Simulation of the impact of dangerous road incidents on driver ’ s loss of time on express roads

Incidents on roads are an important factor in traffic flow disruption and a consequent loss of time for drivers. Disruptions can be the result of unexpected road incidents or planned repair works after an incident. These situations differ in the availability of information about the incidents and the resulting rerouting undertaken by drivers. The first part of the paper presents a literature review on the impact of road incidents on traffic and driver's loss of time modelling. Statistical analysis of the database of road incidents on motorways and express roads in the region of Pomorskie was conducted. The average time of arrival of emergency services to a scene and the average time of the rescue action were determined. Simulation research on road incidents was performed for different scenarios with modifications of traffic volume, duration of the road incidents and the degree of road section capacity limitations in various options. The simulation was performed by PTV VISUM software, with the DUE (Dynamic User Equilibrium) module for dynamic traffic modelling. The result of the research is the estimation of the average loss of time for the different variants of the incident, which enabled building a model of the driver's loss of time for specified event parameters.


Introduction
On their daily commute, road users choose their means of transport, the route and the time so that the journey is the most efficient in terms of duration, convenience and expense.With time drivers use the best route variant, which results in the traffic reaching equilibrium meaning that no other decision would result in a lower cost for drivers' journey [1].The network is in a condition of equilibrium as a typical state, that contrary to appearances is very rare.Changes in traffic conditions occur frequently, caused by planned events such as holidays or mass events.The relevant information can be distributed by different methods so that drivers have a chance to change the route, means of transport or decide not to go.In the event of an unexpected incident such as an accident or collision it is impossible for drivers to change the route before setting off.Such events are unexpected and impossible to plan for [2].

The impact of road incidents on traffic
Road incidents can result in obstruction to normal passage on a section, interchange or junction, which involves a change in the parameters of traffic on the network.The character of this phenomenon is dynamic.All resulting actions and effects of an incident affect relevant interconnected parameters such as [3], section capacity and average speed of vehicles.
The decrease in capacity associated with the traffic incident depends on the number of lanes on the road and number of lanes blocked as a result.The study conducted in 2002 [4] suggests, for example, that a block of one lane on a two-lane road in each direction causes a capacity reduction of about 68% in the direction in which there is a traffic incident.Table 1 shows the detailed results.The main effect of reduced capacity is the loss of time of drivers who are indirectly affected by the incident.Loss of time is understood as the difference between total travel time during normal average conditions and total travel time during the incident until normal conditions are restored.The analysis looks at the same time, duration and area for both situations.

Driver time loss modelling methods
There are several methods to estimate the time loss for road users when an incident occurs on a developed road network.Time loss may be estimated for a particular case referring to the road network, traffic volume, incident duration and type.Macroscopic, mesoscopic and microscopic computer simulations can be used for the calculation.For the analysis of road users' time losses as a result of road accidents each of these methods can be used [5].
For example, time loss estimates with the use of macrosimulation means introducing relevant restrictions on properly calibrated network.These changes will contribute to a change in the distribution of traffic on the network and make it possible to determine the changes in traffic volume in each section.In addition, it will be possible to calculate the loss of time for road users who will benefit from an alternative route bypassing the section where the incident took place.

Statistical analysis of road incidents
Databases used in the paper relate to traffic incidents that occurred in the years 2012 -2015 on the motorway and express roads in Pomorskie.This database was made available by the Regional State Fire Service in Gdansk.In total, in the analysed period there were 177 road incidents on road S6; 55 incidents on the S7 and 166 on the A1 motorway where: -‫ݐ‬ ௦ -time loss, -ܰ -volume, -‫ݐ‬ ௭ -incident duration,

Summary
Based on the analysis, it was found that it is possible to map the phenomenon of road users' time loss caused by a traffic incident, using a mathematical model.
It was noted that the most important parameters affecting the total time loss was traffic volume and the level of capacity reduction.These parameters are closely related and have a similar effect on the upward trend in time loss with increasing duration of the traffic incident.A different pattern of time loss increase is related to the extent of the restriction, the nature of the queue and the time needed to restore the traffic conditions to the state before the incident.Due to these differences, the time loss in the model is calculated using three formulas for different levels of restriction.
Loss of time per driver depends on the level of capacity reduction, traffic volume and duration of the traffic incident.The most important factor is capacity reduction because it alters the behaviour of the queue of vehicles.With the increase in restrictions, average time loss rises constantly, though to a decreasing extent.The maximum time loss per driver in given conditions will not be greater than the duration of the incident.
Due to the high importance of the level of capacity reduction for time loss, it is important to remove vehicles from the road or move vehicles to one lane as soon as possible to make at least one lane passable.

Future research
The proposed model of time loss is rather simplified in spite of the many variables.It refers to a situation where a driver cannot change the route.The analysed section was also simplified to one road with unchangeable cross-section and parameters.
Future research is expected to develop a model with more parameters which will allow a mapping of each traffic incident and estimating the time loss for a particular case.In addition to increasing the number of analysis parameters, it will provide a calculation of the additional variables dependent on the calculated time loss and resulting difficulties, such as increased fuel consumption or increased environmental pollution.
The analysis based on a simulation study is expected to be extended by adding field research and statistical analysis of the road incident database with greater detail than the study presented in the paper.The extended model will also be confronted and calibrated with actual data from national roads.

Fig 4 .5
Fig 4. The graphs of average time loss per driver (own study).