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# Moving Matrix Data Between Different Zone Systems

In many applications, more than one single level of zone sub-divisions exist. Depending on the context, the same geographical region may be modeled using very coarse zones (neighborhoods), medium sized zones (street blocks) or very detailed small zones (individual buildings). Also, data required for a project using one level of zone aggregation may only be available for zones of a different level of aggregation. It is thus often necessary to move EMME/2 matrix data between two different zone systems. Since a lot of people seem to have the misconception that this task may not be accomplished within the EMME/2 system, we shall briefly outline three methods that can be used to transfer matrix data

• from a detailed zone system to an aggregate one,
• from a aggregate zone system to a more detailed one,
• from a regional zone system to a focused sub-area zone system.

a) Detailed to Aggregate:

This is the simplest case, since it suffices to define a zone group ensemble in the data base containing the detailed zone system; one defines for each aggregate zone a group containing its corresponding detailed zones (see section IV-3.01 of User's Manual). The matrices may now be punched out (module 3.14) using origin and destination "sum" type aggregation with the zone group ensemble so defined. If non-additive data is to be transferred, create also a full matrix containing 1's in all cells and punch it in the same manner; this matrix will be used as weight matrix to scale down the "sums" for non additive data in the target data base. In the data base containing the aggregate zones, define a zone group ensemble (using the same identifying letter) in which each group corresponds one-to-one to the aggregate zone of the same number. Read in the matrix data punched previously. Since the matrices read in this way contain the sum of the corresponding detailed O-D pairs, this is correct for all additive data (demand). However, for non-additive data (socio-economic, cost, time, car occupancy, ...), this must be corrected by dividing all matrices containing non-additive data by the contents of the weight matrix, using module 3.21, in order to obtain the corresponding average values.

b) Aggregate to Detailed:

Define in both data bases the same zone group ensembles as described in a). In the aggregate data base, punch all pertinent data using (pseudo-)aggregation with the one-to-one zone group ensemble. Read now the data into the detailed data base. While reading in, the matrix values are duplicated into the elements of all possible detailed O-D pairs combinations that correspond to the aggregate O-D pair. This is the right thing to do for all non-additive data, but need further processing in the case of additive data (demand). To do this, define an origin matrix `mo`X that contains, for each detailed zone, the fraction of the corresponding aggregate origin it represents in terms of productions. Also, define an destination matrix `md`Y. that contains, for each detailed zone, the fraction of the corresponding aggregate destination it represents in terms of productions. Multiply (using 3.21) each transferred full matrix (containing additive data) by the factor `mo`X*`md`Y, each origin vector by `mo`X and each destination matrix by `md`Y.

c) Regional to Sub-Area

In this case, we assume that the sub-area zone system is more detailed in the focus area, case b) above, and more aggregate than the regional zone system in the areas far from the focus area, case a) above. Define a zone group ensemble in the regional data base that represents the aggregation far from the sub-area. Punch all matrix data as described in a), including the weight matrix. In the subarea data base, define the zone group ensemble and the fraction vectors `mo`X and `md`Y. that represent the splitting up of the sub-area (containing 1's everywhere else), as described in b). Read in all matrix data that was punched from the regional data base. Divide all matrix containing non-additive data by the (imported) weight matrix, as described in a). Multiply all matrices containing additive data by the fraction vectors, as described in b).

Next: Scattergrams - A New Module Up: EMME/2 News 2 March 1987 Previous: On Algorithms for the Traffic

Heinz Spiess, EMME/2 Support Center, Thu Jun 6 14:03:46 MET DST 1996