1. A numerical comparison of three heuristic methods for path reassignment for dynamic user equilibrium
Ying-en Ge and Malachy Carey
16 September 2004
School of Management & Economics
Queen’s University Belfast
BT7 1NN
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Introduction
Dynamic traffic assignment (DTA)
Network loading,
with inflows/ assignment to spatial paths taken as given
compute new path travel times
Spatial path reassignment (based on travel-times from 1)
Three methods for path reassignment
Pair-wise swapping method
Wu et al. (1998) method
Lo & Szeto (2002) method
16 Sep 04
Transport Workshop at Queen's

3. Pair-wise swapping method
Step 1
At iteration n, for each time interval i, note the path with current highest cost (travel time) and path with lowest cost
[ or variants of this, e.g. choose the same paths for several time intervals, etc.]
Step 2
For each time interval i, switch proportion sin of inflow from higher cost to lower cost path
sin = an
where an is a chosen parameter (1 > an > 0)
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Wu et al. (1998) method
VI formulation
The solution of the VI formulation is obtained by solving a series of quadratic programs below
(1)
where a is a positive constant.
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Lo & Szeto (2002) method
Step 1. Compute gipn and vin for all i and p by:
gipn = max{0, fipn –b[hipn – (uipn –b(p fipn – di))]}
vin = uin -b(p gipn – di)
Step 2. Compute fipn and uin for all i and p
fipn+1 = fipn - tn gn (fipn - gipn)
uin+1 = uin - tn gn (uin - vin)
where tn = dn( bm-1), dn(0,2) such that
tn(0,1) and gn = r1/r2 with
r1 = ip(fipn - gipn)2 +b2i(gipn–gi) and
r2 = r1 + bi(p fipn – gipn)2
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Transport Workshop at Queen's

6. Numerical experiments
Scenario Settings
2-link network
Network loading
Travel demand
Convergence measure
Maximum absolute difference
Numerical experiments
Effects of parameters in three methods
Convergence measure values over iterations, and
Accuracy of numerical solutions
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9. Minimum values of convergence measure
Maximum absolute difference
Pair-wise swapping method (an = 1)
Wu et al. method
(a = 2)
Lo & Szeto method
(b = 0.5 and tn =1.0)
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11. Stopping iterations when given tolerances for
maximum absolute difference are satisfied
tolerance for maximum absolute difference
(5%)
(1%)
(0.5%)
Pair-wise swapping method (an = 1) 17
112 
Wu et al. method (a = 2)
290
Lo & Szeto method
(b = 0.50 and tn = 1.00)
305
630
783
Note: The percentages given in the round brackets after each tolerance represent the proportion of a tolerance to the free-flow travel time of the shorter of the two paths [1.25 minutes].
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Summary
Preferred parameter values
Not able to set an arbitrarily small tolerance
Performance of three methods
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