Local sensors

1
Local sensors
At (local) detector utms 20 km/u ! (18 gt
space mean) TT 3 min/km! (17 lt real TT)
Round 1 30 km/h Round 2 20 km/h Round 3 10 km/h
Average travel time TT 3.6 min/km So space mean
speed usms 16.36 km/u
Detector
2
Local sensors
At detector after 1 hour utms 23 km/u ! (17
gt space mean) TT 2.6 min/km! (14 lt real TT)
Red car 30 km/u Yellow car 20 km/u Blue car 10
km/u
After 1 hour TT 3 min/km thus usms20 km/u !
Detector
3
Does it matter ?
4
Yes it matters time mean induces serious bias
(speeds)

• Difference instantaneous space mean, time and
  harmonic mean
• Data from measured vehicle trajectories (over a
  section)
• Differences in speeds gt 100!
• Strongly related to measurement location
• Proportional to variance in individual speeds

5
Yes it matters time mean induces serious bias
(also in estimated travel times)
Measured travel time
Estimated travel time (harmonic mean speed)
Estimated travel time (Time mean speed)
6
Solution harmonic averaging local quantities

• Average of quantity z over space
• Fill in z v (speed) and you get

7
Relevance harmonic averaging

• Most ITS need the space mean of a quantity
  unbiased proxy with harmonic average (premise
  stationarity and homogeneity)
• Continuity relation q ku density from flow
  and speed k q/u
• Only valid with space mean speed (thus harmonic
  local mean!)
• Differences (estimated and real density) up to
  100 and more