$10\mathrm{.}2$ A study area contains two residential zones A and B and three workplace zones J$,$ K and L$.$ The zones are connected by a road network as shown in Figure $10\mathrm{.}18,$ which also depicts travel costs in either direction; these are independent of the traffic flows. Figure $10\mathrm{.}18$ Simple network for Exercise $10\mathrm{.}2($a$)$ Use a systematic procedure to find the cheapest routes from nodes A and B to destinations J$,$ K and L and obtain the matrix of travel costs C$.($b$)$ The total number of trips originating and terminating in each zone during the morning peak are given by: Origin T rips Destination Trips $1000200070010001300$ Run an origin$-$constrained gravity model in which the deterrence function is proportional to exp$(-0\mathrm{.}1$ Cii$)$ and obtain a trip matrix. Use this matrix to calculate flows on all the links of the network. $($c$)$ Run a doubly constrained gravity model with the same type of deterrence function and obtain a new trip matrix and link flows. Compare your results of $($b$)$ and $($c$)\mathrm{.}10\mathrm{.}2$ A study area contains two residential zones A and B and three workplace zones J$,$ K and L$.$ The

zones are connected by a road network as shown in Figure $10\mathrm{.}18,$ which also depicts travel costs in

either direction; these are independent of the traffic flows.

Figure $10\mathrm{.}18$ Simple network for Exercise $10\mathrm{.}2$

$($a$)$ Use a systematic procedure to find the cheapest routes from nodes A and B to destinations J$,$ K

and $L$ and obtain the matrix of travel costs $C.$

$($b$)$ The total number of trips originating and terminating in each zone during the morning peak are

given by:

Run an origin$-$constrained gravity model in which the deterrence function is proportional to

exp$(-0\mathrm{.}1C_{ij})$ and obtain a trip matrix. Use this matrix to calculate flows on all the links of

the network.

$($c$)$ Run a doubly constrained gravity model with the same type of deterrence function and obtain

a new trip matrix and link flows. Compare your results of $($b$)$ and $($c$).$