So what is this node modeling stuff? What do they mean when they say TMODEL2 models intersection operations?

By modeling nodes and better specifying the delays through intersections, TMODEL2 is able to choose better short paths and to construct more realistic vines (trees) over the roadway network. The elements of this capability are discussed below.

But first, node modeling does not mean that one can expect that turn movements at an intersection can be modeled as accurately as the assigned link volumes which enter that intersection. Quite often turn movements are very reasonable. The changes in turn movements between a calibration scenario and an alternative scenario are even more reasonable. Further, there are some frataring techniques which when used on turn movement assignments, can produce even better results (watch for an article in the next newsletter). The bottom line, however, is that it can be prohibitively difficult to calibrate some turn movements. We can't depend on being able to model turn counts to a specified accuracy.

The reasons for this are that modeling, which relies on movements of incremental groups of vehicles rather than individual vehicles, cannot allocate all vehicles to the best turn movement. The link volumes contain some of the same misallocations but those volumes are larger, and the resulting compensating errors render the problems essentially invisible.

Vineland The Good - While we knew that modeling turn movements was a grape idea, it was first necessary to change our notion of routing. A tree showing the best paths from a zone to all others is a branching structure. A tree is node-to-node routing and has a basic rule that no path can pass through the same node twice.

In changing the short path algorithm to handle turn movement penalties, the best path back to the origin node through a given node depends on which turn movement the vehicle uses. The best example is of a driver who wishes to turn left when it is prohibited. He or she may go to the next corner and make a series of three right turns to get on the desired path. This ability to pass through the same intersection twice prompts the possibility of occasional loops in "tree" branches prompting the image of a vine. A vine is a link-to-link routing with the rule that no path can use the same link twice.

Specifying the delays through nodes can occur at several levels. It is important to understand that they are additive. The delay, as a driver would perceive it, is the total of delays through that intersection at all levels. Take care not to duplicate delays inadvertently. Delays are calculated in hundredths of minutes.

Delays can be calculated at the overall intersection level and/or at the level of an individual turn movement through that intersection. The intersections are described in the Node (.NDE) file and the turn movements are described in the Turn Penalty (.TNP) file. Intersection delay times appear ultimately in the link file. The A to B Time column contains the time it takes to cover that link given the link constraint equation added to the time it takes to get through the subsequent intersection given the intersection delay equations.

Turn movement delays, because they are the result of a two-link combination, cannot be shown in the link files. The only place they are kept is in a cell value of the travel time matrix. They are there in combination with all the links which comprise the path from one zone to another.

Keep in mind when looking at travel times for links in link files or for paths in travel time matrices, that the travel time matrix is calculated only for the last increment, that is, before the loading of the last increment is included. This suggests that if the final travel times and matrices are of special interest, a final, very small increment would properly calculate them.

The next three paragraphs describe intersection delays and the following four are for turn movement delays.

• BASE DELAY is, aptly, the most basic of all intersection delays. It is entered as a fixed time for an individual node in the Node file (.NDE) or for a CLASS of nodes in a Node Delay Parameters (.NDP) file. If both are used, they are additive. It may be best thought of as the delay the average vehicle will experience regardless of volume, for examples are, a portion of the red time at a fixed cycle signalized intersection or the average delay at an intersection near a campus where students walk at any and all times despite traffic controls.

• DYNAMIC INTERSECTION DELAY changes with volume and is a function of the V/C of the intersection at the time of calculation. So, when volume increases, delay increases. Including this delay is done by entering an overall intersection capacity in the Node file. That capacity is used to calculate V/C and the delay is calculated by the intersection capacity constraint function, Delay = K₁ * (V/C)^E + K₂ + B₀ are the base delay an individual node and K₂ for a CLASS of nodes mentioned in the paragraph above. The parameters for the dynamic intersection delay may be set for each CLASS of intersection in a Node Delay Parameters (.NDP) file. If not set, default values are automatically employed.

• SPECIAL DELAY LINK is a declaration in the Node (.NDE) file that overall intersection delays (as opposed to turn movement delays) are to be applied to that link but are not to be applied to non SDL approaches at that intersection. Typically, approaches to an intersection with stop or yield signs, except in the case of all-way stops, are identified as SDL's. The non-SDL's, which are the through streets, do not have intersection delays applied to them.

• TURN MOVEMENT BASE DELAY is entered in the Turn Penalty Type (.TPT) file. It is analogous to intersection base delay except that is applies only to vehicles moving through the specified movement as described in the Turn Penalty (.TNP) file. It is entered as a fixed time and should be used only where appropriate. It is often used as a turn prohibition by setting a base delay for that movement as some large number of hundredths of minutes, e.g., 200 or 32000.

• TURN MOVEMENT DYNAMIC DELAY is analogous to intersection dynamic delay except that it applies only to that movement through the intersection. For the movement the Delay = K * (V/C)^E. In the Turn Penalty Type (.TPT) file, the capacity, C, is set for that movement only, and the other parameters are also set.

• OPPOSING MOVEMENTS DYNAMIC DELAY provides another dimension for calculation of delay. The notion is that the more crossing and opposing traffic that exists, the greater the delay to vehicles taking the turn movement in question. Again, Delay = K * (V/C)^E. The volume and the capacity are those of the sum of the crossing and the opposing movements, and, again, the modeler sets the equation parameters.

• TERMINAL TIMES. Finally, those nodes which are also zones can have an additional delay in the form of terminal time. This value is entered in the Land-Use (.LU#) file and is carried into the distribution and assignment run in the Origins-Destinations (.OND) file. It represents the additional time perceived to be added at the beginning or end of a trip due to the move between the parking space and the actual origin or destination.

GET REAL! One has to decide which of these options to employ. The first consideration is that a good distribution and assignment is achieved when all paths, distances, and times are relatively accurate. The ability to derive operational speeds, accurate travel time matrices and resulting trip length frequency distribution depends on approaching absolute accuracy in all distance and speed inputs and employing appropriate constraint functions.

We recommend making the model as simple as possible to achieve your objectives. Add complexity when necessary to increase assignment accuracy and to approach absolute speed accuracies. The tools exist to go as far as you need to. Enjoy!