Introduction
There has been a phenomenal growth of motor vehicles in India in the recent past. The disproportionate growth in the traffic vis-a-vis growth in road length, along with unauthorised encroachments on road space, lack of traffic and lane discipline and deficiencies in traffic control have contributed to the increasing problem of congestion in urban areas. In addition to increased travel time and delays, traffic congestion increases air pollution due to vehicular emissions.
There is no consistent definition of congestion in terms of a single measure or set of measures that considers severity, duration, and spatial extent. Measures related to travel time and speed are the most flexible and useful for a wide range of analyses. Congestion can be defined as follows.
- Congestion is travel time or delay in excess of that normally incurred under light or free flow travel conditions.
- Unacceptable congestion is travel time or delay in excess of an agreed upon norm. The agreed upon norm may vary by type of transportation facility, travel mode, geographic location and time of day.
Research organization and technical bodies have recommended standards and specifications for all design parameters to the generalized situations. But the congestion severity on an urban road is affecting the general design condition in a diverse ways and the recommendations become ineffective. The type and intensity of congestion depends on many quantifiable factors such as volume, speed, headway, ratio of slow moving and fast moving vehicles etc. In this context, the quantification and evaluation of congestion severity has been taken as an important research to give a modification to the generalized design procedures and also to suggest the remedial solutions for releasing congestion. In this study an approach is given to identify the suitability and type of technique that can be effective and also a model is built to quantify the congestion using fuzzy logic.
Fuzzy set theory is based on a set theory, which allows for the vague boundary of a set, and thus, it enables the analysis of problems involving ambiguity & uncertainty.
"As complexity rises precise statements lose meaning and meaningful statements lose its precision"- Zadeh's law of incompatibility.
Quantification of Congestion Using Fuzzy Logic
- Quantification of Congestion is done using Mat lab (fuzzy tool) software with Speed and Inter Vehicular Distance (IVD) as inputs. The ranges for Speed are set based on IRC 106:1990 guidelines and IVD are calculated from the Green shields formula given below.
S = 21 + 1.1 V, Where S = Spacing in feet and V = Speed in M.P.H
In this study, this formula is converted to S.I Units and reframed as follows:
S = 6.42 + 0.21 V
Where S = Spacing in meters and V = Speed in KM.P.H
Using this equation the ranges are mathematically fixed for the inputs in this model.
- Based on the above values, the membership functions (ranges) for the inputs are defined in linguistic variables (i.e. in words rather than numbers).
- The rule base (user defined conditions) was developed using nineteen rules in the rule editor. Actually 25 rules are applicable to this model, since some of the rules are not existing in reality; they are removed from the model (e.g. When Speed is VHigh and IVD is Vlow the Congestion can't be defined, since these are not possible in reality). Then the output 3D surface is obtained from the model. If there are any spikes in 3D surface, it indicates errors in the model. These errors can either due to rule base or due to membership values. The errors in the membership functions and rule bases are corrected by the trial and error method. Therefore, if a user enters the value of Speed and IVD, the model displays the level of congestion.
The above equation is based on the assumption that all vehicles travel at the same speed and are spaced at equal intervals. This formula provided a basis for measuring capacity in relation to speed and spacing, relying mainly on the empirical approach wherein relationships between two or more variables were developed from field observations. There are totally 19 rules framed for this model. The rule viewer through which the values of congestion is obtained .
From the analysis and results it is inferred that the output obtained from fuzzy model is depicting the real time dynamic nature of the traffic congestion. Hence, the model is validated for its reliability.