Link Travel Time

This section discusses some traffic rules and patterns, which display the traffic congestion levels and the relationship of spatial and temporal dimensions in traffic network. The influences of traffic network may cause traffic flow to raise the delay of vehicles. Also, LTT traffic patterns are the main component to produce our historical TTP. As shown in Figure 8, there are the three knowledge patterns of LTT: Spatial and Temporal Patterns (STP), Crossover of Spatial and Temporal Rules (CSTR) and Crossover of Spatial and Series Temporal Patterns (CSSTP).

Figure 8. Concept of Three ITT

Spatial and Temporal Patterns (STP)

The first knowledge of LTT presents about the traffic condition between time and location as shown in top of Figure 8. We denominate this kind of pattern as “Spatial and Temporal Patterns“. The STP is mined from historical traffic database by aggregating the TIS table in spatial and temporal dimensions. Support and confidence of each STP are determined by calculating numbers of days and times of each traffic levels in every time interval. Spatial dimension stands for the link identification attribute, and temporal dimension is the classified index of time domain. The classified temporal dimension categories include peak or off-peak hour, and holiday or workday, etc. Congestion level, support and confidence can be calculated by aggregating the TIS table in the same spatiotemporal conditions. The STP flow chart is shown in Figure 9 and the format of STP is listed in (3). The Time index are 1~48 and each for half hour of 24 hours a day. If today is holiday then the holiday slot is 1, but for workday is 0. Loc. is road section, Dir.

is vehicle’s direction, and traffic level stands for congestion level ranged from 1~9, respectively.

Figure 9. Flow Chart of STP

[Example of STP]

Considering 8 AM Monday (office day), support value on July 2005 (31 days) is (21/31)*100%= 67.74%. The confidence value is concerned the traffic condition of objective location. If congestion occurred in workday 18 times during that month, then the confidence is (18/21)*100%= 85.71%. From above discussion, the meaningful STP is:

STP-(Date, Time index, Holiday, Loc., Dir., Traffic level, Support, Confidence)..(3) Î (Mon., 16, 0, FuXing S. Sec. 1, ↑, 4, 67.74%, 85.71%)

Traffic status is in congestion.

Additionally, STP are stored in the knowledge class, and can be easily transformed into rules for the TTP inference at run time by combining the link attribute in table of traffic network. The congestion level can be transformed into estimated traveling speed on that link, and thus the estimated travel time can be calculated by dividing the length of the link with the estimated speed.

Crossover of Spatial and Temporal Rules (CSTR)

The second LTT knowledge is used to find the traffic information of crossover road sections, which consists of two space dimension and one time dimension. So the name

of this knowledge is “Crossover of Spatial and Temporal Rules”. The CSTR is generated by integrating two traffic sequences of the crossover road sections. The correlations between two crossover road sections may be independent with each other.

Thus, what correlation (positive or negative) in the target crossover is concerned? If positive correlation, it means that the traffic flows of vehicles’ directions on the former road section has a tendency to drift towards the latter road section. This is called as

“transmit probability” on this intersection. According to the CSTR knowledge, we can understand the impaction of congested vehicles, and realize the drivers’ behaviors that they used to route. The correlation value between two road sections can be calculated as follows (4).

Correlation = P(A)^P(B) / P(A)P(B) …(4)

Here the equation, P(A)^P(B) = P(A)*P(B), means traffic sequences of two crossover road sections (A and B) are in congested status in the same time interval. Also, support values in CSTR are calculate by P(A)^P(B). The CSTR flow chart is shown in Figure 10. The first process executes to encode the sequence patterns of the target direction road sections. If average speed of road section is below 25 km/sec, encode 1 (Because we are interested in congested status). Higher the average speed 25 km/sec is encoded 0. After this transformation, the road section congestion sequence can be generated. Then, the computation of correlation values of crossover sections can refer to the equation (4) for generating CSTR. Thus, if A and B is negatively correlated, then the result of correlation value is less than 1.

[Example of CSTR]

Considering two STP on Monday of FuXing S. Sec. 1 (↑) and RenAi Sec.3 (Æ), we encode the average speed in binary code with half hour interval from 6 AM to 11 PM, as following:

FuXing S. Sec. 1 (↑): 00111 10101 11111 11011 11111 11111 1110 RenAi Sec.3 (Æ): 00011 11111 11111 00001 10011 11110 1100

Then, the support value is 20/34 = 0.5882, and correlation value is 0.5882 / (22/34)

* (28/34) = 1.104 that calculated be equation (4). From above discussion, the meaningful CSTR is:

CSTR-(Date, Holiday, Location, Direction, Support, Correlation) … (5) Î (Mon., 0, FuXing S. Sec. 1, ↑)

^

It’s positively correlated congestion in this crossover, Sup.= 58.82%, Corr.= 1.104

Figure 10. Flow Chart of CSTR

Crossover of Spatial and Series Temporal Patterns (CSSTP)

The third LTT knowledge: CSSTP, which is shown in the bottom of Figure 8. The main difference motive between CSSTP and CSTR is, “how long the traffic condition status will continue?” In other words, the CSSTP can find out a period of time that the congestion status will continue on crossover road sections, or it is just a short period phenomenon. This knowledge patterns can provide more useful information for the

traffic center manager, and help them to do some actions for improving the traffic flow.

The name of this knowledge patterns is called “Crossover of Spatial and Series Temporal Patterns” (CSSTP). The format (6) and a CSSTP record are listed below:

[Example of CSSTP]

CSSTP-(Date, Time index start, Time index end, Holiday, Loc.1 Dir., Loc.2 Dir., Traffic level, min. Sup., min. Con., min. Corr.) …(6) Î (Mon., 16, 19, 0, FuXing S. Sec. 1 (↑), RenAi Sec. 3 (Æ), 4, 60%, 80%, 1.1) Traffic status is congestion in this crossover from 8AM to10AM.

In CSSTP, the ARCS (Association Rule Clustering System) [9] technique is applied to find out the continue traffic condition (e.g. congestion) of CSTR. As the flow chart of Figure 11, first, ARCS use the binning method to replace the data of attributes (e.g. space, time) with their corresponding bin number, and segmentation criteria separate every crossover road sections of CSTR into parts by human expert.

Figure 11. Flow Chart of CSSTP

In association rule engine of ARCS, we recomputed support and confidence of CSTR in order to compare the min. support and min. confidence of the heuristic optimizer. Then, we transform these association rules into two dimensions bitmap and use grid clustering technique to find out the temporal continuity of the traffic condition in the same crossover road sections. The bitmap clustering is shown in Figure 12.If the association rules of CSTR are corresponding to threshold of min. support, min.

confidence and min. correlation, it will encode “X” on the bitmap. Then, the Euler formulation is used to compute the distance in grid map for clustering the nearest grids.

The clustering mechanism may extend the temporal dimension of traffic levels and group them together. (Here, we consider the time dimension). Thus, the results of these groups are regarded as CSSTP. In order to make CSSTP more accurate, the clustering analysis is verified with test data, and use heuristic optimizer to adjust the parameters (e.g. min. support, min conf., min. corr.) in loop procedure. Finally, more accurate results of CSSTP can be generated after the loop process of ARCS.

Figure 12. Bitmap clustering of CSSTP