The first situation that has been tested is where a single entry link gives way to either one or two circulating (major) links. The two models have been made to be equivalent in the following way. In Figure 1a, link 30 is giving way to link 31: the only give-way coefficient required in this case is A1. In figure 1b, link 35 is giving way to 31 and 32: in this case two give-way coefficients are required, A1 and A2. For the two situations to be exactly equivalent, A1 and A2 in 1b must both be the same value as A1 in 1a (not half or any other contrived value). ARCADY would normally be used to obtain the parameters. When modelled in this fashion, the results for link 30 are exactly the same. Shared links can be added as needed in either situation, although it is essential that the entry link gives way to only the master link(s). Specifying a minor link as a priority link will give the wrong results, but it will not lead to any run-time error or warning.

The second situation is the reverse of the above, where the give-way entry is split into two links (see Figure 2). Using two links to model the entry has been considered by some to be more correct when traffic forms distinct queues in separate lanes. We have not been sure that this is the case and have for some while now wanted to see if a priority approach can be modelled with two or more give-way links.

To consider this I have split the single give way link (link 30 in Figure 1a) into two give-way links (links 35 and 36 in Figure 2). To engineer the two situations to be equivalent, the maximum flow values on links 35 and 36 need to total to the maximum flow on link 30. The coefficients on links 35 and 36 need to be reduced in proportion to the maximum flows. In the model set up for comparison, I halved both the maximum flow and coefficient for links 35 and 36 as compared with link 30. With half the traffic flows as well, the results from the two models might be expected to be similar. It turns out that the capacity of the two situations is, indeed the same, with identical degrees of saturation. The uniform component of delay is also the same. However, differences occur in the random-plus-oversaturation part of the calculations, which, with two links instead of one, make the two-link model predict higher stops, delays and queue lengths. There are examples of figures from the final TRANSYT output table shown at the foot of this page.

As can be seen, the differences between the two models are quite marked with the two-link model significantly worse in delay terms. It should be noted, however, that these two models probably are not directly equivalent after all. In this single link example, all lanes are equally used with queues being nearly equal. In the above two-link model, the average queue will be the same for both lanes, but the randomness of arrivals will mean that the links will ‘take it in turns’ to have the longer queue. Such unequal queueing is likely if lanes are used for different destinations, in which case the more pessimistic two-link model may be more appropriate. A single link model will be appropriate when adjacent lanes share a common movement so giving the opportunity for drivers to choose between two or more lanes. When using a two link model it will be necessary to derive the maximum flow and give-way coefficients using ARCADY by, in effect, modelling the two parts on an approach as separate entries. This will give the two sets of parameters required.

The final issue concerns the two-link model again (Figure 2). It might be argued that a nearside lane does not give way to all the circulating traffic, because drivers can see that some of the circulating traffic is not going to impede them. If using a single link model with parameters derived from ARCADY, this will not be an issue because ARCADY will have already accounted for this effect (if it exists). For a two-link model, it might be reasonable to increase the capacity of an entry if (and only if) it is clear that the nearside lane will not in practice have to give way to all the circulating traffic. However, you will need to be confident of this as there has been no work that we are aware of to calibrate or test this. It would, perhaps, be more justifiable to reduce the give-way coefficient for the nearside lane, rather than simply say it only gives way to a sub-set of the circulating traffic. How much to reduce it by needs careful thought, unless you are prepared to go to the trouble of measuring it on-street (and how to do that is a story for another day!)

In conclusion:

  • There is no difference between modelling the circulating traffic with either one or two (master) links
  • The give-way entry can be modelled with one, two or even more links, depending on how much choice drivers have as to which lane to use to reach their intended exit

There is little research as yet about whether any particular entry stream gives way to some or all of the circulating traffic streams and whether it is acceptable to modify the parameters because (for example) a nearside entry lane can ignore (partially or wholly) traffic in a particular circulating lane.