No Federal Aid to Transit Operations, Please

This is the third in a series of four posts about the poor state of political transit advocacy in the United States, following posts about the Green Line Extension in metro Boston and free public transport proposals, to be followed by an Urban Institute report by Yonah Freemark.

In the United States, political transit activists in the last few years have set their eyes on direct federal aid for operating subsidies for public transport. Traditionally, this has not been allowed: federal aid goes to capital planning (including long-term maintenance), and only a small amount of money goes to operations, all in peripheral bus systems. Urban transit agencies had to operate out of fares and local and state money. Demands for federal aid grew during corona, where emergency aid to operations led to demands for permanent subsidies, and have accelerated more recently as corona recovery has flagged (New York’s subway ridership is only around 60% of pre-corona levels). But said demands remain a bad idea in the short and long terms.

In the early 20th century, when public transport was expected to support itself out of fares, operating costs grew with wages, but were tempered by improvements in efficiency. New York City Transit opened with ticket-takers at every subway entrances and a conductor for every two cars; within a generation this system was replaced with automatic turnstiles and one conductor per train. Kyle Kirschling’s thesis has good data on this, finding that by the 1930s, the system grew to about 16,000 annual car-miles (=26,000 car-km) per employee.

And then it has stagnated. Further increases in labor efficiency have not happened. Most American systems have eliminated conductors, often through a multi-decade process of attrition rather than letting redundant workers go, but New York retains them. The network today actually has somewhat less service per employee than in the 1930s, 14,000 car-miles as of 2010, because fixed costs are spread across a slightly smaller system. Compare this with JICA’s report for Mumbai Metro comparing Japanese cities: Tokyo Metro has 283,871,000 car-km (PDF-p. 254) on 8,474 employees (PDF-p. 9), which is 33,500/employee, and that’s without any automation and with only partially conductor-less operations; Yokohama gets 40,000.

Moreover, the timeline in the US matches the onset of subsidies, to some extent: state and local subsidies relieved efficiency pressure. In Canada, TTC saw this and lobbied against subsidies for its own operations in the 1960s, on the grounds that without a breakeven mandate, the unions would capture all surplus; it took until the 1970s for it to finally receive any operating subsidies.

Federal subsidies make all of this worse. They are other people’s money (OPM), so local agencies are likely to maximize them at the expense of good service; this is already what they do with capital money, lading projects with local demands for betterments figuring that if everyone else hogs the trough then they should as well.

Then there is the issue of wages. Seniority systems in American unionized labor create labor shortages even when pay is high, because of how they interact with scheduling and tiered wage structures. Bus drivers in Boston earn around $80,000 a year, a pay that German bus and train drivers can only dream of, but starting drivers are in probational status and have a lower wage (they are not even given full-time work until they put in a long period of part-time work). Moreover, because drivers pick their shifts in seniority order, drivers for about the first 10 years are stuck with the worst shifts: split shifts, graveyard shifts at inconsistent intervals, different garages to report to. New York manages to find enough bus drivers to fill its ranks but only by paying around $85,000 a year; other American cities, paying somewhat less, are seeing thousands of missed runs over the year because they can’t find drivers.

And outside aid does nothing to fix that. Quite to the contrary, it helps paper over these problems and perpetuates the labor gerontocracy. New York City Transit has learned to react to every crisis by demanding a new source of income; there is not enough political appetite for transparent taxation, so the city and state find ever more opaque sources of funds, avoiding political controversy over wanton inefficiency but creating more distortion than a broad income tax would.

Instead of subsidizing current consumption, a developmental state should subsidize production. Don’t pay money to hire more bus drivers; pay for automating subway systems, for better dispatching, for better planning around intermodal integration. Current American wages, not to mention the unemployment rate, scream “invest in labor-saving technology” and not “expand labor-intensive production.”

76 comments

  1. fbfree

    You argue for a well-structured subsidy then? In that case, the question becomes what metrics should a subsidy pay for? The easiest would be to subsidize ridership, by providing say a fixed $1 per boarding, but only in systems with a free transfer policy.

  2. Eric2

    Federal subsidies for construction have the same issue (“it’s free money so let’s take it whether or not it does anything useful, if not it’ll just get spent elsewhere”). And you have the cross-over issue of “let’s build a useless trolley rather than improving bus headways, because the feds only pay for the former”.

    So maybe all federal transit subsidies should be ended. But then you still have federal subsidies for cars and roads, and incentivizing those over transit is bad. So maybe the solution is for the feds to stop paying for any form of transportation – instead, individual states or coalitions of states could tax themselves to build whatever projects they think are needed. But good luck achieving this politically.

    • Arlington Traveler (@ArlingtonTravel)

      @Eric 2, the problem is not with federal subsidies for capital. For the most part they go to good projects as the competition for available $ is stiff. The issue are twofold.

      First, American’s aversion to taxation means there simply haven’t been enough $$ to operate the better bus headways. Our transit spending per capita in many middle sized American cities are insanely low. Couple that with high labor costs, much of which is driven by employee and retiree healthcare costs which agencies have little control over (and union’s won’t give up their health benefits and rightly so)

      Second, is that our average residential population densities are insanely low so even if you half the headways on bus routes, you’d be lucky to get a 25% increase in ridership. I’m a big advocate for operating good transit where there is demand, and laving vast swaths of suburbia unserved until they densities increase and the pedestrian and bicycle infrastructure is built.

      • Eric2

        “For the most part they go to good projects” – lol.

        “American’s aversion to taxation” – Americans do want to get places. The problem is that roads are paid for with their federal taxes, so then the question is, why tax yourself a second time for transit when you already have roads. Understandable, but it would be great to change those incentives.

        “our average residential population densities are insanely low so even if you half the headways on bus routes, you’d be lucky to get a 25% increase in ridership” – It depends on the place, but I think Alon (who has done the research) probably disagrees in general.

        • adirondacker12800

          American’s aversion to taxation
          Is because they have been told the myth that giving rich people more money will make us all rich. It makes rich people richer.

          roads are paid for with their federal taxes
          No they aren’t. And they only get spent on Federal roads. Which have a contribution from the state. When your exit from the Federal highway leads to a state road the state pays for that. It leads to a county road it doesn’t. The county roads and the municipal roads are paid for out of local taxes, usually sales and property taxes.
          If it’s restricted to passenger vehicles only, which is quite common in certain parts of the county it’s not eligible for Federal funding. If it’s a toll road, which is quite common in the Midwest and Northeast, it doesn’t either.
          Fuel taxes paying for road, either federal or state, is a myth almost everybody tells each other.

      • df1982

        Increasing off-peak headways to be closer to peak headways is low-hanging fruit. The marginal costs are small, as has often been pointed out here. If you already have all the buses, bus stops, depots and the like, then the only added cost is fuel and drivers’ salaries. The latter is also defrayed by less need for deadheading, split-shifts and the like. So your added costs might be such that even a 25% increase in ridership is still worth it.

        That’s the good thing about fbfree’s proposal to have a flat federal subsidy per ride (or passenger mile so as not to perversely incentivise short trips). Local agencies would try to find ways to economically boost ridership, and increasing off-peak frequencies is a great way of doing this.

        The problem with Alon’s “no operational subsidies” line is that it creates situations where cities build lavish infrastructure with federal dollars but then run self-destructively low frequencies on them to try to contain opex. Going to 100% local funding would also exacerbate the problem with city administrations surrounded by transit hostile suburban counties, which makes it hard to provide service in a coherent manner.

        • Alon Levy

          The flip side is that the presence of OPM leads these transit-hostile county and state administrations to extract funding from transit agencies that want more service, in effect using federal money for road widening and maintenance greenwashed as BRT. The origin of bus lanes in FHWA engineers who hated public transit unless it was peak-hour buses doesn’t help.

          • df1982

            If the OPM is tied to ridership, though, then the agencies have to “earn” it (by getting more riders) rather than simply extract it through political machinations.

            Actually the bigger downside is that it exacerbates cost-cutting spirals when ridership dips due to external events (economic crises, pandemics and the like). But perhaps some kind of rainy day fund can be set aside for these moments.

          • Alon Levy

            True. But at least the demands being made by agencies and activists are specifically not about ridership. They’re about random demands; in Phoenix apparently the demand is to add a second crew member on every light rail vehicle to watch over passengers and handle conflicts.

          • Richard Mlynarik

            The flip side is that the presence of OPM leads these transit-hostile county and state administrations to extract funding from transit agencies that want more service, in effect using federal money for road widening and maintenance greenwashed as BRT. The origin of bus lanes in FHWA engineers who hated public transit unless it was peak-hour buses doesn’t help.

            I don’t see how the BRT bogeyman plays any role here. (Show me on the doll where the bad bus touched you inappropriately!)

            US “public” agencies running rail do exactly the same thing, I could give you hundreds of examples from Caltrain and San Francisco Muni, but who needs to hear that again? (I mean like in 2022 seeking to spend $350 million for bridging one pair of railway tracks over over one single road, in a way that is actively incompatible with placing four tracks, actively incompatible with grade separating adjacent rail/road crossings, and then … planning to run one train per direction per hour heads except at weekday commute hours? Death is far far far too kind a fate.)

            It’s all greenwashed earmarked funding. Nobody cares what’s built, nobody cares if it’s used, nobody cares about capital costs (except maximization), nobody cares about operating efficiency.

            Incinerating dumpters full of cash is the sole aim, no matter what superficial vehicle mode is the supposed justification.

  3. plaws0

    I don’t want people being fired in the name of efficiency. But here’s the thing – everyone has a buyout price. If you dangle enough dollars per displaced employee, even if it’s several years’ salary, they will take the cash and find other gainful employment. *And* will probably *still* be cheaper than letting them attrit away.

    Yes, more labor-saving tech, please. I’ve heard that in the face of paying burger flippers $15/hr that they are mechanizing a lot of the actual burger flipping. Works for me as a customer: I’d rather have 3 employees making $15/hr than 6 making $7.50. Not that $15/hr is a great wage, but you get they idea.

    If they ever get the CBTC working on the L and the 7 trains, it will be interesting to see if the MTA actually learns anything from the endless projects. Will they speed up the trains and increase productivity? Or will there just be endless delays because of “CBTC failure” because they don’t maintain the equipment?

    • Alon Levy

      The L and 7 are already CBTC-equipped. NYCT chose not to use this to speed up the trains, but rather to slow them down to reduce brake wear (P.S. rolling stock maintenance costs are not unusually low on NYCT due to this). They also don’t run a lot of trains on weekends because of constant service changes.

      • plaws0

        I wondered. So those systems are in service but they don’t really make use of them. Sounds like PTC on “steam” roads. All the testing of primitive PTC in the 70s and 80s said that PTC would boost efficiency. The steam roads made sure that wasn’t the case.

      • adirondacker12800

        Does whoever told you they did it to reduce brake wear know that the R-10s, first delivered in 1948, had “dynamic” brakes in addition to pneumatic brakes? And that modern trains are regenerative?


        …. the braking system is “combined dynamic-electro-pneumatic”.

        • Stephen Bauman

          “And that modern trains are regenerative?”

          Yes and no.

          Regenerative brakes require a device to receive the power generated from braking. Electric vehicles use regenerative baking to charge their batteries. The idea for the NTT trains was that they would power another NTT train on an adjacent track. It never worked. They also tried to install stationary electrical mechanical batteries (flywheels) at a station and have them supply starting power to provide a boost to trains leaving the station. That also did not work.

          Unfortunately, the dynamic and pneumatic brakes on the NTT trains were sized assuming that regenerative brakes would work. This meant that brakes were wearing out much faster than on the old equipment.

          The MTA’s typical solution was to slow down the trains to compensate/hide the braking deficiency.

          • adirondacker12800

            Passenger trains have a “hotel power” load. Whatever it is, that’s better than dumping it into a resistor grid. According to nycsubway.org the New Technology Trains, the R-110s, were delivered in 1992 and have since been retired. They were prototypes. They didn’t fix this in in the R-142? Or the R-143? Or R-160, R-179 or R-188?

          • Stephen Bauman

            1. Most of what I’ve read refers to all the purchases based on the R110’s as NTT. This includes the R142, R143, R160, etc.

            2. There’s also battery power on subway trains. It’s around 37 volts and powers the control signals on all equipment from the introduction of the LV’s. This might be equivalent to “hotel power”. However, NYCT was hoping to reduce their power requirements by 20% or more. Powering the on-train batteries from regenerative brakes would not have come close to this achieving this goal.

            They thought they could drop the regenerative power directly into the third rail and have it picked up by an adjacent train. I thought this was a risky scenario from an electrical engineering standpoint. They would not know whether it worked until they had a fleet operating on an entire line. There were not two R110’s on adjacent tracks for concept testing. Their first test would be when the R142’s and R143’s were delivered and operating in quantity.

            They were trying to get the concept working for quite a while after delivery of the R142’s and R143’s. Resizing the friction brakes would require a redesign of the trucks. All I know is what I read from public sources. I believe they are using the same truck design on later NTT cars. They did not retrofit the R142A, trucks when the trains were retrofitted for CBTC operation. The only change I’m aware of was removing motors and brakes from 1 truck per 5 or 6 car unit to prevent slippage for distance traveled calculations.

          • anonymouse observer

            Are these NYC subway specific situations or in general in DC-electrified railways? I’m curious and hope this is only in NYC Subway because the regenerated electricity from the braking has been feeding power to other trains, and wayside solutions to store/repurpose/consume/burn off the excess regenerated electricity from the braking in other DC-electrified rail systems in other parts of the world. I heard that regenerative braking sometimes fails when the voltage on catenary/third rail becomes too high (i.e. low density lines with long continuous grades, no other trains accelerating nearby, etc.) but never heard that high-density system like NYC subway having constant issues with regenerative braking.

            By the way, why has these solutions which has been working in other properties been failing in NYC subway?

        • Alon Levy

          The issue isn’t power consumption, it’s that faster braking wears the brakes more and increases brake maintenance costs by a little bit. And in addition to what Stephen mentions, electric brakes are never perfectly regenerative, they save you some energy but there’s still frictional braking.

          • adirondacker12800

            If it’s working well the friction brakes don’t start to work until it’s going so slow the dynamic brakes are losing their effectiveness. It doesn’t matter, at that point, how fast the train was going a minute ago.

            I’m finding this all hard to believe. The electrical engineers at ConEd would have been deeply interested in this. And the electrical engineers at the MTA. And the electrical engineers at Kawasaki/Bombardier. And the pneumatic brake engineers at the brake companies who would have asked questions like “What happens during a blackout?” And that they didn’t put resistor grids under the R-142s or later trains.
            Accelerating trains realllly really fasts eats a lot of power in short amounts of time. Do that with too many trains the substation that was in installed in 1952 trips it’s circuit breakers and none the trains are accelerating. Volts times amp equals watts and even though third rail is chunky there are a limited number of amps you can shove through it at 600 volts. There might be that kind of stuff going on too.
            I’m finding it all hard to believe and suspect “public sources” is subchat.

          • xh

            “…electric brakes are never perfectly regenerative, they save you some energy but there’s still frictional braking”

            This is not true, however. Japan has been testing pure electric/regenerative brakes since 1997, and put them into revenue service on the Tsukuba Express trains in 2005. In China, metro trains with Siemens traction systems also have this feature since 2018. In these systems, frictional brakes are retained, but only as a fail-safe for emergency brake / parking brake application, so that there’s virtually no wear of brakes.

            The basics of regenerative braking is that the rotor in an induction motor is driven by the rotating magnetic field created by electric currents in the stator. The torque applied by the M-field to the rotor is propotional to the difference in their angular frequencies (velocities). So, the rotor will decelerate if the M-field is controlled to rotate slower than the rotor itself. As the rotor decelerates, at some point the angular frequency (velocity) of the M-field will reach zero. And if the frequency of the M-field remains at zero, the rotor still decelerates, but at a decaying deceleration. This has lead to a myth that regenerative brakes aren’t good at low speeds.

            But actually, at low speeds the M-field can also be controlled to rotate inversely (i.e. against the direction of the rotor) such that the deceleration doesn’t decay anymore. Under this scheme, the inveresely rotating M-field must be cut out immediately once the rotor itself stops, otherwise it would accelerate reversely, which requires very precise speed measurement and motor control at low speeds – something not technically feasible until ~2000s.

            You may refer to this paper for some details:

            Click to access CR02060FU.pdf

          • adirondacker12800

            ……Even it’s if 1960 and you are doing the dynamic braking by switching relays around, it doesn’t matter how fast the train WAS going before it becomes less effective.

    • IAN! Mitchell

      “I don’t want people being fired in the name of efficiency.”

      Well, I do.

      • plaws0

        So you’re a jerk. OK. I didn’t say don’t get rid of dead weight, I said don’t just fire them. Buy them out. Much less drama that way and you *still* save money.

      • Luke

        Isn’t the ultimate idea with efficiency in transportation to offer more? Reduce operating expenses? Great; increase service. Increase ridership? Wonderful; invest in infrastructure upgrades. Otherwise, it’s just cost-cutting.

      • df1982

        On segregated busways it could likely be done right now on a technical level. In mixed traffic areas where you have to deal with pedestrians, cyclists and the like, probably never.

        • adirondacker12800

          when fusion power is cheaper than alternatives. though I have more hope for autonomous vehicles

      • Henry Miller

        About as far away as driverless cars – there are only trivial differences between the two. If your driverless car is safe in normal traffic then you put it on a bus and you are good to go. I know that the companies working on this have lots of partnerships so I expect that in a few years of it on cars it will be one buses.

        10 years ago I said about 10 years. Obviously I was wrong, I refuse to make more predictions. Those working on it have made great progress, but only in very limited situations, I’m not sure if they can expand to buses or not.

        • Henry Miller

          I’m going to backtrack on that a bit. Driverless cars are in some ways limited because you just might drive on some weird road. The Bus companies in partnership with the big auto manufactures (who are funding development for all cars) have a big advantage over cars: random cars. The only thing they need that a car doesn’t is the ability to tell if someone near the road wants to get on, not a difficult problem to solve.

          From there you order a bus, it still has a steering wheel (used to get from the factory to your depot), and some time before engineers come to map the route(s) you want it to drive one. They will gather whatever data they need, tell you about traffic lights to upgrade, and other corrections needed to your city to make it possible.

          Taxi service in the likes of San Fransisco is already starting, so things are close. Though from close to here can still be a while

        • Sascha Claus

          If your driverless car is safe in normal traffic then you put it on a bus and you are good to go.

          You can put it on a bus even earlier if you use it only in low-traffic areas, like suburban feeder routes. The transit company has more control over where it sends its bus than Google has over where somebody drives their driverless car; so a bus can easier be restricted to ‘driverless operation only on such and such roads’ and still find a buyer.

          • adirondacker12800

            If you have self driving cars you give the few people using the low frequency short bus a smartphone and free cabs rides from home and one or two can loiter at their destinations.

    • Stephen Bauman

      CBTC does nothing to increase service level capacity (maximum tph or minimum headway). This is determined by rolling stock and track geometry characteristics, as well as station dwell time. The accepted figure is somewhere around 44 tph for existing equipment with a 30 second dwell time at each station. The existing block signal system can handle 40 tph, provided trains are operated in a manner that is consistent with such operation. Such operation requires a level of train supervision (keeping trains on schedule) that is beyond NYCT’s managerial and operational capabilities. NYCT overcomes these deficiencies by reducing maximum service levels to 30 tph or less. Systems like Moscow and Paris that exceed the 30 tph threshold use positive train supervision methods (keeping operating trains on schedule) that provide frequent periodic feedback to every train operator whether they are ahead or behind schedule.

      There is an optimum speed to achieve service level capacity. Deviating above or below that speed will result in decreased service level capacity for given rolling stock characteristics and dwell time. That speed is between 12 and 37 mph for 40 tph operation. This means that operating trains at 80 mph on 90 second headways is not possible, even with CBTC. Similarly, if a line has a speed restriction below 12 mph, due to a downhill or curve, it will result in a capacity reduction.

      • Richard Mlynarik

        To a shockingly large degree, “CBTC” serves as massively (massively!) expensive cover for “shorter track blocks” (and/or “finer speed control” and/or “more accurate braking curve models” — but mostly “shorter blocks”.)

        In practice these things can be separated, and often are by technically competent operators with sound engineering-economic priorities.

        But most it’s “why analyze where to install a few extra loops or balises when instead we can spend several hundred million on a tailored special-needs one-off CBTC system with a special-needs all-new one-off radio system that theoetically localizes trains to the metre (but in reality is operated by chimps and results in lower availability, equal-or-worse train throughput, and exploding maintenance cost)?”

        • Stephen Bauman

          CBTC’s small block length advantage is a myth in practice. That’s because the only place/time that accurate train position needs to be known is when trains are close together. That occurs only at stations. Block lengths in NYC are quite short approaching station stop points (100 ft and sometimes less). 600 ft trains traveling at 30 mph with 90 second headways are 3450 feet apart. Knowing their relative positions to the nearest 100 feet is unnecessary.

          CBTC’s position uncertainty is a lot greater than a meter in practice. The train has to communicate its position to the central computer. It is polled by the central computer. The system is tolerant of missed communications for up to 2 seconds. This means a train’s position approaching a station at 30 mph (45 ft/sec) could be up to 90 ft off before alarms go off and trains go into emergency. That’s pretty close to a conventional short block length.

          CBTC is a car builder’s dream. All the equipment must be replaced because a single non-CBTC train will force the entire line to operate at the auxilliary wayside system’s (AWS) service level. That’s 3 tph for the 14th St and Flushing Lines. All the old signal equipment makers have been purchased by rail car builders. Nobody is offering existing block system upgrades, using modern and inexpensive components.

          There is a fundamental bias against using inexpensive solutions. People’s pay is based on how many people they supervise or the dollar value of the project they manage. Project management fees average about 1 to 1.5% of the project value. An inexpensive better mouse trap does not stand a chance.

          • adirondacker12800

            They don’t need new trains because they had R-142s? rebuilt to be R 188s with CBTC.

          • Stephen Bauman

            They don’t need new trains because they had R-142s? rebuilt to be R 188s with CBTC.

            Sorry for the confusion. I should have been more specific.

            I was hinting at retrofitting the SMEE fleet that had more body life in them. Specifically the R32’s. The LAHT car bodies rusted out. Budd stainless bodies did not. The cars could have had a gut rehab with new trucks and propulsion system. The R160’s were not cheap. A gut rehab on the R32’s might have been cheaper. PATCO is saving money by going this route.

            There will be a similar situation for the R62’s, when it’s the Lex’s turn to get CBTC. The car bodies are in good shape.

          • adirondacker12800

            Stainless steel doesn’t rust. It does crack. After you’ve been bouncing it around on subway tracks for 60 years.
            According to Wikipedia PATCO rebuilt their fleet in 2009. With scrap motors they had rebuilt. DC ones that have brushes that wear. Controlled by new fangled electronic power controller. That could be supplying variable frequency variable voltage polyphase AC to motors without brushes. That are sealed. Isn’t the usual progression is have a major overhaul around 20 years and evaluate if it’s worth it around 40? They had a major rebuild in 2009. They are going to re-re-build them 13 years later?
            The 142s were due for their 20 year rebuild, why not convert them to R-188s while it’s being done. The R32s were at “when do they start cracking?” So will the R62s when the new cars start to being delivered. I see that they will have open gangways. That would be hard to retrofit. It gives them a tiny bit more capacity. And since I’m old enough to remember passing between cars while they are in motion, has some other advantages.

          • xh

            “CBTC’s position uncertainty is a lot greater than a meter in practice. The train has to communicate its position to the central computer. It is polled by the central computer. The system is tolerant of missed communications for up to 2 seconds.”

            Most CBTC systems correct position of trains by fixed transponders mounted on the tracks. Typically these transponders are at most several hundreds of meters apart. In between these transponders, trains locate themselves by axle-mounted speedometers, accelerometers or radars, which gives a roughly 1% of error. 1% of several hundred meters is several meters, which is definitely not “a lot greater than a meter”. And within the station, transponders may be ~30 meters apart, leading to a less-than-half-meter positioning accuracy – accurate enough for the operation of platform screen doors.

            As for “missed communications for up to 2 seconds”, one should notice that this lag also exists in conventional signalling. Take track-circuit based cab signalling / automatic train control (ATC) as a instance: On WMATA, ATC codes take the form of low-frequency (1-10Hz), on-off modulated audio-frequency (1-10kHz) signals. For redundancy, the on-board computer must receive and decode 5-10 cycles of such signals before it could “pick up” a favorable ATC code. That also leads to a lag up to several seconds, which is never considered to be a big problem.

          • Stephen Bauman

            Most CBTC systems correct position of trains…As for “missed communications for up to 2 seconds”,

            I wasn’t referring to how a train determines its position through the process of dead reckoning plus periodic correction that you described. I was referring to missed communications and comparing that to the current, archaic NYCT block system.

            NYCT does not use cab signalling. It uses wayside signals with relay logic. It’s not subject to the delays you described. Also, blocks are sufficiently short so that the operator can always see the signal for the next block. This removes the wayside signal delay vis-a-vis cab signalling that I’ve seen in several texts. As we used to say, when I worked in aerospace, “if it works, it’s not sophisticated.”

          • xh

            “NYCT does not use cab signalling. It uses wayside signals with relay logic. It’s not subject to the delays you described. ”

            Well, it is, actually. First of all, NYCT has train stops, which take few seconds to move before signal clears. Then, without ATC there’re still motorpersons, who take seconds to react upon wayside signal upgrades or downgrades. This introduces an unpredictable amount of reaction time. Under ATC or CBTC, they are taken out of the loop at the cost of introducing a comparable but consistent lag, which still looks like an improvement.

            That said, “if it works, it’s not sophisticated” is the exact philosophy of the railway signalling/automation industry. There’ve long been successful “automatic” trains operating under simple yet highly reliable physical rules, electrics and electronics (up to SIL4 certification). No one would even try the approach the automotive industry is currently trying (and creating tons of new problems) – i.e. to make trains “autonomous”. No one would ever install cameras onboard a train to determine whether a wayside signal is green or red, by using some artificial-idiot based algorithms. Instead, they just simply replace wayside signalling with in-cab train control systems, under which the position of all trains are known (to various uncertainties) on which braking distances calculations are based.

      • xh

        “There is an optimum speed to achieve service level capacity. Deviating above or below that speed will result in decreased service level capacity for given rolling stock characteristics and dwell time.”

        This is not the case for CBTC (or ETCS level 3 or any moving-block signalling), but for convetional fixed-block signalling, including those under a distance-to-go principle (also known as quasi-moving block).

        Under fixed-block signalling, the exact position of a train is not taken into braking distance calculation by the following train. The following train only “sees” (with the help of wayside component of the signalling system) whether a block is occupied or clear, and it must stop before any occupied block. Under the worst case senario, the following train must be a braking distance plus the length of a fixed signal block apart from the previous train. The headway, on the other hand, is

        t_{headway} = ( L_{block} + L_{braking distance} (v) ) / v

        By law of motion, braking distance = v^2/(2*a), in which a is the deceleration. This lead to a function:

        t_{headway} = L_{block} / v + v / (2*a)

        that has a minimum at v = \sqrt{2*L_{block}*a}. For a 100-meter-long signal block (typical for mainline rail) and a train decelerates at 0.8m/s/s, this is roughly 40 km/h.

        Under moving block signalling like CBTC, L_{block} can be reduced to the length of a single train, which, on the other hand, rarely exceeds 200 meters on most transit systems. Using the same formulae and by assuming a transit train can decelerate up to 1m/s/s, the speed maximizing the capacity is found to be at most 20km/h. No trains would be operated at such a low speed. Thus within the feasible speed range, moving block signalling gives a capacity that always decreases with speed.

        Of course modern moving block signalling doesn’t deliver full “moving block” capacitcy everywhere in the system. I’ll explain later in a separate post.

        • Stephen Bauman

          My derivation for the dependence of headway on train speed is independent of any signal system. Here’s a reference to it, that I posted below to Mr. Eric2.

          Click to access SafeMinimumHeadwayOnASingleTrack.pdf

          Assume the leader of length L passes x=0, while traveling at velocity v. Assume further the leader travels to x=L and stops suddenly due to “circumstances beyond his control.” So far, t1 = L/v seconds have elapsed.

          Assume the follower is also traveling at velocity v and knows of the leader’s predicament with no delay. The follower applies the emergency brakes and will stop in t2 = v/a, where a is the emergency braking acceleration.

          If the headway is greater than t1 + t2, then a collision will be avoided.

          t = t1 + t2 = L/v + v/a (eq 1)

          Set dt/dv to 0 and you get a minimum value of t when v = sqrt(aL) (eq 2).

          This shows a dependence between minimum headway and speed.

          This simplistic model can be extended to complications that include: stations; dwell time; location uncertainty; signal system delays, etc. Lang and Soderberg present a much more detailed derivation in Appendix I.

          • xh

            Great effort! But there’re oopsies in your derivation:

            In your “simple case”, you did a great job in finding the minimum distance the following train should be from the leading train, by assumpting that the leading train may suddenly stop anywhere. In the context of moving block signalling, such a model is known as “bumping into the hardwall”; another model taking the best-case braking distance of the leading train into consideration is known as “bumping into the softwall”, which permits greater capacity but has safety concerns – there’re literally no best-case braking distance – and sees no revenue service. The minimum distance is calculated to be:

            L + \delta * v + T_{s} * v + v^{2} / (2 * a_{EB})

            The problem is that, the senario that enables to minimum distance calculation does not necessarily describle the headway. The leading train is assumed to suddenly stop anywhere, so the following train can never be too close to it, regardless of its status. But under routine operation, the leading train won’t stop. Instead, it just rolls at velocity v along the line, as well as the following train. The headway is defined as the time elasped when the following train travels to where the leading train used to be, in the same pattern without any disruption. And clearly it’s:

            (L + \delta * v + T_{s} * v + v^{2} / (2 * a_{EB})) / v = L / v + \delta + T_{s} + v / (2 * a_{EB})

            That’s why you’re missing a factor of 1/2 in the last term.

  4. adirondacker12800

    If you have a train coming through every 97 seconds, if you speed them up they crash into each other. Passengers aren’t very good at leaping on or off moving trains and they have to… this might be a shock to you… stop the train at stations. Pesky pesky passengers. Think of all the trains they could be moving through if they didn’t have to stop, open the doors, let people off and on, close the doors and start moving again.

    What did more for what is difficult to define. They went and built Hudson Yards, on the 7 train, which gave them more turnback capacity. It’s unclear if the system with 1950s RFID tags would have coped just as well with it. Supposedly the constraint on the L train is how fast they can turn around trains at 14th and 8th. No amount of electronics is going to fix slow switches and creeping into the terminal.

    • df1982

      You’re really outdoing yourself with the moronic arrogance here. There are plenty of systems in the world that run frequencies of ca. 90-100 seconds, at decent speeds, without them crashing into each other. Moscow, Paris, Tokyo, London, just to name a few. There is literally no reason why the New York subway can’t do the same with the right technology (and a minor amount of infrastructure improvements and de-interlining).

      • plaws0

        “It Can’t Be Done” – soon to replace E Pluribus Unum as the US national motto.

      • adirondacker12800

        The Flushing a.k.a the 7 train is isolated from the rest of the system. There’s nothing to “deinterline”.
        Wikipedia and nycsubway.org don’t say what the length of the line Flushing line/7 train is. You have an employee timetable that has the chaining for the Flushing line? So you can tell us what the average speed is? What’s the average speed of the line or lines you claim are faster?
        Do these other lines have local and express service? The expresses on the Flushing line are faster. I come up with a 32 minutes for an express and 36 for a local.
        Looking at the schedule which has almost three hours of “it’s coming soon, we don’t publish exact schedules” the 6:37 express leaves Flushing and makes it to the other end of the line three minutes before the local that left Flushing at 6:33. Get lucky and the bus gets there a bit early I could take the 6:31 express that gets there even earlier.

        • Eric2

          If 1) frequent headways are needed and 2) expresses actually interfere with this [which may or may not be accurate] and 3) the express only saves 4 minutes versus the local, then the solution is to eliminate the expresses.

          • Stephen Bauman

            Why not figure out, what’s required for delay-free merges before eliminating them?

            Let’s assume a switch is 300 ft long, has a 10 mph speed limit . This means a merging train would need to travel 300 + 600(train length) to clear the switch @ 10 mph/15 ft/sec. That’s a total of 60 seconds that the switch is occupied. Let’s assume trains operate at 30 tph or every 120 seconds. The switch is occupied for 60 seconds and idle for 60 seconds. If both the leader and follower are within 30 seconds of their scheduled arrivals, there will never be a merging delay. The switch is still occupied for 60 seconds but idle for only 30 seconds for 90 second or 40 tph operation. This means the leader and follower must be within 15 seconds of their scheduled arrivals.

            NYCT schedules are rounded to the nearest 30 seconds. This means 40 tph operation is impossible and 30 tph operation is problematic. The problem isn’t physical; it’s operational. Moscow and Paris have their schedules down to the second and provide clocks at every station to alert the train operator how he is doing vis-a-vis the schedule.

          • adirondacker12800

            A Flushing line local takes four minutes longer. In the time it takes to run 8 locals they could run 9 expresses.
            8 x 36 = 288
            9 x 32 = 288
            Rush hours don’t last 288 minutes but there is more than one local and one express running during peak hours too.

            The constraint on the Lexington Ave. lines is how long it take people to get off and on the trains. They’ve added platform agents to remind people that they can’t get on the crowded train until people off the crowded train. Reminding entitled people/idiots that they can’t get on the train until people get off the train doesn’t have anything to with the signal system, acceleration or braking or how the fast the doors open and close. I suspect that the major constraint on the Flushing Line is how long the doors are open at Queensboro Plaza and stations west of there. Pesky passengers. If it wasn’t for them the trains could run non stop between Flushing and Hudson Yards a lot faster!

          • Stephen Bauman

            “The constraint on the Lexington Ave. lines is how long it take people to get off and on the trains. They’ve added platform agents to remind people that they can’t get on the crowded train until people off the crowded train. Reminding entitled people/idiots that they can’t get on the train until people get off the train doesn’t have anything to with the signal system, acceleration or braking or how the fast the doors open and close.”

            I got involved with checking out the Lex, when the Second Ave Stubway was being considered. Somebody sent me the actual 1954 am rush hour service levels. They were about 33% higher than those reported in the SAS DEIS. I had to board a rush hour Lex express at Grand Central for a summer job in the late 1950’s. Those 1954 schedules were still in effect. They ran more trains per hour. They had platform conductors in the late 1950’s. However, those platform conductors controlled the closing of the vestibule doors on the LV’s. This meant that doors closed when all passengers crossed the door threshold. These doors remained closed until the train left, regardless of any new passengers running down the stairs onto the platform.

            I checked out the arrival/departure times for all the trains at the various stops to determine the reason for the reduced service level. The dwell time was generally within the 30 seconds permitted. There were many instances when doors remained open for long time periods (15 or more seconds) after all passengers had crossed the door threshold. One problem is NYCT instituted a clock for the conductors to keep doors open. That clock is set to 45 seconds regardless of whether the train is ahead or behind schedule. This excess dwell time problem is due to managerial shortcomings – not pesky passengers.

            Management is also to blame for disabling a feature on the NTT trains. This feature will reverse a closing door, if the edge is touched. It will repeat the reversal 3 times, without any conductor intervention. This is similar to the safety device that’s present in just about every self service elevator.

            Do the following thought experiment. There are 30 doors to close on a 10 car train on the Lex. Assume in any given second the probability for a passenger waiting to cross the threshold is p. Calculate the expected number of seconds to wait for all 30 doors to close if: 1 – each door operates independently – i.e. closes when there are not more passengers waiting to cross the threshold; or 2 – the conductor waits until there are no more passengers waiting to cross the door threshold at all 30 doors simultaneously and closing all doors at once. The answer is 1, for all values of p greater than 0 and less than 1. That’s the option that management disabled.

          • adirondacker12800

            So it’s a waste of money for them to have platform agents even though they claim it helps? Having multiple conductors stand between cars on foot steps that would make OSHA break out in hives yelling things at people that would get them fired today isn’t an option. I hear they were unpleasant when the train came out the tunnel and climbed up onto the El.

            It’s not 45 seconds.

            I had to watch the reflection of the doors in the window at one stop and stopped looking when it got to Union Square. I thought perhaps it was a very old video. It’s not. There are other ones. One of them. I guesstimated where it would be, was almost 30 at Grand Central and it’s even newer. It’s not 45 seconds.

          • adirondacker12800

            If I counted right the Flushing/7 express has 11 stations ( including the terminals ) and the local has 19. The local has 8 more stops and takes an extra four minutes. An average of 30 seconds for everything included in a “stop”.

          • xh

            “Let’s assume a switch is 300 ft long, has a 10 mph speed limit . This means a merging train would need to travel 300 + 600(train length) to clear the switch @ 10 mph/15 ft/sec. That’s a total of 60 seconds that the switch is occupied…NYCT schedules are rounded to the nearest 30 seconds. This means 40 tph operation is impossible and 30 tph operation is problematic. The problem isn’t physical; it’s operational.”

            First, there’s something called automatic train control (ATC), which includes the functionality of automatic train operation (ATO) and automatic train supervision (ATS). The ATS automatically dispatches trains while the ATO automatically executes the orders made by the ATS (under the protection of a third subsytem, automatic train protection or ATP). To reliably run trains at >30tph, at least part of the above mentioned systems should be present. This is especially the case if there’re scheduled merges.

            Then, the switch that has a 10 mph speed limit cannot be “300 ft long”. What might be “300 ft long” is not the physical switch, but the “interlocking”. As I’ve mentioned in an earlier post, even in today’s moving-block systems there’re a hand of places where trains don’t run under the moving-block priciple. Interlocking are one of the few exceptions. Since most of these systems are overlaid on conventional interlocking mechanisms, they observe long-standing interlocking rules.

            Under train-following scenario, since both trains follow the same route within the interlocking, the following train still operates under the moving-block principle. But in the case of merging or diverging- as you’ve noticed: Interlocking rules requires the leading train to be clear of the interlocking – usually of the “opposite” signals. Then the switches are unlocked and moved to correct positions, after which the next train can go beyond the governing interlocking home signal.

            But who says antiquated interlocking rules must be observed? In the last decade or so, the industry has been seeking ways to lift the constraints imposed by these rules. In urban transit, Alstom’s latest generation of CBTC (Urbalis-Fluence) works without conventional interlocking, while in mainline rail, SBB conceived what would be known as a “resource-centric”, “geometric” interlocking under the smartrail40 project.

            The approach is to divide a physical switch into three sections: the “movable” section that can be actually moved by the switch machine, the “fouling” section that is not movable but is still within the fouling point, and elsewhere where the moving block principles still works. Now, once the leading train clears the “movable” section instead of the entire interlocking, the switch just unlocks and moves, while the following train can go all the way up to the “fouling” section rather than have to wait before the home signal. Once the switch is ready, the following train is authorized to use both the “movable” section and the “fouling” section. So, under latest generation of signalling, the time to clear a 10 mph low-speed switch would be 100 ft (length of typical fouling sections) + 600 ft divided by 15 ft/sec, or ~47s, which will no longer impose a constraint on the overall capacity.

          • Stephen Bauman

            Then, the switch that has a 10 mph speed limit cannot be “300 ft long”. What might be “300 ft long” is not the physical switch, but the “interlocking”.

            Thank you for the correction; that’s what I meant.

            First, there’s something called automatic train control (ATC), which includes the functionality of automatic train operation (ATO) and automatic train supervision (ATS).

            NYCT does not have any of them.
            Moreover, they have schedules that guarantee merging conflicts. It wasn’t always thus.

            Our grandfathers operated 42 tph on the Third Ave El. There was a balanced merge on the downtown side between the City Hall and South Ferry terminals. The uptown terminals were 129th St for locals, Bronx Park for expresses and E 241st St for thru expresses. There were no storage tracks or yards on the downtown side. The Third Ave El was 3 tracks. The track in the off-peak direction operated at twice the service level as the peak direction.

            Whether one uses ATO, ATC, ATS or our grandfathers’ unsophisticated methods, the procedures require a certain level of precision, accuracy, [ and competence :=) ]. What I tried to show was a sufficient condition, in the mathematical sense. Namely, if on is within 30 or 15 seconds of schedule then there will be no merging delays nor reduced service levels. ATO, ATC, and ATS might be able to operate at more loose necessary conditions, in the mathematical sense. Namely, if the conditions are not met – merging delays and reduced service levels are guaranteed.

            I stopped with the sufficient conditions because I’m a lazy engineer and it was clear that NYCT had no chance operationally of achieving the sufficient conditions for avoiding merging delays.

  5. Charlie

    What kind of labor efficiencies can bus-based agencies create? I assume they’re already having only one operator per bus.

    • Alon Levy

      It depends on the agency. But, for the bigger ones that I’m familiar with (=NY, Boston):

      1. Better dispatching to reduce bunching.
      2. Bus lanes.
      3. Stop consolidation.
      4. All-door boarding.
      5. Regular annual procurement of buses to avoid spikes in maintenance needs.
      6. Integration of planning with commuter rail (both cities have bus-subway integration already).
      7. In-motion charging where appropriate (Boston has good trunks for it; New York doesn’t).
      8. Better crew timetabling to eliminate the labor gerontocracy.

      • Stephen Bauman

        There are capacity limits to at grade surface transportation. Anything over 100 intersection crossings per hour is problematic. NYC has exceeded them in several instances.

        There are 45 instances where they have scheduled more than 200 buses crossing an intersection within a single hour (data for 6 Apr 2022 – latest GTFS static bus schedule). All but 2 are in Queens. There are 150 instances of scheduling 150 or more intersection crossings per hour and 1582 instances of scheduling 100 or more intersection crossings per hour.

        None of the listed 8 points will address this problem.

        • Eric2

          I’m impressed by the knowledge you have displayed in this thread. Is there a book or reference or site, by you or others, where I can go to get more of the same kind of info summarized in one place?

          • Stephen Bauman

            Thank you for those kind words.

            I earned undergrad and grad degrees in electrical engineering more than 50 years ago. Any references I cite may not be useful to all people. I had an interest in rail transportation, like many EE’s of my generation who specialized in digital design/programming. I never pursued those transportation interests professionally. That may have saved me from following the transportation crowd.

            I first read about the service line capacity in “Urban Rail Transit Its Economics And Technology,” by Lang and Soberman, when it came out around 1965. I remembered that the signal system had little or no effect on service level capacity. I was therefore surprised by the CBTC hype, when it was proposed for the 14th St Line in NYC. I presented some of my views at NYC Transportation Camp in 2017. Here’s a url link to my PowerPoint presentation:

            Click to access CBTC+Presentation.pdf

            I also provided a simplified derivation of service level capacity at NYC Transporation Camp in 2019. Here’s a link to the derivation:

            Click to access SafeMinimumHeadwayOnASingleTrack.pdf

            My interest in bus transportation is more recent and parochial. A year ago, NYCDOT implemented a busway (no private vehicles except local deliveries) that started 2 blocks from my house. NYCDOT said they would not make the raw data for their evaluation public. I decided to capture and save the publicly available GTFS-RT data to evaluate their expected favorable evaluation.

            One thing I found was that neither NYCDOT nor the MTA could tell me was how many buses are scheduled to cross any given intersection during any time interval. The NYCDOT representative at a Zoom meeting assured me there were no more than 100 such crossings per hour along the entire busway, in a followup email.

            That’s a fairly easy question to answer, given the data that’s available in the MTA’s GTFS static bus route files, the centerline shapes of NYC streets and geographic information system (GIS) program library. All are available and open sourced (free to download and use with attribution) off the internet. Essentially every intersection that a scheduled bus passes lies between two bus stops. There’s information regarding the arrival and departure times at each bus stop in the MTA’s GTFS data. It’s simply a question of doing a linear interpolation based on the distance between the stops to find the bus crossing time at the intersection. I had a lot more difficult assignments during my professional career. As you might gather from my remarks, NYCDOT’s representative was mistaken between 6am and 10pm for those intersections.

        • Richard Mlynarik

          There are capacity limits to at grade surface transportation. Anything over 100 intersection crossings per hour is problematic. NYC has exceeded them in several instances.

          That’s true, and relevant, sometimes.

          But in so few other locations in so few other conurbations in North American is nearly any combination of routes coming close to hitting such (soft, mitigable to various extents) limits. There’s so much headroom for tighter headways and for several-times-higher bus ridership pretty much everywhere.

          That’s something that galls when the train fans (our gracious and mostly-correct host Alon not excepted) go on about lim →∞ of bus throughput/cost. It’s true, in theory, but of little practical relevance on most bus routes in most locations until most of us are dead and most of those intersections are under the rising seas.

          Amyway hey we finally got private cars off Market Street here in San Francisco … after 50 years.

      • anonymouse observer

        > Better crew timetabling to eliminate the labor gerontocracy

        I agree and think this is the biggest factor of inefficiency in the U.S. transit operations. the gerontocracy or hierarchy based on years of service allows agencies to do things which doesn’t make sense from efficiency standpoint like leaving a lot of full-time shift which are significantly shorter than 8 hour long (e.g.: driving for 3 hours and get paid as 8 hour day) and all weekend shifts being paid as all overtime (1.5x pay; discourage agencies to increase weekend service). Also, the gerontocracy does not help agencies when they need to lay people off as works with shorter years of service are the first one who get let go in layoffs regardless of one’s performance (wouldn’t save a lot by keeping higher-paying workers).

        One of the ways to eliminate this gerontocracy all shifts are put into rotation and everyone works in different shifts rather than allowing workers to pick the shifts based on the hierarchy, but potential solutions could be too radical and nobody’s favorite like nation-wide right-to-work or banning union shop system and/or craft/industrial unions.

        What would be the best solutions to eliminate labor gerontocracy?

        • Henry Miller

          In my opinion, once you have a route you are first in line to keep it so long as you want to keep it. Once you drive the 24 from 5:30am to 2:30pm (allowing for one hour of breaks in the middle) you always drive that, you know the people who always get on and ask what happened when they missed a day. If your route is canceled you are first in line for a different route on the same schedule – before someone with a lot more years who wants a different schedule. (but if you both want to switch schedules the other guy is first).

          Each shift gets a set pay no matter how many years you have in. There is nothing about 20 years of experience that makes you better than someone with 1 (less than 1 year and there is some training that you need to get yet so you are worth less), loyalty is worth about $.25/hr). People who work the “graveyard” shift are always worth more than people who work “9-5” (this is the least useful/paid shift as it misses both peaks when you need the most drivers). Those who do sick/vacation replacements probably are worth the most, though even then some shifts are worth more than others.

          Unions put too much emphasis on seniority. Mostly because it is all they have and everyone wants to feel better than others. There is really few ways to be better than another bus driver though – other than not doing the types of things that you should be fired for. This is one reason unions work well for bus drivers: you can’t get paid better than someone else based on merit. However that doesn’t mean we should let the unions force bad transit on us just because it isn’t possible to hire new drivers.

          Transit companies need to pay drivers a wage that will attract enough drivers. That might will be $80,000 in NYC to get someone willing to work otherwise bad shifts. IF you decide to switch from a bad shift to a good one your wages go down as there is more competition for that good shift.

          What I don’t know is how to make the union agree to this. Most of the existing members are benefiting from the harm they are doing to transit.

    • Richard Mlynarik

      What kind of labor efficiencies can bus-based agencies create?

      * More passenger-km per hour (= per vehicle-hour = per operator-hour)!
      = More vehicle-km per hour
      = bus priority, route rationalization, stop rationalization, POP, all-door boarding, etc … all the usual 50+-year-old solutions to blindingly obvious stupid obstructions.

      * More passengers per hour
      = higher average speed (above), more attractive network, more predictable service, takt scheduling, reliable transfers, lower headways, buses that aren’t out of some historical re-enactment of the 1970s and aren’t an active insult to riders, etc, etc, etc.

      * And then there are all the various rostering inefficiencies, union capture of local agencies, seniority sinecures, employees-before-riders priorities, etc

      Basic basic basic stuff. If you care, that is.

  6. Tom M

    Taking the OPM argument to its fullest extent, why aren’t there private mass urban transit systems in the US? At least for busses where private companies can react to demand/market changes to dynamically change routes, offer multiple price points and product offerings?

    • Alon Levy

      Good question! There was a lot of historic surplus extraction; John Hylan made it a point to drive streetcar and subway companies into bankruptcy. Recently, I raised the example of a Geary subway, which I believe is the strongest American subway line to be built that neither is an extension of an existing line nor heavily relies on connections to existing lines. It can be built, but government at various levels can extract and destroy the surplus.

      Buses are less vulnerable to this but are also a lot harder to make money on paying 21st-century first-world wages.

      • adirondacker12800

        Mayor Hyland had it in for the BRT because even when he worked for the BRT sending every El train in Brooklyn to the two tracks over the Brooklyn Bridge wasn’t working out. The five cent fare was driving them into bankruptcy without his help.

    • adirondacker12800

      They do in some places. It’s unregulated so more people decide it would be a good idea to compete. They go out and buy a used van, don’t insure it and don’t maintain it. Occasional fights break out over who was going to pull into the stop. It doesn’t work out well.

  7. Pingback: How to Waste Money on Public Transportation | Pedestrian Observations
  8. Pingback: How to Spend Money on Public Transport Better | Pedestrian Observations

Leave a Reply to plaws0 Cancel reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.