MOTORWAY VEHICLE BREAKDOWN DURATION USING LOGIC THEORY

 MOTORWAY VEHICLE BREAKDOWN DURATION USING LOGIC THEORY

ABSTRACT

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.

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 (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.

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 

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