Each row and column of a (square) SATURN matrix has an external numerical “name” associated with it. Thus if the matrix represents a zone-to-zone trip matrix the name associated with the Ith row is the (numerical) name of the Ith zone. The “sequential” numbers are determined by the external zone names in increasing order; i.e., the first row corresponds to the lowest numbered zone, the second to the next lowest number, etc. Since zone numbers need not be sequential in SATURN (i.e., 1,2,3,...) the name of the Ith zone may be much larger than I. The basic advantage of having a non-sequential numbering system is that the user can associate informative and fixed numerical names with each zone, independent of which other zones are included in the network or matrix.
In addition (see 5.1.6) zones may have alphanumeric or text names associated with them as stored on the associated GIS files. For example sequential zone 6 might be named (numerically) 27 and have a text title of “West Ham”.
As a convenient shorthand we refer to ‘titles’, ‘names’ and ‘numbers’ as opposed to ‘alphanumeric names’, ‘numerical names’ and ‘sequential numbers’.
The same system of “sequential” and “external” zone numbers is also used in SATURN networks and is described in greater detail in section 5.1.6. Note, in particular, that zone “names” are restricted to 5 digits (i.e., numbers up to 99999) although a maximum of 4 is recommended (in order, for example, not to fill up the maximum 5-column input fields as used in certain standard file formats (10.5.1)) . Clearly networks and matrices based on the same set of zones will have exactly the same correspondences between sequential and external numbers.
Logically zone names should be positive non-zero numbers and, whereas exceptions to this rule will be fatal errors in network building, it is just about possible to have zone names equal to zero in matrices although the practice is certainly not recommended and will almost certainly be made a fatal error ASAP.
It is essential that users be aware of the differences between a zone’s name and its sequential number. In all SATURN network-based programs the external names are always used in input or output. However in most matrix operations it is possible to refer to either the sequential numbers or the external names; in general options exist to “toggle” between the two systems.
For square matrices rows it is assumed that the same set of numerical names and/or titles applies to both rows and columns.
For stacked (multiple-level) matrices, if zone names are applied to rows in the “basic” square matrix (see 10.2.4) it is generally assumed that the same zone names will be applied to upper levels as well, although this is not mandatory. For example, if the row names are identical to sequential row numbers then this would not be the case.