lecture1

# lecture1 - 1.225J(ESD 205 Transportation Flow Systems 1.225...

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1.225 1.225 J (ESD 205) Transportation Flow Systems J (ESD 205) Transportation Flow Systems Lecture 1 Lecture 1 Cumulative Plots & Time - - Space Diagrams Space Diagrams Prof. Prof. Ismail Ismail Chabini and Prof. Chabini and Prof. Amedeo Odoni Amedeo Odoni

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Cumulative Plots Cumulative Plots ± Observer: count the total number of vehicles, N(t), that passed in front of him/her during time interval [0,t]. Lane 2 Lane 1 Link entry Link exit Observer 1 2 3 4 5 time N ( t ) 0 N(t) ) ( ~ q(t) t N 1.225, 10/29/02 t 1 t 2 t t 3 t 4 t 5 Lecture 1, Page 2
Observations on Observations on N(t) N(t) ± N(t) is a step function. (not smooth) ~ ~ ( ( ± t N ) is a smooth approximation of N(t) t N d ) exists. dt ~ ( ( ± t q ) = t N d ) : instantaneous flow at time t . dt ~ N ( T ) N (0) N ( T ) N (0) ± Average flow = T T 1.225, 10/29/02 Lecture 1, Page 3

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Arrival - - Departure Cumulative Plots Departure Cumulative Plots Single lane Observer A: A(t) Observer D: D(t) 1.225, 10/29/02 Lecture 1, Page 4 D(t) A(t) t 0 t 1 A -1 (n) n 1 D -1 (n) time N(t) 0 0 t ? n
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lecture1 - 1.225J(ESD 205 Transportation Flow Systems 1.225...

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