Towards a standardized flow test suite for simulation models

In order to control the effect of driving rules, Transims provides controlled tests for traffic flow behavior. These tests are simplified situations where elements of the microsimulation can be tested in isolation. This test suite uses the standard microsimulation code in the same way it is used for full-scale regional simulations, and it also uses the same input and output facilities: The test network is currently defined via a table in an Oracle data base, in the same format as the Dallas/Fort Worth network is kept. Input of vehicles is, following individual vehicle's plans, via parking locations, the same way vehicles enter regional simulations.^32.11 Output is collected on certain parts of the network on a second-by-second basis, the same way it can be collected for regional microsimulations. The collected output is then post-processed to obtain the aggregated results presented in this paper.

The test cases we look at in this paper are the following (see also Fig. 32.1 (e)):

• One-lane traffic, in order to see if car following behavior generates reasonable fundamental diagrams.

• Three-lane traffic, in order to see if the addition of passing lane changing behavior still generates reasonable fundamental diagrams, and in order to look at lane usage.

• Stop sign, yield sign, and left turns against oncoming traffic, in order to see it the logic for non-signalized intersections generates acceptable flow rates.

• A signalized intersection, in order to see of we obtain reasonable flow rates, and in order to check lane changing behavior for plan following purposes.

Measured quantities

We look at three minute averages of the following quantities:

• Flow, Volume. Flow $q$ is defined as usual by:
  

  $${\it q\/} = \frac{\it N\/}{\it T} \;\;\;\;\;\; [vehicles/hour]$$

  
  
  N is the number of cars which pass a certain site at a time period T.

• Density. Density is in principle easily defined, $\rho = N / L$, where $N$ is the number of vehicles on a piece of roadway of length $L$. Yet, given current sensor technology, this is not easy to achieve since one would need a sensor which counts, say once a second, cars on a predefined stretch of length $L$ of the roadway. For that reason, empirical papers sometimes resort to occupancy, which is the fraction of time a given sensor has been occupied by a vehicle. Currently Transims measures density according to its original definition, i.e., once a time step, we count the number of vehicles on a stretch of roadway of $L=5$ sites $=5 \times 7.5$ m $= 37.5$ m.^32.12 We add these counts for $k=180$ measurement events and then divide the resulting number by $L$ and by $k$:
  

  $${\it\rho\/} = \frac{\it N\/}{\it k * L}$$

  
  
  The result can be scaled to convenient units, for example ``vehicles per km''.

  Note that this way of computing density averages the counts over a length of 37.5 m, which is longer than most traffic detectors. The effect of this should be systematically studied.

• Space Mean Speed, Travel Velocity. It is well known that one can measure velocity either analogous to our flow definition (Time Mean Speed, Spot Speed) or analogous to our density definition (space mean speed, travel velocity). Under non-stationary conditions, the measurements give different results, since, for example, the first definition never counts vehicles with velocity zero. Time mean speed is easier for field measurements; space mean speed is easier to interpret since it is equal to the travel velocity and it is also the velocity which needs to be used in the fundamental relationship between flow, density, and velocity, $q = \rho \cdot v$. Since in a simulation model both are similarly easy to measure, we measure the more meaningful travel velocity. Once a time step, we sum up the individual velocities of all vehicles on a stretch of roadway of $L=5$ sites $=5 \times 7.5$ m $= 37.5$ m. We add these sums for $k=180$ measurement events and then divide the resulting number by $N$ and by $k$, where $N$ is the same number as obtained during the density measurement above:
  
  $$v = {\sum v \over k * N}$$
  
  

• Lane usage. Lane usage of a particular lane is the number of cars on this lane divided by the number of cars on all lanes. It can be computed as:
  
  $$f_i = {\rho_i \over \sum_{j=1}^n \rho_j \cdot n} \ ,$$
  
  
  where $i$ is the lane we look at and $n$ is the number of lanes.

Test networks

Essentially two test networks are used: a circle of 1000 sites $=$ 0.75 km in various configurations, and a simple signalized intersection. Most of the tests are run on the circle networks. The circle can have one, two, or three lanes. In all tests, the circle is slowly loaded with traffic via a parking location at site $x=1$ (where the unit of $x$ is ``cells''). Velocity, flow, and density are measured on $486 \le x \le 490$, thus generating the fundamental diagrams for one-lane, two-lane, and three-lane traffic. Since the circle gets slowly loaded, the complete fundamental diagram is generated during one run.

For testing yield signs and stop signs, an incoming lane is added on the right side of traffic at $x=501$. The characteristics of the incoming traffic are measured by a detector on the last 5 sites of the incoming lane. The incoming lane is operated at maximum flow, i.e. with as many vehicles as possible entering. The incoming vehicles are removed at $x=900$ via a parking accessory. The result of this measurement is typically a diagram showing the flow of incoming vehicles on the y-axis versus the flow on the circle on the x-axis.

For testing left turns against oncoming traffic, an opposing lane is added so that it ends at $x=500$. The traffic control here is again a ``yield'' logic; the difference from before is that vehicles only traverse the opposing traffic, they do not join it.

Last, a three-lane intersection approach is used. The left lane makes a left turn, the middle lane goes straight, the right lane makes a right turn. Incoming vehicles have plans about their intended movement at the intersection and attempt to reach the corresponding lane. The intersection has signals with 1 minute green phase and 1 minute red phase. The typical output from this run is the flow of vehicles which go through the intersection, and the number of vehicles which cannot make their intended turn because they did not reach their lane.

Results

The results are shown in Figs. 32.2 to 32.5.

• Single lane traffic (Fig. 32.2a) has a realistic value of maximum flow ($=$ capacity), but one may argue that it is at a somewhat low density. The problem here is that we do not include slow vehicles; introducing slow vehicles into a single lane closed circle simulation just means that all fast vehicles bunch up behind them, which does not result in a very useful fundamental diagram. In terms of the ``building block'' philosophy, we prefer to run the single lane test with identical vehicles.

• Our lane changing rules do neither change maximum flow per lane nor the density (per lane) at maximum flow. That need not be the case, (102). Again, the density at maximum flow seems a bit low. This changes considerably when one introduces slower vehicles: The free flow part of the curve then bends more to the right and the maximum is at higher densities (90). Also, there are measurements in Germany where traffic with trucks reaches maximum flow at approx. 20-22 veh/km/lane (126), so without more specific data this discussion seems pointless. - We think that the curve without slow vehicles is ``cleaner'' and thus facilitates comparison between models; in reality, the problem is more complicated anyway.

  Also, we generate equal lane usage between the lanes, as should be expected for a symmetric lane changing model (in the absence of on-ramps).

• The flow through a traffic signal that is 50% green should be at half the value of the maximum single lane flow, i.e. at 1000 veh/hour, which is what we find (Fig. 32.4).

• The curves for traffic through stop and yield signs follows the general form of the curve of the Highway Capacity Manual (114). We added the HCM curves for comparison only. In general, we find that a yield sign, when there is no traffic on the major road, generates the same traffic as if there were no sign at all, which should be expected the way the simulation is set up. (It is a bit lower than for the ``circle'' before because the speed limit is lower here.) The stop sign generates a much lower flow in the same situation, because the explicit stop decreases capacity.

  From there, the curves for ``traffic into'' the major road decrease roughly linearly to zero when the flow on the major road reaches capacity. The curve for traffic across a single lane road looks similar to its ``traffic into'' counterpart, which is to be expected because the number of opposing lanes is one in both cases. The curve for traffic across a two lane road provides roughly half the flow of traffic across a single lane road.

  For densities above capacity on the major road, all curves bend ``back on themselves''. If the major road is congested, the speed there is zero, and the gap acceptance criterion ``accept if $gap \ge 3 \cdot v_{oncoming}$'' is always fulfilled, even for $gap=0$. Nevertheless, for ``traffic into'', very little traffic makes it through the yield or the stop sign. The reason is that in Transims, vehicles on the major road that may go through the intersection ``reserve'' the first cell at the beginning of the next link, thus blocking this link for vehicles from the minor link even if the gap acceptance rule would allow the movement. For ``traffic across'', this restriction does not exist, and many vehicles make it through the intersection, probably many more than is realistic. - Note that the HCM does not provide any information in the congested regime.