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Trip Matrix

Properties of a Trip Matrix

An O-D Volume is a set of Trips. Trips start from an Origin Zone and ends at a Destination Zone. There are two types of O-D Volumes: Assign O-D Volumes and Fixed (Route) O-D Volumes. An O-D Volume can be presented in a Trip Matrix, which is a table wherein the row headers are Origin Zones and column headers are Destination Zones. The sum of all Trips in the same row of a Trip Matrix is the Trip Generation of the Origin Zone. Similarly, the sum of all Trips in the same column is Trip Attraction of the Destination Zone. The sum of Trip Generation for all Zones is equal to the sum of all Trip Attraction of all Zones.

The values in the diagonals of the Trip Matrix are referred to as Intrazonal Trips (i.e. Trips whose Origin and Destination is the same Zone). In ASSIGN, Intrazonal Trips enter the Network and find a route to exit the Network. Therefore, there must be at least one viable route for Intrazonal Trips.

Trip Matrix Growth Projection

A future Trip Matrix can be estimated from a present Trip Matrix and Growth Rates. The Growth Rates applies to:

  • Generation, i.e. all Generated Trips from the same Origin Zone will grow at the same rate.
  • Attraction, i.e. all Attracted Trips to the same Destination will grow at the same rate.
  • Generation and Attraction, i.e. Furness Method, see below.
  • O-D Pairs, i.e. growth rates are specified for each O-D Pair.

The Furness Method is a method to estimate a Trip Matrix from another Trip Matrix that simultaneously satisifes user-given growth factors for Generation and Attraction. Growth Rates for Generation and Attraction of each Zone is specified. The Furness Method uses an iterative algorithm to estimate from the present Trip Matrix a future Trip Matrix wherein the Generation and Attraction of the future Matrix is close to the projected Generation and Attraction of each Zone. The user can specify the Percentage Stopping Condition (%) and the Maximum Number of Iterations as the terminating condition for the Furness Method iterations. If the maximum percentage difference between the Generation/Attraction of future Trip Matrix and the projected Generation/Attraction for any Zone is less than the Percentage Stopping Condition (%) then the Furness method iterations is stopped, and the solution is accepted.

In ASSIGN, Growth Rates applying to Generation, Attraction, and Generation and Attraction (Furness Method) are used only for Assign O-D Volumes. Growth Rates applying to O-D Pairs are used only for Fixed O-D Volumes. Fixed O-D Volumes are associated with O-D Volumes that have defined Routes, such as buses and trams. Growth Rates for individual O-D Pairs offers flexibility and specificity that is needed for Fixed O-D Volumes.