Application of Queuing Theory to a Toll Plaza-A Case Study

Queuing areas are the junctions involving vehicles waiting in lines and are characterized by an arrival pattern, a service facility arranged in a particular manner and service time. Since the maximum capacity of roads and service facility (i.e. number of booths in case of tolls) are fixed for certain period (i.e. design period), it is necessary to measure the efficiency of a facility. In case of toll booths on high-ways/freeways which are attractors of vehicles from different origin presumes the flowto be continuous and the vehicle inter-arrival random, adding to this is variability in demand and service (service time in toll booths), poses a problem in optimizing the service facility. In the present study, an existing toll plaza on a 4-lane divided highway having two-way movement (N-S and S-N) is evaluated based on queuing theory. Parameters like traffic volume, space-mean speed and time headway are expressed in 1 h intervals. The vehicle arrival patterns on both directions are postulated to be Poisson distributed and the observed data were fitted to the Poisson distribution. In case of N-S movement, observed frequency and theoretical frequency are found out to be equal indicating the postulated Poisson distribution to be the true population distribution. The use of chi-square test as an index of the goodness of fit for significance level 5% with 10 degrees of freedom justifies the postulated Poisson distribution can be used for future analysis of vehicle arrivals in the respective direction. Finally, the utilization factor indicates a single booth in N-S direction to be under steady-state condition during the study period.