Heinz Spiess
EMME/2 Support Center, CH-2558 Aegerten, Switzerland

March 1992

Abstract:

When assigning a transit network with EMME/2, the basic results are the volumes on the transit segments and the boardings/alightings at the transit stops. Means to produce line-to-line transfer matrices at transfer nodes are not provided as a standard result output.

In this paper we show how such line-to-line transfer matrices can be computed for selected transfer nodes, without changing the assignment results. This is done with the standard EMME/2 software , by using a special network transformation at the selected transfer nodes. Details of this transformation are discussed and we show how the process has been automated by implementing it as a macro. The method is illustrated with an example from the Winnipeg standard demonstration data bank.

In the conclusions we discuss how this methodology can be extended to model other complex situations which are not covered by the standard model.

Introduction

When modelling transit networks, the basic results provided by the transit assignment in the EMME/2 software package are the volumes on the transit line segments, as well as the boardings and alightings at each transit stop. Of course, other information is also computed during the transit assignment, such as the number of initial boardings and final alightings at nodes, the auxiliary link volumes (e.g. pedestrian movements) and the various OD time component matrices.

These standard results cover the need of the great majority of transit planning applications. However, in certain applications it is not sufficient to know the total number of transfers at each transfer node, but it is necessary to assess the number of trips that transfer at a given node from one particular line (and direction) to another. This means that instead of just the total number of transfers at a given node, a line-to-line transfer matrix is needed. Ideally, such a transfer matrix could be computed for each transit node in the network. But this would amount to a huge quantity of data, in general requiring orders of magnitude more storage space than is needed for the standard assignment results. For the Winnipeg standard demonstration network, there are 57'333 possible line-to-line transfers, but only 4'272 transit line segments. Given this and the fact that the number of possible line-to-line transfers at a node is the square of the number of lines stopping at the node (which by the way is not restricted in EMME/2), it is clear that these transfer matrices are not provided as a standard result in EMME/2. However, in practice it is most always necessary to know the transfer matrices at only a few transfer nodes in the network (which ones, of course, depend on the particular issues that are to be studied in the application).

In the past, two types of simplistic approaches to solve this problem have been used in practice by some EMME/2 users.

In the first type of methods, the network topology is changed by splitting the transfer node into different nodes which are interconnected with a ``matrix'' of walk links. The big drawback of this approach is that this network transformation changes the route choice and, thus, the assignment results, since the lines at the transfer node can no longer be combined to reduce waiting time.

In the second type of approach, the network is left unchanged, but instead of a simple assignment, a series of assignments is carried out, mimicing a transit version of an ``additional options auto assignment''. In the first step of this process, a partial demand matrix representing the trip using a given line (or set of parallel lines) is extracted. In the second step, this matrix is assigned again to the transit network. The resulting boardings to and alightings from the other lines passing at the transfer node can then be interpreted as the line-to-line transfers between the selected line and the other lines calling at the transfer node. While this method does not change the route choice of the trips, it is very time consuming (several assignments needed), it gives only partial information relative to one line and it is only applicable if the line (or set of lines) in question are not used combined with other lines at the transfer node.

In the following sections, we will describe a new methodology designed to overcome the problems mentioned above. The approach allows to compute such line-to-line transfer matrices for selected nodes with the standard EMME/2 software release, as a by-product of a single standard transit assignment. This is done by a special network transformation at the transfer node, which does not alter the mathematical formulation of the transit assignment problem (i.e. yields the same results as before the transformation), but which renders the line-to-line transfers accessible as boardings and alightings of special transfer segments.

Network Representation at Transfer Node

In a standard network, a transfer node is connected by incoming and outgoing links. Each link can carry an arbitrary number of transit line segments and allow a subset of auxiliary modes for accessing to or egressing from the transit lines. For the sake of simplifying the presentation, we assume that all lines actually stop at the transfer node and allow both boarding and alighting. This is illustrated in Figure 1 below:

 
Figure 1: Simple transfer node.

The key idea of our method is to ``blow up'' the transfer node, by adding dummy nodes, links and segments in such a way that:

• The mathematical structure of the transit assignment is not altered. This means that no time or cost element is added and that the new topology still allows exactly the same set of strategies.
• The elements of the line-to-line transfer matrix appear as boardings or alightings at the dummy nodes.

This goal is possible to achieve by using the following transformation: Let's assume that we have