t get the priority it deserves city-wide, and severing this completely grade-separated trail (one of the few we have) should be highly questioned. But if our options are squeezing cyclists/peds in a 10′ ROW immediately adjacent to LRT, building a $150m tunnel, or re-routing the trail to run through the Dean Parkway grassy median and along 2 city blocks of Cedar Lake Ave… I guess the latter would have been my preference. We could build a ramp entrance/exit from the parkway space to the Greenway and completely re-do the Cedar Lake Ave stretch to be 9′ lanes and mostly bike/walk trail for far less than the tunnel. If funding worked this way, we could earmark that money for the Greenway Streetcar project (maybe dedicate some of it to the additional cost of turf-tracking to maintain the “green” in the trench).

        Not a popular opinion, I’m sure..

  4. Obvious Oscar

    Remember that time when an LRT project managed to provide new and improved service to low-income communities (and political leverage for BRT projects to make the situation even better) while opening up a new route to stitch together two historically separated parts of the city, AND whose alignment’s most disruptive section was through a high-income White community (a massive historical anomaly if there ever was one) — and meanwhile urbanists, a self-styled “progressive” bunch, tried to stop the project at every step of the way?

    Following the support of Northside community organizations like Neighborhoods Organizing for Change, I for one have no complaints with this alignment. If building one short tunnel is what it takes for there to be political will to get this project done, that’s fine with me.

  5. Clay

    By everyone saying “But, FRA,” are you referring to the Federal laws that prohibit the smaller LRT vehicles running on the same tracks as the freight trains?

    I like that some people are beating this dead horse, but to get Congress to change those laws for the FRA would be a looooooong process (if ever). 🙁

  6. paul udstrand

    The current freight rail can only go 10 MPH because of the curve in the existing track. The reason those town homes would have had to come down was not only to make room for more track, but make a curve that can be taken at higher speeds for the LR. We’ve already decided that we don’t want to demolish buildings to make this work above grade.

    It currently takes around 15 – 20 minutes for 100 car long freight trains to get through that corridor (I know because I’ve had to stand with my bike waiting for the train to pass a few times). If you have 2-3 or more freight trains taking up the track for up to 60 minutes or more every day that will obviously create delays for the LR trying to run through every 3-5 minutes.

    I don’t where you got the idea that those freight trains are or can go 30 – 45 mph through that corridor. If you want to this you have to calculate the number of town homes that would need to be demolished, and the cost of acquiring them and tearing them down. Maybe that would still be cheaper than the tunnel but putting people out of their homes and tearing down property is off the table at this point.

    The other consideration is the fact that the freight and LR tracks aren’t the same. LR is electric and freight is diesel. Are they really the same tracks? The commuter rail isn’t electric so sharing those tracks is obviously not a problem. Is there anywhere else where electric LR trains are sharing tracks with freight like you suggest?

    1. Stuart

      There was one paragraph about freight and LRT sharing tracks, but the rest of the article (and mathematical analysis) was for a single track LRT next to a single track of freight.

      Nowhere in the article does he mention the speed of the freight line. The 30 – 45 mph figure is for the LRT.

      Finally, yes, the tracks are the same (from what I have read. Not an expert). The vehicles are different and the overhead power is of course different, but the two lines of steel attached to the ground are the same.

      1. I live here

        I hadn’t even noticed the proposal to hold freights to only running at night. The trains are run in the middle of the night, occasionally. When they do, the trains are often run at higher speeds. This increases the noise levels dramatically – you snap awake in the summer when windows are open. If it were a nightly phenomenon, the townhomes and apartments along the track would be dramatically affected by the increased noise levels. You would be talking, at minimum, MAC-level upgrades to make it tolerable.

          1. I live here

            I disagree that the existence of freight traffic here should been used over and over to argue that the primary characteristic of the corridor is a rail transit corridor. I’ve lived along the trail south of Cedar Lake Parkway for almost a decade and I can tell you that the lived experience is that it is a recreational corridor that features trains a few times a day. Its recreational value is enormous, not just to those of us who are lucky to live here. I don’t care that the land has been owned by HCRRA since Moses was plucked from the river; that is not how it is perceived and used by thousands of Minneapolitans. It would be fundamentally altered by co-lo. To paraphrase Ian Malcolm, you’re so preoccupied with whether you could that you won’t stop to think if you should.

            1. Adam FroehligAdam Froehlig

              By that logic, perhaps the Park Board should purchase the land from HCRRA so that it can be used for its current function instead of its originally intended function. Of course, that would require the Park Board and the city to scrape together money at a time when they’re claiming “poverty”…

            2. paul udstrand

              The prior existence of the freight rail isn’t being used as an argument, it’s existence is just a fact, and it was a fact when people choose to live near it.

              That being said, I agree with “I live here” basic premise that the LRT should go into a shallow tunnel in that stretch, and I’m willing to help pay for it as a taxpayer. The tunnel preserves the existing character of the area such as it is, and gets the LR through that curve efficiently.

              I think the idea of using one set of tracks for a LR going both ways may work in theory, but in practice I tend to think physics, weather, and changing schedules might be stronger than a spread sheet. I’ve seen smaller street cars and automated monorails using the same tracks to go both ways but larger full on LR might more problematic. Finally, if Mr. Levinson’s suggestion turns out to be a fail, the solution would require a complete re-do, so saving money now would cost more later or we’d be stuck with a crappy stretch that mucks up the entire SW corridor permanently.

              And “I live here” is correct, unlike the stretch up by the millionaire homes, THIS stretch brings the track within 30 feet of some of these properties so 200 trains a day would be much more problematic for those residents than for the millionaires.

              1. I live here

                I appreciate your nuanced take on the issues. I know that development can’t take every parochial interest into mind. I also think this route was chosen because it is obvious and presents fewer logistical headaches than 3C, and a post-hoc study was conducted to give it the green light. That’s in the past. Is it really fair to say that because rail runs through the corridor that we should expect that anything on rails can go through the corridor? I also have a street out front, which was there when I moved in. Would that make me a whiner or a NIMBY if Met Council decided to take out most of the trees, widen the street, and turn it into a highway? It’s the same process.

                1. Matt SteeleMatt Steele

                  While I agree this is a nuanced issue deserving of a nuanced solution, my point is that it seems really strange how the Kenilworth constituency changed its tune over the course of the last couple years. Just think how much different the corridor would be with dual track LRT at grade, which was the accepted solution without colocation.

                  I think the point of this article and my previous article (SWLRT Triage Now, Rehabilitation Later) is that the single track freight plus single track LRT would have basically the same Kenilworth impacts as the previous freight reroute plan.

                  When I hear about the legitimate concerns of the Kenilworth constituency, it’s clear to me that colocation does not describe the concerns.

                  The first concern, which was a concern from the start, is that sandwiching three tracks (colocation with dual-track LRT) would harm the nature of the corridor, adjacent properties, and the trail. Nobody is pushing for three tracks at grade. The point is that we could do this all with two tracks at grade, the same number of tracks as the freight reroute plan, while saving possibly nine figures that could be invested more wisely.

                  The second concern, which is new, is that moderately fast LRT trains plying the corridor at grade roughly every 5 minutes would harm the nature of the corridor. While that may be true, this is the component of the colocation argument that seems extremely disingenuous… because if SLP had taken the freight reroute, we would absolutely have two at-grade tracks with moderately fast LRT trains every few minutes. It seems like the Kenilworth constituency was fighting colocation without thinking through how LRT frequency and speed would impact the corridor, and then they went and changed their tune years into the planning process.

                  1. I live here

                    That may be true. I was involved in the public comment process for as long as I’ve been tuned in to the debate, arguing for 3C. I have always thought that two at-grade tracks in the corridor south of about 21st Street would be ruinous to the recreational value of that stretch of the corridor. Have you spent much time there? It has an urban wilderness feel not present anywhere else in the city except perhaps along isolated parts of Minnehaha Creek and parts of Wirth Park. Don’t get me wrong – it’s no wilderness, it’s an incredibly human-influenced landscape, but it is essentially separate from the motorized transportation landscape of the city. No more.

                  2. paul udstrand

                    I think it’s important to note that “Kenilworth” hasn’t been speaking with one voice, there are two Kenilworth’s, one is north of Cedar Lake Ave. and the is south the ave.

                    Matt is absolutely correct that behavior and consent North of the Ave. has been fickle and disingenuous. They pretend to have signed off on a trade for two light rail tracks and 200 trains a day in exchange for moving one freight rail with 2 trains a day over to SLP. That trade was obviously never really considered. It looks like the real agenda all along was to simply rid the entire corridor North of Cedar Lake Ave. of any visible tracks at grade. In other words, I suspect that even if SLP had taken the re-route, those residents would still be trying to push the LR into tunnels up there.

                    South of the Ave. residents seem to have been a little more consistent in that they never wanted their homes demolished, and their main concern was cramped and disruptive rail traffic close to their homes. Since the tunnel at that crunch point is a shallow one that doesn’t endanger any of the water features, and since the other concerns are perfectly legit, I can support the shallow tunnel and it’s costs.

  7. I live here

    You know, the most affected community isn’t the millionaires. It’s those of us who live in apartments on the pinch point, sometimes as close as 30 feet from the tracks. Compared to other apartment neighborhoods, we are stable and civically involved. We have middle class lives, kids, we take the bus and light rail and commute by bike, and we cherish our peaceful neighborhood. OK, maybe it is NIMBY, but the project as is makes no goddamn sense. Does it make more sense for it to destroy the character of this place because at-grade is a bit less than the cost of the tunnel?

    1. I live here

      By the way, when I say “destroy the character of this place,” I’m not talking about the disruptions of construction (e.g. University Avenue worries). The existing Green Line may have been a long construction project but it essentially added a new mode of transit to a heavily used transit corridor. The Green Line extension is turning an entire non-motorized transitway into a high-frequency commuter rail corridor. Having those trains above ground in the space where we live (yes, we live with a few freights a day, but those are slow-moving) would totally transform the feel of the place. It is more like running an LRT line through an alley.

      1. Nathanael

        They ran the Chicago elevated lines through alleys.

        Seriously, is there anyone who actually dislikes having a passenger rail line behind their house? I’ve never met one. People are paranoid about them before they’re constructed, but they never object after they’re built; rather, they walk to the station and ride the line. Freight lines are anotehr matter.

  8. Nathanael

    “First, the freight and LRT can share the track at different times.”

    Want to know the rules on that? Contact New Jersey Transit and ask about the RiverLine, which does this. It does some bad things to your schedule because you have to shut down LRT service overnight for the freight trains to run.

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