Question

Figure 1 presents a simple three-zone system, the link travel times in minutes (wij) for this system, and the observed zonal productions and attractions. Assuming a doubly constrained gravity model with friction factor F_{ij = Wij^-b}

a. Compute P-A flows (production-attraction matrix) for this system for values of b of 1.0, and 1.5.

b. Table 1 below presents the observed P-A flows for this system. Which value of b provides the “best-fit” to the observed data? Note: Best-fit should be measured by R2 , the coefficient of determination.

Show the steps of your solution to the problem.

Table 1: Observed P-A flows for three-zone system

From	To
	1	2	3
1	130	5	15
2	80	40	80
3	30	5	55

W12=W21=5min

P1 = 150 P2 = 200 A1 = 250 A2= 50 P3 =100 A3 = 150

w13=w31=4min w23=w32=3min

w11=w22=w33=2min

Answer 1

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