Lowry Model (Land Use - Transport)

The Process of Lowry As mentioned earlier that at the beginning, basic employments are given to the model. By this employment zones houses allocation will be found endogenously. With this residential model, population/households are allocated to places of residence in zone i from their places of work in zone j by the zones attractivity and travel cost . Demand of services will be generate by this population. Services employment is linked directly to the location of population/households. This implies that services employment is relatively mobile and is located either contemporaneously with, or soon after, the location of population/households (Webster et al. 1988). The major determinants of the location of services employment are accessibility to consumers, and rental costs for services sites. The Lowry model follows an iterative procedure. It first estimates the location of population/households based on total employment (basic and services), of which services employment is set to zero for the first iteration. It then proceeds with the location allocation of services employment based on the previously determined location of population/households. The estimated location of services employment will then be added to basic employment to form the basis for the next iteration. In each iteration, a number of residents and services employees are added. By the iteration the additional number of residents and services employees becoming smaller and converges to zero after a reasonable number of iterations. The process will be halted if it convergence. Following is the procedure of the model; which will be described step by step. 1) Total employment, E=B+S

B = basic employment S = service employment

2) Inverse of activity rate, α = P /E

α = inverse of activity rate, factors which reflects the proportion of total population to the employment

3) Level of service employment, β = S/ P

β = population serving ratio, the amount of service Employment will emend by the population

4) Population allocated in each zone,

Pj = G ∑ Ei / dij-1

Pj = amount of population allocated to j Ei = basic employment in i dij = impedance or deterrence factor between i and j G = scaling factor, to ensure ∑ Pj = P

5) The amount of activity allocated from zone i to j , Tij = EiAidij -1

Ei = total amount of activity to be located from Zone j (basic empl), people employed in zone i

Ai =(∑ Pj dij-1)-1 6) Total number workers ( basic) living in anyone zone j, ∑ iTij 7) Total basic population living in anyone zone j , Pj (1) = αΣi Tij 8) If Pj (1) < P ………….singly process 9) If Pj (1) > P …………doubly process Ei = additional supply Rj = demand excess Ai = 1/  ( Bj x Ei x dij ) ; assume Bj = 1 Bj = 1/  ( Ai x Rj x dij ) Pj = Ai x Bj x Ei x Rj x dij

10) Demand for service employment by the people in j, Dj (1) = ß Pj (1)

11) No of service employees demanded by population resident in zone j who work in Zone i, Sji (1) = BjDj (1) SiDji-a, where, Bj = (ΣsiDji-a)-1 12) Total of service employment in zone i , Si(1) = Σj Sji

13) If Sj (1) < S ………….singly process 14) If Sj (1) > S …………doubly process Ei = additional supply Rj = demand excess Ai = 1/  ( Bj x Ei x dij ) ; assume Bj = 1 Bj = 1/  ( Ai x Rj x dij ) Sj = Ai x Bj x Ei x Rj x dij 15) Total service employment in all zones, S (1) = ΣiΣj Sji 16) Number of population dependent on Si(1), Tij = Ai Si (1) Pjdij-b, 17) Total service dependent population, DJ (2) = βPj (1) 14) The whole sequence of calculation is repeated until the increments become insignificant, and the total converges.