How a Single-Track Section Limits Headways on the Old Colony Trunk

Peter Furth, 3/8/2021


Single-track sections are common enough on branch lines, but Old Colony has a single track section on its trunk line, from just north of Andrew Station to Victory Road, a distance of 2.6 miles. It is well recognized that single-track sections limit headway; but how much? Here’s an analysis.

Data estimates are in red. Numbers in black are derived from them.


Length of single track: 2.6 mi. (From just north of Andrew Station to Victory Road)

Effective length of single track (add 1 train length (1000 ft) at either end): 3.0 mi.

Average speed in this section without stops:   40 mph, or 1.5 min/mi. So one-way travel time on the effective length is 4.5 min.

The section includes one stop, JFK/UMass, which adds 2 min to running time (accounts for decel delay, dwell, accel delay).

For determining the needed margin between opposite direction trains, see table. Schedule slack is to allow for variability in speed, delays, etc. Assumes a block for deceleration leading to the merge point.

Southern end Northern end
full speed mph 55 30
deceleration mph/s 1 1
decel time s 55 30
time at full speed s 27.5 15
decel block Length mi 0.420 0.125
time at full speed min 0.46 0.25
schedule slack min 4 4
oppDirectionMargin min 4.46 4.25


Minimum time between same direction trains: 6 min. (Dwell time + station clearance + slack for variability)

Minimum headway into which an opposite direction train can fit:

  • With stop at JFK/UMass: 2*(travel time + station delay) + (two oppDirMargins) = 2 * (4.5 + 2) + 4.45 + 4.25 = 21.7 min, call it 22 min
  • Without stop at JFK/UMass: 18 min. (People can transfer to Red Line at Quincy or Braintree)
  • Because we prefer headways that repeat every hour, aim for 20 minute service. Either give up the stop at JFK/UMass, or keep it while reducing the schedule slack to achieve a 20 min headway. Result: 3 trains/h on the trunk, i.e., 1 train per hour for each branch.

If instead we run 2 inbound trains followed by 2 outbound:

  • With stop at JFK/UMass: in each direction, 2 trains every (21.7 + 6) = 27.6 min, call it 30 min
  • Without stop at JFK/UMass: in each direction 2 trains every (17.7 + 6) = 23.7 min, still rounds to 30 min if we want clockface headways.

For this operation, nothing is gained by eliminated the JFK/UMass stop, so keep it. The service could be:

  • Every 30 min a Middleborough/Brockton train. This is the only branch with substantial ridership and serving a city beyond Quincy (Brockton)
  • Other branches (Plymouth and Greenbush) alternate every 60 min.