## A Model of Efficiency

December 30, 2011 by: Samuel Scheib

In the previous post I discussed the inherent difficulties of a radial system based on observations of many systems but also from my own work at the agency in Tallahassee where we took apart a radial system and created a decentralized, grid-like pattern.  Or at least as close to a grid as possible in the highly radial-oriented street network of Tallahassee.  After six months of operation, a difficult period including a couple tweaks along the way, we have a system that is working well and we are proud of.

My colleague was working on some numbers for our city commission (our board) and he was using raw boarding data to show ridership.  For those not familiar with transit data, a route that has service every 20 minutes should have significantly higher ridership than one running every 40 minutes, but if one accounts for the extra service provided (i.e. the additional cost to the agency) you may find the ridership between the two to be much closer to one another.  I asked him to use a measurement of efficiency, passenger trips per revenue mile, to see a truer measure of transit consumption.

The revised chart sent me reeling.  If you imagine transit on a Cartesian plane (all things being equal), raw ridership numbers would be much higher on routes with greater frequencies, but passenger trips per revenue mile would be the same across the board, i.e. twice as much service generates twice as much ridership and so forth.  But there is no transit service on the planes of Cartesia; we provide additional service where there are major destinations:  large apartment complexes, regional malls, low-income residents, universities and community colleges expecting a greater need and a greater return on our investment.

Chart 1. Sorted by efficiency

On chart 1 (click on it to enlarge) we see the radial routes in order from most efficient to least efficient by passengers per revenue mile.  The frequencies are written beneath the route number (30T means there is a peak-hour tripper, or 30-minute service in the morning and afternoon) and the first thing to jump out is that the second-most efficient route runs only once an hour.  The most frequent service in the radial system was 20 minutes, all day, on the paired routes 13 and 14, which served predominantly low-income, minority communities.  Those were the fourth and fifth most efficient.  There were three routes that ran every 30 minutes all day, the 23/24 pair and route 25.  All the others were either hourly, 40-minute routes, or had peak hour trippers.  Let’s reorder the chart by frequency.

Routes 23 and 24 were special cases, essentially campus routes operating between a large community college, dense student housing, and Florida State University (44,000 students), all of it west of the central terminal.  In short, most passengers on those two looped routes completed their trips before making it to the terminal and thus did not need a transfer.

Chart 2. Sorted by frequency.

Chart 2 shows us there is not a strong correlation between the amount of service provided and the level of use.  Two of the 40-minute routes are less efficient than 13 60-minute routes and as noted above the two 20-minute routes are 4th and 5th.  Looking at the same two charts from the new, decentralized system there is a very different picture  (note bene: the decentralized routes are mostly twice as long as the radial routes, so the reduction from 26 daytime routes is closer to 24 than the 12 routes shown on charts 3 and 4 would indicate).  Chart 3 shows the routes in order of efficiency,  chart 4 in order of frequency.

Chart 3. Decentralized sorted by efficiency.

Chart 4. Decentralized sorted by frequency.

What got me so excited when I first saw these charts was that the three 20-minute routes were clearly the top performers.  One of the things we have been telling the public is that with the new system an increase in service on any one route improves the whole system and that this was not true in the radial system.  The structure of a radial system is to have an originating route and a transfer at a central location to a destination route.   The 20-minute service on 13/14 and 30-minute service on 23/24 (campus routes) and 25 (serving a regional mall) were about capacity not mobility.  If we could have run 80-foot buses the additional service would have been largely unnecessary because all three of those routes were largely dependent on connections made at the bottom of the hour.  A rider might take the route 13 bus before the one that arrives for connections at the bottom of the hour because getting a seat was more likely but unless that person was going to a destination on route 14 (which included the 12,000-student Florida A&M university) the additional service did not get the passenger to the final destination any faster.

The decentralized system provides multiple paths for the same trip, so given the choice of taking a 40-minute route to connect to a 40-minute route or taking a 40 to connect to a 20, a reasonable and prudent person will always choose the latter.  Chart 4 shows this is what is happening.  In other words, despite the heavy investment in greater frequency in the radial system we did not see a corresponding increase in ridership.  In the decentralized system we are seeing that we do and that is a good return on investment.