Local sensors Round 1: 30 km/h Round 2: 20 km/h Round 3: 10 km/h

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Presentation transcript:

Local sensors Round 1: 30 km/h Round 2: 20 km/h Round 3: 10 km/h At (local) detector: utms= 20 km/u ! (18% > space mean) TT = 3 min/km! (17% < 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 a) If we observe each vehicle only once: Average travel time / km: (1/30 + 1/20 + 1/10)/3 = 11/(60*3) =11/180 u/km = 3.6 min/km Average speed 180/11 = 16.36 km/u at detector: u = 20 km/u (+18%); TT = 3 min (-17%) b) If we observe for one hour Average travel time / km (30/30 +20/20 +10/10)/(30+20+10) = 3/60 u/km = 3 min/km 60/3 = 20 km/u at detector: u = (30*30 +20*20 +10*10)/(30+20+10) = 23.3 km/u (+17%) TT = 2.6 min (-14%) Detector December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation

Local sensors Red car: 30 km/u Yellow car: 20 km/u Blue car: 10 km/u At detector after 1 hour: utms= 23 km/u ! (17% > space mean) TT = 2.6 min/km! (14% < 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 usms=20 km/u ! a) If we observe each vehicle only once: Average travel time / km: (1/30 + 1/20 + 1/10)/3 = 11/(60*3) =11/180 u/km = 3.6 min/km Average speed 180/11 = 16.36 km/u at detector: u = 20 km/u (+18%); TT = 3 min (-17%) b) If we observe for one hour Average travel time / km (30/30 +20/20 +10/10)/(30+20+10) = 3/60 u/km = 3 min/km 60/3 = 20 km/u at detector: u = (30*30 +20*20 +10*10)/(30+20+10) = 23.3 km/u (+17%) TT = 2.6 min (-14%) Detector December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation

Does it matter ? December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation

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 > 100%! Strongly related to measurement location Proportional to variance in individual speeds December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation

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) December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation

Solution: harmonic averaging local quantities Average of quantity z over space: Fill in z = v (speed) and you get December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation

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 December 28, 2018, CT5804 Lecture 5: traffic monitoring & state estimation