Lecture 13-1. 4-step Model – Trip Assignment. Trip Assignment. Definition Assign T ij onto alternative routes on the network to predict the Link flows and to evaluate the network performance. Trip Assignment. Generalized Cost = function of time, distance, $$ + possibly others.
Assign Tij onto alternative routes on the network to predict the
Link flows and to evaluate the network performance.
Generalized Cost = function of time, distance, $$ + possibly others.
From the user’s perspective; shortest path (stochastic vs. deterministic)UE
From the planner’s perspective: minimize the network wide travel cost SO
Each path has an associated Link performance function (LPF):
t = t0eV/C
t = t0ab(V/C)
Most common from the Bureau of Public Roads (BPR)
t = t0(1 + a(V/C)b)
which becomeswhen linear (b = 1, a = aC/t0): t = t0 + aV
Assuming a known network with a known deterministic link performance, the objective is to find a path from an origin to a destination at the least cost.
Shortest path calculations are idealistic, but are most fundamental to the network flow problem and to the network traffic assignment problem. Many sophisticated algorithms are built with the shortest path algorithm.
There are many variations (Dijkstra, Moore), but all get to the same results. The complexities are different slightly.
This is the algorithm to summarize based on the example
All-or-nothing Assignment, use Dijkstra to find S.P. for each O/D pair and then assign all flow to it
A-C = 400; A-D = 200; B-C = 300; B-D = 100