This paper presents an analysis of vehicle breakdown duration on motorways. The distribution of breakdown duration was shown to be statistically significantly different for three categories of vehicle type and were shown to conform to a Weibull distribution. A predictive vehicle breakdown duration model was developed, based on fuzzy logic theory. The variables used in this model were: vehicle type, breakdown time, breakdown location and reporting mechanism. The performance of. the model was tested with encouraging results. Clustering of data was shown to be due to rounding errors when the operator reported an incident duration of 60 and 120 minutes. Code Shoppy The unexplained variation in the model was due to the limitations in the specification of the model parameters. This was because the incident data set available was incomplete. This paper highlights the need for standardisation in the recording of data used in incident management.
Incident data is collected from the MANTAIS CYMRU traffic management and information centre. This centre, developed by a publidprivate partnership led by the National Assembly for Wales, provides a cost efficient method of improving traffic management. It covers the M4 from junction 22 to junction 49, (which is 129 kilometres long), and part of A4042. A449, A470, A48M, and M48. In total, there are 88 CCTV cameras that survey the traffic along the motorway and trunk roads. The incidents are reported by several technologies including: Road Transport Information and Control, 19-21 March, Conference Publication No. 486 0 IEE 2002
CCTVsystems Traffic sensors Emergency telephone system (ETS) In-vehicle radio Police traffic reports Automatic Vehicle Identification (AVI) At this stage of the research, only the breakdowns on the M4 and M48 were analysed. From the database, details of 717 breakdowns recorded during the period of 1″ May 2000 to 30’h April 2001 were available for the analysis. The duration of 95% of the breakdowns was no longer than 120 minutes. In the database, the following information for each incident was available: Vehicle type Breakdown occurrence time Breakdown clearance time Breakdown location (obtained from the CCTV location) ETS usedlnot used Response type (including police) Useful information not available from the database, included the reason for the breakdown, name of the recovery company, weather condition, etc. Moreover, some of the aforementioned information was not complete. For example, the response time was not recorded for every incident. In some incidents, the vehicle type is just recorded as “vehicle”. Such incomplete information results from a non-standard mechanism for the collection of the data in the incident management process. This incomplete, vague information makes the modelling of the breakdown duration difficult for traditional mathematical and statistical methods. Fuzzy logic theory is a promising approach to the modelling of problems characterised by subjectivity, ambiguity, uncertainty and imprecision. It was for this reason that fuzzy logic has been used in this analysis.
VEHICLE BREAKDOWN DURATION MODEL BASED ON FUZZY LOGIC THEORY
The concept of fuzzy logic set was first introduced by Zadeh in 1965 (Zadeh, 7). In this section fuzzy sets, with membership functions and fuzzy rules, are formulated to enable the somewhat vague, incomplete information of the accident duration data set available for this study to be processed (Pedrycz and Gomide, 8). Data concerning the breakdown time, location, vehicle type, and report format were used as the input variables of the model. Firstly, the relationship between the vehicle breakdown and these variables were explored. Discussions with the incident management team revealed that the duration increases according to the size of the breakdown vehicle. This was shown to be the case as illustrated by Figure 4. The next step in the analysis was to subdivide the vehicle breakdown durations according to the type of vehicle involved in the incident. The subsequent statistical analysis showed that there I were statistically significant different categories of vehicle types that can be described by the Weibull distribution but with different parameters. These were cars; van, light vehicles and heavy goods vehicles. This is illustrated by Figure 5. The incident report mechanism is another important factor that is known to affect the vehicle breakdown duration. The relationship between breakdown duration and report mechanism is complex. Experiences show that the vehicle breakdown incident is easily located when ETS is Vehicle Breakdown Duration YS Vehicle Type Me “an U. HG” Unm M Vehicle Type Figure 4 Relationship between Breakdown Duration and Vehicle Type
154 Output Variable Figure 5. Vehicle breakdown duration used and the proportion of use of ETS by the car driver is high. However, police can provide more details so that further response can be more appropriate. Few HGV drivers use ETS to report the breakdown. The results of the statistical analysis show that vehicle breakdowns, not reported by ETS. have an average duration of 51 minutes. Whilst, breakdowns reported by ETS have average duration of 46 min. Breakdown location is another factor that affects the duration. Statistical analysis showed that the breakdowns at the junctions, on slip roads, near roundabouts have short durations. When a vehicle breaks down in the middle of the link, it suffers a longer duration often in excess of sixty minutes
The relationship between vehicle breakdown duration and breakdown time during the day is complicated. The experience shows that breakdowns occurring in the peak hours and in the evenings have longer duration. However, the analysis showed that whilst statistically significant, the differences were small. Figure 6, shows the average duration of breakdowns at midnight, early to late evenings are high. However, this result is not statistically significant because there are fewer breakdowns at night, compared with that in the daytime. The conclusions drawn from this comprehensive statistical analysis was used to define the fuzzy sets for the vehicle breakdown duration model. These are given in Table 1 for the 4 variables shown to be most important, namely vehicle type, breakdown time, breakdown location, and report mechanism. The vehicle breakdown duration times were predicted, based on the four input variables specified in Table 1 and compared with the observed. The results are shown in Figure 8. It can be seen that whilst the fuzzy logic model approach shows promise there is a good deal of unexplained variation. The clustering of data due to rounding errors (at reported incident durations of 60 and 120 minutes) is clearly visible. A further investigation of the data was carried out in Figure 7, which shows the relationship between breakdown duration, day Figure 7. Surface of the vehicle breakdown duration model based on breakdown time and vehicle type