Queuing theory (appeared on L'Express, Mauritius, April 2011)



I was restless. This guy and I, we were seated in different sofas across the room, quasi-equidistant from the mobile phone technician serving another customer. I was on the edge of my seat, ready to claim my due to be served before him, because I came in first – at least I believe so! But my torment transformed into relief (and some embarrassment) when he gave me a slight nod, which among men, can translate into copious conversation: “no worries amigo, relax, I know you were first, and you are rightfully next”. I hardly had the time to nod back in pretense that I am cool and it did not really matter to me, when this woman just walks in straight to the nirvana of service. She was actually oblivious of her faux-pas, and I was restless again.

So, when I was asked to queue up for customer support at the MRA office, I was not ready for yet another survival-of-the-fittest (with a good dose of randomness) queuing regime, especially with the impending tax burden. But it was as smooth as driving through Port Louis on Sunday night. This polite guy stood at the right place and through a simple question gave me a ticket that was a triage for the right counter. I was seated comfortably in front of a display and waited serenely for my number to appear. Furthermore, my query was answered politely and properly, by a lady with a smile. It went so smoothly that I was happy I paid my taxes, well almost.

To me, the queuing method to greet customers reflects a lot on the organization. So, it came with no surprise when I received excellent service from MRA – convenient online taxes, proper information on the phone, service through email.  This is unfortunately an exception.  In so many organizations, public and private, you walk in and you have no clue how to proceed, when, by whom and in what order you will be served. The most obvious queuing discipline is First In First Out (or First Come First Served), and sometimes the highest priority first. But I have come across bizarre queuing regimes (or lack of). Serve the loudest first, serve the cutest first, or the worst I have encountered: after lining up for 10-15 minutes to pay an electricity bill, the remaining queue was told to come back in 30 minutes, because it was lunchtime!

Queuing has a complete theory, since it can be a little more complicated than the self-assembled formation for “dalpuri” at lunchtime. Queuing is studied mathematically to analyze queuing processes (arrive, wait, served and depart), and evaluate performance of the strategy of providing service: how long you have to wait on average, or how many customers are served in a given period of time.

It is applied in telecommunications, traffic engineering, call centers, computer operating systems, as well as shops, offices, and hospitals.  The most famous formalization of queuing was by David Kendall, who in 1953 developed a notation to describe queue characteristics like arrival time distribution, service time distribution, the number of servers, etc.  

Developing the optimum queuing model is by no means easy, especially since in most systems the arrivals in the queue can be random (or stochastic) and the interval between arrivals can be independent (referred to a Poisson process). This uncertainty makes it challenging to mathematically (or through computer simulation) develop the best method. 

One of the laudable initiatives by our health ministry was to stagger arrival times in our hospitals. We can only wish that someday our keepers of justice will realize how unfair (and unproductive) it is to call everybody at the same time to the court. 

Mathematical formalisms are sometimes useful, but in the first place, some common sense and attention to details can bring a huge improvement in quality and fairness of service. Some discipline from queue makers would be nice too, like Brits for instance, who are well-known for queuing enthusiasm. As George Mikes puts it, even if alone, an Englishman forms an orderly queue of one.

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