225 350 Duval Street B 125 400 + х Monroe Street 800 +300 D 250 600 he above figure shows a typical transport network in the city area of Jacksonville, in lorida, U.S.A, at a particular period of the day, with traffic flow measured in terms of ehicles per hour (vph). he streets are all one-way with the arrows indicating the direction of traffic flow. Ve let x, y, z and w denote the vehicles per hour in the directions indicated in the figure. Kirchhoff's point rule states that 'at any node (junction) in an electrical circuit, the sum of currents flowing into the node is equal to the sum of currents flowing out of that node'. This ule applies to the intersections here as well when there is a steady flow of traffic through he intersections. i) Form four equations involving x,y,z and w, and solve this system. ii) Suppose that road works have to be carried out along Monroe Street. As such, we want to minimise the traffic along Monroe Street, given that the inflows at B and D and the outflows at A and C remain the same as before. What is the minimum possible value of z? Discuss the implications. Hogan Street
225 350 Duval Street B 125 400 + х Monroe Street 800 +300 D 250 600 he above figure shows a typical transport network in the city area of Jacksonville, in lorida, U.S.A, at a particular period of the day, with traffic flow measured in terms of ehicles per hour (vph). he streets are all one-way with the arrows indicating the direction of traffic flow. Ve let x, y, z and w denote the vehicles per hour in the directions indicated in the figure. Kirchhoff's point rule states that 'at any node (junction) in an electrical circuit, the sum of currents flowing into the node is equal to the sum of currents flowing out of that node'. This ule applies to the intersections here as well when there is a steady flow of traffic through he intersections. i) Form four equations involving x,y,z and w, and solve this system. ii) Suppose that road works have to be carried out along Monroe Street. As such, we want to minimise the traffic along Monroe Street, given that the inflows at B and D and the outflows at A and C remain the same as before. What is the minimum possible value of z? Discuss the implications. Hogan Street
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ISBN:9780470458365
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Transcribed Image Text:225
350
Duval Street
- 125
400
Monroe Street
S00
300
C.
250
600
The above figure shows a typical transport network in the city area of Jacksonville, in
Florida, U.S.A, at a particular period of the day, with traffic flow measured in terms of
vehicles per hour (vph).
The streets are all one-way with the arrows indicating the direction of traffic flow.
We let x, y,z and wdenote the vehicles per hour in the directions indicated in the figure.
Kirchhoff's point rule states that 'at any node (junction) in an electrical circuit, the sum of
currents flowing into the node is equal to the sum of currents flowing out of that node'. This
rule applies to the intersections here as well when there is a steady flow of traffic through
the intersections.
(i) Form four equations involving x, y,z and w, and solve this system.
(ii) Suppose that road works have to be carried out along Monroe Street. As such, we want
to minimise the traffic along Monroe Street, given that the inflows at B and D and the
outflows at A and C remain the same as before. What is the minimum possible value of
z? Discuss the implications.
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