INTRODUCTION 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 Click Here (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
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.
Figure 8 Expected Value vs. Observed Value vehicle type and breakdown time of the vehicle. From the figure, it is clear that there are two waves illustrating that the breakdown durations are longer in the morning and at night for all vehicle classes. The vehicle types, namely motorcycle, car, van, HGV, tanker, and bus were classified into 2 fuzzy sets in the model. It was found that whilst in general the bigger the vehicle, the longer the breakdown duration at night, the duration of the bigger vehicle breakdown is shorter than that of small vehicle at night. This is probably because normally, a heavy vehicle driver does not use ETS to report the breakdown.
SUMMARY AND FUTURE PLAN
This paper has presented the results of a statistical analysis of the duration of vehicle breakdowns on motorways. It has shown that the duration of vehicle breakdown conform to Weibull distribution of different parameters depending on vehicle size. The vehicle duration model, based on fuzzy logic theory, was specified and developed using the input variables vehicle size, breakdown time, location, and report mechanism. The performance of the model, although encouraging, illustrates a good deal of scatter. A standard of message set for incident management should be developed. Further analysis of the model results helped to identify shortcomings of the existing model. These were shown to include time of day when breakdown occurred, location and report mechanism. Additional work is needed to improve the performance by using more variables to modify the fuzzy set, membership, and fuzzy rules. This work will be conducted in the future.