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. 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 duration analysis has an important role to play in estimating the efficiency of incident management strategies. In particular, informing the drivers of the traffic condition can assist in alleviating congestion problems with consequential benefit to the environment. Recently, traffic incident has become one of the main causes of traffic congestion. Studies have shown that incident-induced congestion is between 50% and 75% of total traffic congestion in the urban area (Lindley. 1). Traffic incident is the event that is not planned, one about which there is no advance notice, for example emergencies, accidents, breakdowns, traffic crashes, etc (IEEE. 2). Simply, the traffic incident can be referred to as any non- recurring event that causes a reduction of road capacity or an abnormal increase in demand, (Farradyne, 3). Among all the incidents, breakdown is the most common. The incident data on the M4, collected by WS Atkins and made available for this study, demonstrated that 66% of all incidents were vehicle breakdowns during the period 1 May 2000 and 30 April 2001. Incident management is the systematic planned and co- ordinated use of human, institutional, mechanical and technical resources to reduce the duration and impact of incidents and improve the safety of motorists, crash victims and incident responders (Farradyne, 3). In the main, there are three different methods of analysing incident duration. These are regression (Sullivan, 4). hazard duration (Nam and Mannering, 5), and fuzzy logic (Kim and Choi, 6). The first two methods are statistical analyses that require a large volume of data. The advantage of the hazard duration method is that it allows the problem to be formulated in terms of the conditional probabilities of the entities of interest. Such a formulation can provide valuable insight into the empirical estimation of the model. However, often, there is insufficient data available to achieve statistical significance. The alternative approach, using fuzzy logic, can simulate the human mind in analysing the data as a complex decision making process. This paper presents the results of a preliminary study that has looked at the feasibility of using fuzzy logic theory as a method of predicting incident duration on motorways. The next section presents a description of the data and is followed by analysis of the characteristics of breakdown duration data to establish statistically significant differences. The next section presents the breakdown duration model based on fuzzy logic theory and the results. The final section provides a summary and recommendations for the future.
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.
CHARACTERISTICS OF VEHICLE BREAK- DOWN
Vehicle breakdown, is a type of traffic incident that suggests that the vehicle is disabled on the road for a period of time. The main reasons for vehicle breakdown include: Low battery Flat tyre Mechanical failure Starter motor malfunction Engine fault Electrical failure Figure 1 Relationship between Vehicle Breakdown and Month of Year Normally, only one vehicle IS involved in this kind of incident, and there is no casualty. The duration of the vehicle breakdown consists of the time to report, verify, respond to and clear away the breakdown vehicle. After the vehicle breakdown is reported to the traffic control centre, by using the ETS or other communication media, the recovery company is informed to deploy staff to the incident scene to repair the vehicle or tow it away. Sometimes, the police may be involved to manage the traffic as appropriate, or offer help, especially if a female driver is involved. Figure 1 shows the frequency of the breakdowns occurring on the M4 according to the month of the year (starting in May 2000 and ending in April 2001). The figure shows that the number of vehicle breakdowns increases from May to August 2000 when it decreases, varying little up to April, 2001. It demonstrates that more breakdowns occur in the summer compared to the winter. Figure 2 shows the relationship between the number of breakdowns and time of the day. From the figure, as expected, most breakdowns occur in the day time. In contrast, few breakdowns occur at HOW Of Day igure 2 Number of Vehicles Breakdown vs Time
night and early morning. The number of breakdowns reaches its peak in the early afternoon. Unfortunately, trafk flow data was not available for stretches of roads along which vehicle breakdowns had been reported and therefore no direct relationship between the number of breakdowns occurring per hour as a function of the vehicle flows over the month and year could be explored. However, knowing the characteristics of the traffic along this road, it can be hypothesised that the highest number of vehicle breakdowns are coincident with the higher vehicle flows measured during the summer, reaching a peak during the month of August, and during the daytime hours reaching a ,peak early afternoon. The availability of appropriate traffic flow data is currently being explored. The next stage of the analysis studied the distribution of vehicle breakdown duration for all vehicles and then disaggregated according to vehicle type. The distribution of the vehicle breakdown duration for all vehicle types is given in Figure 3. This distribution was shown to conform to a Weibull distribution. A goodness-of-fit analysis was conducted, and the results showed that the Weibull distribution. It is interesting to note that there are two sharp peaks in the distribution that are coincident with 60 minutes and 120 minutes. This was believed due to rounding errors in the reported breakdown durations of one and two hours. A test was carried out to prove that this indeed was the case. This was achieved by randomly generating breakdown durations using the Weibull distribution fitted to the data. It was shown that these peaks could be reproduced by assuming the incident durations of 58. 59,’61 and 62 were also 60 and incident durations of 118, 119, 121 and 122 were also 120 minutes. This result was shown to be statistically significant at the 70% confidence level.
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