In the 2015 Railway Budget of India presented yesterday, it was announced:
We are introducing ‘Operation Five Minutes’ to ensure that a passenger travelling unreserved can purchase a ticket within five minutes. Provision of modified ‘hot- buttons’, coin vending machines and ‘single destination teller’ windows will drastically reduce the transaction time. (Shri Suresh Prabhu, Minister of Railways, India)
The “Operation Five Minutes” initiative has been welcomed by commuters, and seen as a move towards shorter queues at ticketing counters. Now, as an operations researcher, I see some ambiguity in the above announcement. Is the 5 minutes duration the target average time spent by commuters across all stations? Or is it average time spent by commuters at a station? Or is it the average maximum time spent by commuters at a station? Is it the target during peak hours, or non-peak hours, or an average among both? Or is the 5 minutes a sort of service level guarantee for the say 90% of the commuters? The solutions (and investment) will depend on the specific problem statement.
Let us begin by understanding the link between ‘time spent in station to purchase ticket’, ‘transaction time’ and ‘queue length’. Little’s Law states:
Avg. Queue Length = Avg. Transaction Rate x Avg. Time spent in System (at station).
The Law is applicable in steady state systems where average transaction rate keeps pace with the average arrival rate. Let us suppose that it takes about 30 seconds to get an unreserved ticket (transaction rate = 2 commuters/ minute) at one counter, and on an average 20 commuters are in queue, then the average time spent in ticketing office = 20/2= 10 minutes. Now, to reduce the time spent to purchase ticket to 5 minutes, we need to increase the transaction rate to at least 4 commuters/ minute. We can achieve this in two ways, either reduce the transaction time to get ticket at each counter to 15 seconds, or have two counters where each takes 30 seconds to issue the ticket.
Let us pause here to see the enormity of the problem. A recent study showed that about 8,00,000 (8 lakhs!) passengers purchase unreserved ticket per month at a major station. This translates to about 8,00,000/(30*24*60) = 18.51 commuters per minute (=transaction rate). The average queue lengths was about 250 commuters (considering parallel counters), which means the time spent in system = 250/18.51 = 13.5 minutes. The implications are far reaching. On an average 1 commuter ‘wastes’ 13.5 minutes to purchase a ticket ⇒ 8,00,000*13.5 minutes = 7500 man-days lost in waiting at just one station!
Now, if the average time spent in system is 5 minutes, and 8,00,000 commuters are served per month, then the average queue lengths that is going to greet the commuters will be 18.51*5 = 92.55 commuters. Suppose there are 10 parallel counters/ vending machines etc, the average length of each queue is approx. 9 commuters only! Sounds really good.
This move by Railways to guarantee ticket purchase “within 5 minutes”, if implemented only at the major stations with an aim to reduce the average time, is still a significant move. The use of technology-based solutions (hot buttons, smart phones, etc) as well as operational solutions (dedicated windows) are all needed to reduce the transaction time. However, their deployment needs to be carefully planned so that the intended benefits are achieved, and keeps pace with the very increasing number of commuters to be served per day.
Doing Operations Research, etc 