8.3.2. Example

Trips originating from zone 1,2,3 of a study area are 78,92 and 82 respectively and those terminating at zones 1,2,3 are given as 88,96 and 78 respectively.

In this example, we start with data showing the number of trips originating from three different zones in a study area. The trips from each zone are quantified as follows: Zone 1 has 78 trips, Zone 2 has 92 trips, and Zone 3 has 82 trips. Additionally, we observe the trips terminating at the same zones: Zone 1 receives 88 trips, Zone 2 receives 96 trips, and Zone 3 receives 78 trips. This data is essential for understanding travel patterns and distribution in the specified area.

Imagine a small city divided into three neighborhoods. In neighborhood 1, 78 people leave their homes to visit other neighborhoods, while neighborhood 2 sees 92 people venturing out, and neighborhood 3 sends 82 people on their way. Meanwhile, these neighborhoods also attract visitors: neighborhood 1 welcomes 88 newcomers, neighborhood 2 attracts 96, and neighborhood 3 draws 78. This scenario helps city planners understand the flow of traffic between these neighborhoods.

If the growth factor is 1.3 and the cost matrix is as shown below, find the expanded origin-constrained growth trip table.

The growth factor used in this example is 1.3, indicating an increase in trip numbers by 30%. To find the expanded trip table, each cell in the trip matrix must be multiplied by this growth factor. This means taking each of the previously calculated trips for every zone pair and increasing them by 30%. This process allows us to estimate how many trips would be generated under the new growth conditions.

Suppose there’s a bakery that sells 100 loaves of bread each day. If the demand suddenly increases, and the owner predicts that they can sell 30% more bread due to popularity, they can calculate that they now expect to sell 130 loaves daily. Just as the bakery multiplies its daily sales by a growth factor, the trip distribution process uses a growth factor to project how many trips will occur in an expanding city.

Given growth factor = 1.3, Therefore, multiplying the growth factor with each of the cells in the matrix gives the solution as shown below.

In this section, we apply the growth factor of 1.3 to each of the cells of the initial trip matrix, producing new values for the trips between the zones. For example, if the original number of trips from zone 1 to zone 2 is 30, the new number becomes 30 multiplied by 1.3, resulting in 39 trips. This process is repeated for each cell of the trip matrix, helping create an updated representation of the expected journey patterns.

Consider a growing school where the number of students increases by a certain percentage each year. If there are initially 100 students in a class, applying a growth factor of 1.3 means the class will eventually have about 130 students. By calculating how each class size will grow, the school can prepare for additional resources and staff!

1 2 3 O 1 26 39 36.4 101.4 2 46.8 41.6 31.2 119.6 3 28.6 44.2 33.8 106.2 D 101.4 124.8 101.4 327.6

This section illustrates the completed expanded trip table after applying the growth factor. The new table shows the number of trips originating from each zone and how many trips are expected to be attracted to each zone. The totals in the last column ('O') represent the expanded origin trips for each respective zone, while the totals in the last row ('D') signify the expected attractants to each zone.

Think of this final expanded table like a busy seating chart in a restaurant. If the restaurant sees an uptick in customers (by applying our growth factor), all sections in the seating plan adjust accordingly. The restaurant manager can then anticipate the increases in certain areas, guaranteeing they have enough staff and food to meet the new demand!

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