NYC-WTC_000187725

NYC 9/11 Public Portal Document

129 of problems of various sizes and with alternative starting points and aggregate vacancy rates in the following tables. The data in these problems was artificially generated but is fairly realistic. Table 5.1 explores the use of MINPACK to solve four problems. The first two problems have 400 equations (obtained as the product of 100 residential zones and 4 housing types). The second two problems have 1800 equations (1800 residential zones and a single housing type). The vacancy rate for the first three problems is set at 40% and then dropped to a much more realistic 4.5% for the last problem. Each problem is solved using three different starting points; o the equilibrium rents (hence only one iteration is required to confirm that the starting point is the solution and the computational time is the time needed to do one evaluation of the Jacobian matrix); o a randomly determined set of rents which are low relative to the equilibrium rents; o the assumption that rents are zero for each residential zone.

Table 5.1 Solutions of Various Size Problems Using MINPACK with Different Starting Points and Vacancy Rates on the CRAY-YMP

Dimensions Jacobian Vacancy Starting Point

Equilibrium Low Random Uniformly i, j/k Rents(1) Rents(2) Zero Rents £ ,in, n JK X JK % 1,100,4 n 1 4 12 100,2,2 400 X 400 40 CPU 19.251 19.466 20.074 3,100,4 400 X 400 40 n 1 4 12 100,2,2 CPU 52.371 52.632 53.896 3,1800,1 1800 X 1800 40 n 1 4 12 6,2,2 CPU 377.120 380.133 386.401 3,1800,1 1800 X 1800 4.5 n 1 6,2,2 CPU 378.510 > 900 (3) •?

(1) Average equilibrium rent is about $ 4,500. (2) The starting rent of each zone is a random number generated from the range ($0 - $1,000). (3) 900 second CPU time was exceeded. n : the number of iterations needed to converge. CPU : the computational time includes input-output time.

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