Node delay is the leading cause of traffic congestion. It is important that you understand the implications of node capacity and operation in order to model traffic well. The April 1996 (Volume 6, Number 1) newsletter discussed the classification schema that we have been using to describe nodes or intersections. It briefly described some of the tools available to you to improve your models. This article is a continuation of the previous newsletter and is intended to improve your use of node modeling and your model in general.

Capacities

We described a method of estimating the capacity of a node based upon the entering link capacities in Table 3 of the April 1996 newsletter (reproduced on the next page). In general, you would expect that each approach to a standard 4-way signalized intersection would have a green ball about one half of the time. If operation on all approaches were similar, then the node capacity should equal one-half times the sum of the capacities of all the approaches. However, given some lost time (for yellow or amber time, all-red time, and start up time) the multiplier may be less than one-half. This is how we derived the K4 factor for node type 30 of .45.

What if the intersection is of different classifications of streets, so that operation is not similar? Let's derive this by looking at the most extreme case. If the intersection is a principal arterial with a minor street that has no traffic and a demand actuated signal, the capacity of the node should be 1.0 times the capacity of the principal arterial. The capacity of the node based upon total entering capacities could be estimated as:

For the example of the Principal Arterial and the Minor street with no traffic the Capacity would be:

and the multiplier to be used for this case would be:

If you followed this logic, you can see how we derived the general rules as used in Table 3. These rules generally work very well when an area being modeled has balanced or close to balanced operation. By balanced, we mean that the flow is not highly directional. That is, the eastbound traffic is similar to the westbound traffic. These rules also work very well for a standard four-legged intersection. If you have three-legged intersections or highly directional flows, you may want to include some model rules that reflect the different types of operation.

Three-legged intersections have a reduced number of conflicts and therefore more usable green time per approach. In models where three-legged intersections are abundant and a special rule is warranted, we have increased the capacity multipliers for these cases. Where there are also additional turn lanes and channelization we have also modified the rules to increase the capacities to reflect these improvements.

If you want to modify the intersection rules to deal with directional flows more specifically, TMODEL2 contains a module 1.7.1) Node Capacity Adjustment. This module will adjust intersection capacities for those situations where the V/C ratios on the "critical approaches" differ significantly from those on the other approaches. To use it, one should make a distribution and assignment run, adjust node capacities, and then make another distribution and assignment run. This module reads in an existing node file, adjusts the node capacities for all nodes with three or more entering links, and then writes out a new node file with the new capacities.

Green time ratios are computed by dividing the critical V/C ratio by direction (NS or EW), by the sum of the V/C ratios, then subtracting 0.025 (to account for lost time). The adjusted capacity is the sum of the critical approach lane capacities times the Green/Cycle time ratios plus the non-critical volumes.

Assignment of the capacity may be limited by Class, Area, and Type. We have typically been applying this adjustment only to signalized intersections. In situations where data is available for comparisons, this method improves the veracity of the model.

Special cases may need special capacities. You may wish to use special nodes to reflect the capacities of toll booths, railroad crossings, or even park and ride lots. In one special case, we gave park and ride lots a capacity based upon the number of available parking spaces. It was assumed that the delay and walk time would increase as the capacity of the was approached. The Node Delay Coefficients were established so that they would reflect this additional delay time when the lot was full.

SDLs

For signalized intersections we assume that the delay will be more or less evenly distributed to all of the approaches; that is, the signals are timed based upon the demand volumes. This assumption is also used for four-way or all-way stop signs.

However, what if there are partial way stop signs or other conditions that warrant giving the delay to one or more of the approaches and no delay to the other approaches? This is where you will want to use SDLs or, as they were previously known, Special Delay Links. By assigning a SDL, the delay that is computed based upon the node V/C ratio will only be assigned to the approaches designated with the SDLs. Up to three SDLs can be designated for each node. If you have more than three stop signs at a location, you will typically have an all-way stop. This does not need SDLs because the delay should be applied to all approaches equally. SDLs can also be used to model the unequal delay at yield or give-way intersections.

Turn Penalties

Typically in UTPS based models turn penalties have been applied to prohibit or discourage turns using the addition of a constant amount of time. A constant is used to calibrate the model until the volumes match. We at TModel have a different philosophy on this. We think that turn penalties, if they are used, should be based upon an equation that is responsive to the conditions causing the additional delay.

Now, if the turn penalty is being used to discourage movements through a zone centroid, a constant amount is acceptable. But if you are modeling left turns (or right turns in Australia) that are impeded due to capacity constraints or the influence of opposing traffic, an equation based upon these conditions should be used. This is very easy to implement using the turn penalty type equations in section 1.5.3. These equations can be composites of the volume and capacity of the movement to be penalized, the volume and capacity of the traffic on the other approaches--including opposing traffic, and a constant amount of delay.

Remember that the rules you are developing for the calibration must be used or adjusted in the future. If you change rules in the future, the changes must be based on logical, rational reasons. You do not want to simply change the rule because something looks funny. If it looks funny in the future it should be examined in the base year calibration as well.

We have been experimenting in recent models with using small amounts of delay for left turns at all signalized intersections. This is being used to reflect the perception of drivers that left turns are more undesirable and often have more associated delay. It also seems to alleviate the stair-stepping that can occur in some networks.

This and the previous article are intended to convey the current practices we are using at TModel Corporation in our modeling efforts. In addition to developing and supporting the software, we use it for consulting projects which not only provide a service to our clients, but also allow us to use and stretch the limits of the software, often leading to improvements for all of the users.