Statistical distribution and analysis of secondary queue of railway passengers

Millions of passengers commute through trains in India every day. Still, thousands of waitlisted tickets are cancelled due to the non-availability of accommodation in the desired train on a particular day. Such cancellations result in dissatisfaction and discomfort to the waitlisted ticket holders and loss of business to Indian Railways. The queue of waitlisted ticket holders, called secondary queue, form when the berths in demand are less than the number of berths available in the desired class of accommodation in a particular train on a specific date. The small number of passengers from this queue are served with confirmed tickets surrendered by the passenger from the primary queue holding confirmed tickets. This paper, a portion of a larger study, attempts to identify the statistical distribution of arrivals and service for the secondary queue. Stationarity and interdependence have been examined for inter-arrival time and service time in context of sleeper (SL) class accommodation of Vaishali superfast express train. It has been found that the secondary queue of the Indian Railways advanced reservation passenger system follows the G/G/C/K model of queuing theory. The results are expected to help the Indian Railways determine various queue parameters and hence optimise the system.