Sunday mornings are very special for everyone. It starts with laziness and happiness. Pace of every work slows down and we become insouciant for that day. But a Sunday of November 2016 was not so peaceful for an Indian. He was collecting old notes of Rs. 500 and Rs. 1000 to deposit in banks since these were no more legal tender. People gathered in scrum to enter banks. They had to wait in long queues for hours. Line is an integral part of the society. We can see line at bus stops, ticket counters, polling booths and even religious places. I was wondering how a line is formed and why do we need it to get something?
Why to wait?:
Take an example of a multiplex ticket counter. There are four counters and four customers. Each customer would approach four different counters separately to get tickets faster. Now a fifth customer enters. If any of the counter is vacant, he would approach it. If it is not, he would stand behind a person to wait for his turn. Since number of counters did not match number of customers, line was formed. Stated differently, line gets formed when there is demand-supply mismatch. We use queues for short-term demand fluctuations as we cannot increase number of counters in short run. While stinting through various articles and papers, I found the Freakonomics podcast – What are you waiting for?. This podcast is an interesting source to understand queues. (I would give reference of this podcast at various instances) Felix Oberholzer-Gee, an economist at Harvard Business School said in the podcast, “As a consumer in a market economy, you should expect that everything happens for you instantaneously all the time. Then when that’s not true, you need to ask, “What’s the constraint?” The constraint is sometimes cost, is sometimes availability of skilled personnel, sometimes availability of space, but there’s got to be some constraint otherwise we wouldn’t see a line.”
Time is Money – But can you buy it?:
Let us understand significance of time in a queue and its impacts from following examples
- Let us take a very common example of any famous temple or pandal. Generally we see more than one type of line. One being a line for commoners, which is free of cost and other is called as ‘VIP Line’, where you pay to get immediate darshan. Free line is too long and time-consuming while VIP line is shorter and reduces waiting time. Why this system was developed? As time is an important factor in a queue, we give value in order to save it. If you consider your time to be more precious than the cost of VIP entry, you might pay and buy your time.
- What if you are in hurry and have no time to wait in line? Can you cut the line in between? Is it allowed? Generally, it is not allowed. An experiment was designed by Oberholzer-Gee, where volunteers would cut a line by offering some dollars to people standing in front of the line. They gave reasons to cut line which appeared genuine. The result was interesting. People would allow to cut line if you ask nicely and some would allow even without taking any monetary compensation. Monetary compensation also varied from person to person. Since each person valued his waiting time and compared it with the compensation, negotiations resulted in rise in monetary compensation too. The next part of the experiment was that same volunteers would go and ask same persons to cut the line the next day. In this situation, the results were more interesting – “One of the social norms around line-standing is that it’s not cool to refuse someone who wants to cut in line — until it becomes a regular thing. Because now the transaction moves from the moral realm to the financial realm: you are stealing time from me!”. As we could see, cutting the line is allowed under genuine reasons unless it becomes a usual thing.
- Given a choice, would you stand for a slice of pizza or for lunch? We always prefer one thing over another after considering costs, benefits, time, intensity, efforts and opportunity cost. So in this situation, we would calculate time required to stand (say 1 hour), benefit one gets (pizza slice / lunch), intensity of the need (How hungry are you? If you are very hungry, you would probably have lunch) and efforts for standing in queue (leg pain, sweat, etc.). We would also take into consideration other restaurant which might give food instantly or just avoid going out and get a home delivery instead. This is opportunity cost. Thus we evaluate whether standing in line is worth the benefits we get and time we invest.
- Now suppose you are in a line of ticket counter. Consider two scenarios; one where the tickets are free of cost and the other where you have to pay some amount say Rs. 100. Under the first scenario the cost of waiting is the time we stand. So, one who is desperate to watch the movie, would go early and try to be the first in line. Those who are not might go late and would be indifferent of getting ticket or not. Under second case, the cost of waiting is the time we stand plus the cost of tickets. Hal Varian, professor at University of California, Berkeley, in his book Intermediate Microeconomics – A Modern Approach said, “If you allocate a good using a price set in dollars, then dollars paid by the demanders (i.e. buyers of tickets) provide benefits to the suppliers (i.e. ticket sellers) of the good. If you allocate a good using waiting time, hours spent in line don’t benefit anybody. Waiting in line is a form of deadweight loss – the people who wait in line pay a price but no one else received any benefits the price (price here means the time they spent in line waiting) they pay.”
Fall in line:
We are surrounded by many queues on daily basis. After dialling a number, we hear a dial tone which is the queue of signals formed while transformation. Similar is the case when our YouTube videos buffer. On assembly line in factories, units queue up before, during and after the process. Vehicles queue in traffic and service stations. Patients queue at doctor’s clinic and various deliverables at work line up during busy seasons. All are very common examples of queues. And yes, queues have rules too. In most of the cases, ‘first come, first served’ is a rule. We can witness this at doctor’s clinic, banks, counters, etc. There are some cases of ‘random selection’ (e.g. Random pick of a token from pool of tokens) and very rare instances of ‘last come, first served’ (e.g. While getting in and alighting from the train or elevator). Rules give line a structure to arrive, wait and depart. While discussing on podcast, the importance of line, Fishbach, a professor of behavioural science and marketing at the Booth School of Business at the University of Chicago, drew his attention to an experiment he designed. He divided participants in half to taste a smoothie. In the first group, few researchers acted as participants and stood in front of actual participants. The other group had no line. It was found that the group which waited said that smoothie tastes better. If we waited, we become more curious and enthusiastic when we get the desired thing. He concluded that we value something once we wait and get it. He also compared line system with an auction system. He said, “Everybody is being served based on the amount of time they invested, than a system of auction, a system where people are getting products or services based on how much money they have.” Queues give justice to the time people or things invest in waiting. Hence he concluded that people prefer a system in which there is a queue.
In schools, we were told to walk behind each other in a straight line by our teachers. At ticket counters we were forced to be in a single line by railing or security guard. Even in geometry, we could not draw a straight line without ruler. So, do we always require someone to maintain line? I guess this is psychological. When students are in classroom for hours waiting for the recess bell to ring, they would swoop out of the class quickly once it rings. This is an emotional outburst and hence students would never be in the position to form a line. Hence we need teachers to control the line and emotions. Just imagine how schools, theatres and other public places would function without a disciplined line. It would pressurize public systems and resources & disrupt law and order.
Discipline must come as a habit otherwise it must be forcefully imposed. Britons are supposedly the creators of queuing concept. Queue discipline is considered as an essential part of Britishness. However, the podcast mentioned that proper line behaviour is not an universal concept. India and China are the most populous countries in the world and proper behaviour is not seen in such countries. It also argued that a queue behaviour represents and depicts more of demand supply gap than culture of the region. Hence, forming proper queue is always considered as the second best. As it is considered secondary, we lack in maintaining proper line behaviour even if the line is not long. This habit has been rooted in our nerves.
A Science of Line and it’s Future!
Ever thought of such deep study and analysis of a line? Let me surprise you with more of such interesting facts! There are few theories in operations research like queuing theory, critical path analysis and linear programming problems which are applied to allocate resources, curb waiting time and reduce costs. These theories have historical significance as they were written during world war. Queuing theory has been applied to analyse queue patterns, developing mathematical models to reduce waiting time and suggest a better pattern that would reduce complexities. Agner Krarup Erlang, a Danish mathematician, statistician and engineer, was the pioneer of queuing theory. He studied patterns of queues in a telephone exchange. Critical path analysis is useful in projects where different tasks having their own lead times, durations and costs. It helps us to analyse which task should be completed first in order to reduce total time of the project and thereby reducing costs. It was applied for the first time in military projects. Linear programming problem helps in managing demand supply mismatch and costs associated with them. However, it is also widely used in creating models in diets, chemical formations, engineering, etc.
What is the future of line? Technology has made our lives very happy and convenient. Multiplexes and railway stations have no more long queues as we can book tickets online. Though we have managed to curb lines with the help of technology, queues and its’ theories don’t become redundant. These theories have allocations and costs at their centre and not humans. So queues formed by technology are also part of these theories. Assembly line, data buffering and online queues will continue to dominate our future. Recent examples of online iPhone and Coldplay concert bookings were also queues. Online booking gives businesses clear picture of expected demand. It helps them to plan their production and forecast their profits. As we embrace newer technologies physical queues will extinguish and digital queues will increase. It is a topic of separate research whether digital queues change these theories. Major concerns for digital queues are security and privacy. We need to think about the data traffic and ability of infrastructure to handle it. Whether such queues would have the same rules? Whether people’s behaviour would affect such queues? Answers to these questions would be required early to ease the burden on resources and make people happier in future. It is equally important how policy makers analyse and use these theories and plan our future.
So next time you see a queue don’t be impatient. Some constraints might have created it. So keep calm and enjoy standing!
I finished this article while I was standing in an ATM queue to withdraw cash. So make the most of it.
– by Swapnil Karkare
photo credit: paul_appleyard <a href=”http://www.flickr.com/photos/20342758@N00/7279490200″>Windlesham Arboretum 27 May 2012 049 via photopin (license)