Homework No. 2
(Due: 12 November 2010)
1.
Find the UE flow and travel times for the network shown in the figure below,
where
tx
11
2
22
33
2
44
2
3
12
24
=+
1
2
3
1
2
3
4
(The link numbers are shown on the respective links.) The OD trip rate is 4
units of flow between nodes 1 and 3.
2.
Figure 1 shows a network with two links connecting one OD pair.
1
2
Link 1
Link 2
Figure 1
Link 1 performance:
2
1
1
2
Link 2 performance:
t
x
3
=
+
Demand function:
q
u
=−
5
1
Flow conservation:
q
x
x
=
+
where
t t
,
are the travel times on links 1 and 2, respectively.
x
x
,
are the
flow on links 1 and 2.
u
is the OD travel time, and
q
is the OD flow.
(a)
Plot the demand function
(b)
Plot the performance function
for the OD pair:
u
as a function of
q
.
(c)
Solve for the equilibrium flows by locating the intersection between the
demand and performance functions.
3.
Formulate problem 2 as an equivalent minimization problem. State the first
order conditions and solve for the equilibrium flows.
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 Fall '10
 HKLO
 Shortest path problem, Flow network

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