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1 Origin, Destination, and Travel Time Distribution Without Surveys Copyright, 1996 © Dale Carnegie & Associates, Inc. INFORMS SLC May 2000 Larry George.

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Presentation on theme: "1 Origin, Destination, and Travel Time Distribution Without Surveys Copyright, 1996 © Dale Carnegie & Associates, Inc. INFORMS SLC May 2000 Larry George."— Presentation transcript:

1 1 Origin, Destination, and Travel Time Distribution Without Surveys Copyright, 1996 © Dale Carnegie & Associates, Inc. INFORMS SLC May 2000 Larry George Problem Solving Tools

2 4/28/00PST2 Sample or population? zAir travel surveys ~10%, on the day surveyors choose zCommuter surveys have non-response, bias. “Why are they surveying me?” zWant O-D population proportions and travel time distributions “It’s human nature to doubt statistically significant conclusions based on a sample that is a small fraction of the population”

3 4/28/00PST3 M/G/  G(t) is estimable, without customer id  Input Poisson, service time distribution is G(t), infinite servers  Output is Poisson at rate  G(t) zArrival and departure times or counts, without id, are sufficient zDitto M t /G/  under mild restrictions

4 4/28/00PST4 Tandem M t /G/   Input Poisson  G 1 (t) to a second M t /G 2 /  zOutput is Poisson at rate  G 1 (u)G 2 (t-u)dG 1 (u) zEstimate G 1 and G 2 from input, intermediate, and output observations

5 4/28/00PST5 M/G 2 /  2 /p zTwo M/G/  systems, one N-S and the other E-W, customers switch with pr. p zObserve 2 inputs and 2 outputs  Estimate 1 and 2 from inputs yEstimate p and G(t) from output rates  r 1 = ((1-p) 1 +p 2 )G(t)  r 2 = ((1-p) 2 +p 1 )G(t)

6 4/28/00PST6 M/G 2 /  2 /p with one obs. zObserve output rate r j at time t  p = ( 2 *r *r 2 ) / (( )*(r 1 + r 2 ))  G(t) = (r 1 + r 2 )/( ) zExample  r 1 = 4, r 2 = 3, 1 = 10, 2 = 20 y=> p = 5/7 and G(t) = 7/30

7 4/28/00PST7 Solutions for several obs. zTwo obs. gives multiple solutions. Use lse.  r 1 (1) = 3, r 2 (1)= 4, r 1 (2) = 6, r 2 (2)= 8, 1 = 10, 2 = 20 y=> p = , G(1) = , G(2) = zMultiple obs. yp 1, p 2, G 11 (t), G 12 (t), G 21 (t), G 22 (t)  yDepends on whether you want t or all (i,j)

8 4/28/00PST8 M t /G k /  k net with switching zObserve node I/O; inputs can have nonstationary rates zAssume stationary switching and travel time distributions zRoute frequency is product of switch probabilities (assume independence) zTravel time is convolution of intra-node travel time distributions

9 4/28/00PST9 Summary zO-D proportions and travel time distributions don’t require customer id zPopulation data beats sample data zWorks for transient processes: e.g. commutes, BART, other daily cycles and traffic light cycles


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