Resumen
Indian Railways is one of the largest rail systems in the world. It has a unique passenger reservation system, wherein a passenger can book or cancel a ticket online and check the number of available seats. Sometimes efficient alternative modes of transport are not available to a particular train from one location to another. The objective of this paper is to study the trend of ticket booking in Indian trains from the day of opening of reservations to the day of closing of reservations, when the train under study is only means of communication available. Five trains are selected in Indian Railways network so that any other alternative mode of transport between source and destination (such as bus, flight, other trains or an option of including a transit changeover) is avoided by the passengers either due to cost issues or time issues. The trains selected for study include Gwalior-Barauni mail, Pune-Patna express, Mumbai-Okha express and Jaipur-Jabalpur express. Total available seats can be found out by knowing number of coaches in the train. Booking for Indian trains open 60 days in advance and closes around 12 hours prior to departure of train. The total ticket availability is checked every 12 hours during this period for all three trains in different classes (namely, third and second air conditioned and sleeper class), using the online booking website of Indian railways irctc.co.in. Based upon this, trend of booking can be calculated. The general nature of cumulative number of bookings with available seats is seen to increase with time, inspite of seats getting full. For trains with heavy rush, there are high amounts of bookings thus curve has higher slope at beginning and then inflects to have lesser slope. For trains with medium rush, occupancy increases linearly with time. For trains with less travelers or off-peak period, larger number of bookings occur during end of advanced reservation period. Equations can be modelled and simulated if many such trends are studied over the rail network.