Application of Queuing Theory to a Railway ticket window

Abstract

Waiting time in a queue is a common problem in all the service disciplines and some people may reluctant to join a queue due to long wait. These phenomena can be seen in the case of a railway ticket service also. A well-drafted model is needed for the management to comprehend the circumstances better. This paper centers on a single server queuing model in which the arrival process is a Poisson process and the service times follow an exponential distribution or a constant. In this work, we have studied queue management at a railway ticket counter with a single server. For this, we have collected data for one week from an NSG-3 category railway station and analyzed the data to find the pattern of arrival and service distribution. It has been seen that performance measures and service distributions of neither of the queuing models M/M/1 and M/D/1 conform to reality. So, we propose an approach to apply the mathematical queuing model more efficiently for such systems. We have used an M/G/1 model in which service time is calibrated based on a normal distribution. Based on the data collected from an NSG-3 category railway station for a day, a normal distribution is fitted for the service rate and found that the fit is good statistically. It is found that the resulted performance measures show significant conformity with the observed field data.