«BASIC HUMAN DECISION MAKING: An Analysis of Route Choice Decisions by Long-Haul Truckers John Holland Knorring Advisor: Professor Alain L. Kornhauser ...»
The two different calculations were done using two different sets of inputs. For the sections dealing with CoPilot, the inputs for the times, and thus derived speeds, were taken from the output of the trip calculation performed by CoPilot. The other section uses an assumption of 55 mph on the downtown route and 65 mph on the bypass route. The
following are the observed number of trucks on the downtown (light green) and bypass (pale blue) for each city used in the calibration of the model:
5.4 Derivation of Perceived Speeds After obtaining the parameters of the ∆Utility function through the maximum log-likelihood estimation program, it is now possible to determine the perceived speed on the downtown route.
Where Z is set equal to the ∆Utility function and P is equal to the probability of choosing the bypass.58 Equation (5-10) is equivalent to function (5-7).
In generating the forecasted probabilities for usage of the bypass route, the
following were the results:
One of the most valuable aspects of the truck data set that this thesis utilizes is that the probability of trucks on the downtown and bypass routes is known. Because of this fact, it is possible to back out the value of the ∆Utility function. Logit models are generally used to make predictions of the expected probability of usage for the routes
based on the ∆Utility function. However, because the actual probabilities of usage for the routes are available, it is possible to use the ∆Utility function to derive the perceived speed on the downtown route and by perturbing the input probability for the bypass route, it is possible to generate a curve for the perceived speed for all probabilities.59 Using the two sets of speed assumptions, CoPilot and 55/65, when looking at the Logit function, the only variable that is free to change with the probability on the bypass route is the time spent on the downtown route. Because the distance of the downtown route is known, it is easy to solve for speed on the downtown route.
6 Commentary on Results The previous chapter covered the intricacies of Logit models and the parameter estimation that is used to develop an appropriate model for this data set. Ten of the thirteen possible case cities were used as inputs in running the optimization model that predicted the maximum log-likelihood estimators for the parameters. The other three cities did not have significant data that would allow for any reasonable estimation of parameters. The results of the optimization can be put into a single formula that can then be applied to all of the case cities to generate the perceived speed curves. All one needs to input are the respective distance ratios and time ratios for the case cities. The format
of the equation is as follows:
The parameters derived via the optimization model are the result of an aggregation of all the probabilities and distance and time ratios for all of the case cities.
Therefore, the perceived speed curves generated will not necessarily be in line with the observations of the percentage of trucks on the bypass route and the assumptions for speeds: both CoPilot speeds and 55/65 speeds. However, the overall qualitative aspects of the perceived speed curves are a good estimate of the actual perceptions that truck drivers have base on their perceptions. The portions that are of significant value are the coefficients for the distance and time ratios. These coefficients represent the tradeoffs that the truck drivers have displayed between distance and time. Discussion of the coefficients will follow the results of the perceived speed curve generation.
80 70 60 50 40 30
80 60 40 20
6.1 Interpretation of Perceived Speed Curves The perceived speed curves, while time consuming to generate proved to be quite interesting to analyze. The meaning of the perceived speed curves is as follows. The percentage of trucks that follow the bypass route can be written as a function of the trucker’s perceptions of conditions on the downtown route. The assumption is that the truck drivers know the distances of the downtown and the bypass routes. They do not know the traffic conditions on either route with certainty. However, they might be able to form some sort of view or perception of the conditions on the downtown route. These perceptions are formed in a number of ways. One example of a way to form a perception is if a truck driver has driven on the downtown route before, he might be familiar with the layout of the route and be able to form a guess as to the level of congestion on the route.
If when the last time the truck driver chose the downtown route, there was a significant amount of congestion, the driver might suspect that there currently is congestion on the route and his perception of the speed on the route will therefore decrease. When the perceived speed decreases, the probability that the driver chooses the bypass increases.
When examining the perceived speed curves, it is important to note that the curves were generated strictly using observed probabilities of usage, distance ratios and time ratios. As was stated earlier, there are many more factors that contribute to the cost function for the drivers. However, this revealed preference data set did not include any other data besides location and time. As a result, it is impossible to determine the exact values that drivers put on distance and time. However, one can speculate that, based on the relatively flat slope of the curves that drivers value distance and time at very different levels. The flat slope at the point of indifference signifies a very high level of risk
aversion. In other words, there is a fairly large change in the percentage of people that use the downtown route for an incremental change in perceived speeds. This means that the truckers are very risk averse when picking their routes.
6.2 Points of Indifference The interesting aspects though are the tradeoffs that the drivers make. The slope of the perceived speed curves at the 50th percentile, or the indifference point (the 50th percentile is the indifference point because there is a 50/50 chance that the driver will take the downtown or the bypass route), is remarkably flat. There is only a 10% decline in usage for a 4 mile per hour change in the perceived speed. However, when one considers the speed difference when the percent of trucks that use the bypass route in the 90-94 case moves from 80% to 20%, the increase in perceived speed is almost 25 mph.
If one considers a 25 mph change in travel speed, over a 1000-mile trip, the savings of time is enormous.
It is also interesting to examine the plot of the perceived speed in relation to the ratio of distances on the bypass route and the downtown route at the point of indifference.
The following is a chart of perceived speed vs. the distance ratio at the point of indifference between the bypass and downtown routes for the truckers. The plot uses the perceived speeds generated using the 55/65 assumption.
20 10 0 0.0 0 0 0 0.10 0 0 0.2 0 0 0 0.3 0 0 0 0.4 0 0 0 0.50 0 0 0.6 0 0 0
There are a few interesting aspects of this graph. First, the intercept of the regression is approximately equal to 62 mph. This is an interesting quality because the perceived speeds were generated using an assumption of 65 mph on the bypass route.
The Y-intercept corresponds to the point where the X value is equal to zero. For this graph, the meaning of X equaling zero is the ratio of distances for the two routes equals zero. One would expect the Y-intercept to equal 65 mph. Additionally, it appears as if the value for the perceived speed drops off rather precipitously as the distance ratio increases only a relatively small amount.
6.3 Interpretation of the Parameters When analyzing the results of the optimization program, it was interesting to contemplate the meaning of the coefficients of the R variables. The ∆Utility function is essentially the gain in utility for an incremental change in either time or distance in the trip. Based on the parameters it appears as if the magnitude for the time parameter is significantly higher than for the distance parameter. This would suggest what this study suspected all along is true: truck drivers are first and foremost time minimizers before anything else. Truck drivers look for the shorter routes, but only take them because they are also the minimum time routes.
6.4 Pitfalls in the Analysis After performing the analysis of the data and performing the analysis of the perceived speed curves, it became evident that this analysis is not entirely perfect and there are a number of areas where the analysis could be improved. Some of the specific areas that could be improved on are: small sample size for certain cases, infrequency of data collection, inaccuracy of stop definition, and inaccuracy in selection of trucks on both the bypass and downtown route.
6.4.1 Small Sample Size for Specific Cases After performing the analysis, it became evident that certain cases were not as fertile as this study had hoped. There are a few reasons why there was not a significant amount of data for a given case. One reason, which will be covered shortly, relates to the
heuristic used for the counting of trucks on routes. Another explanation relates to the small area for some of the cases. The Wilmington, DE case was especially difficult.
Each of the routes, both bypass and downtown, were approximately 9 miles in length. If one assumes that all of the trucks that could have potentially been on the route were pulled from the data using the Box Algorithm (this is quite and ambitious assumption), then of those trucks selected, assuming and average interval of data collection of 45 minutes, the probability that the truck reported its location while on one of the routes is only around 20%. This percentage is would result in the maximum number of trucks pulled from the data set. Wilmington was not the only case where infrequency of reporting was a problem.
6.4.2 Infrequency of Data Collection The previous section alluded to some of the problems relating to the infrequency of data collection. This was especially problematic for most of the cities. Because of the infrequency of data collection, it was significantly harder to determine stops. For example, if a truck came into a city, chose the downtown route, then got of the road to make a quick delivery, and returned soon after the delivery, the truck should have been removed from the data set, however, the truck probably was grouped into the slower end of the 30-75 mph selection heuristic.
mentioned problems with infrequency of data collection, it was quite difficult to determine stops. It was entirely possible, in fact likely, that a truck made a stop between observations, but the stop selection heuristic showed that the truck was still moving. It is possible to argue that the inability to discern stops was equally detrimental to the bypass data as the downtown data, however, the strength of this argument is fairly limited. It is much more likely that a truck made a stop on a downtown route than on the bypass route.
There are far more potential stops that a truck could make that are closer to the downtown area than the bypass zone.
6.4.4 Problems Associated with the Box Algorithm One of the most pressing issues that should be addressed in future analysis is in regards to the Box Algorithm. The Box Algorithm is a heuristic used to simplify the collection of truck data from each of the routes. The problem that this thesis encountered though was when the bypass and downtown routes were significantly close to one another. It was very difficult to find a box that would maximize the length of road in the box while at the same time no include any portion of the alternate route or another major highway. Additionally, it was very difficult to ensure that the length of road selected by the downtown box was equal to the length of road selected by the bypass box. Because of this, the count of trucks on either one of the routes could be skewed towards the route with the larger box. Lastly, the boxes did not include the entire bypass or the entire downtown route. Because of this, it is even more likely that the count of trucks on the
routes was biased downwards. Also, in picking the boxes, it was harder to find a box to pick the bypass route because of the fact that the bypass route generally had much more curvature because it skirted the city whereas the downtown route was generally a straight shot through the city. When the road was straight, it was much easier to select data.
6.4.5 Overall Impact on the Model All things considered, a majority of the previously mentioned pitfalls in the analysis should only have a limited impact on the analysis process. Because the model is should be used in qualitative applications, the soundness of the model should remain unchanged. However, the problems associated with the Box Algorithm were significant.
Possible solutions to the problem will be covered in the following chapter.