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First-year student Rohan Rajiv is blogging once a week about important lessons he is learning at Kellogg. Read more of his posts here.

I’ve been sharing a run of operations learnings of late as a part of this series. This has been surprising as I never considered myself a fan of the subject. However, thanks to a combination of a professor (Gad Allon, who last week was named Kellogg Professor of the Year) who’s more than managed to pique my interest and a realization that learning to manage business operations isn’t very different from managing life operations, I’ve enjoyed my time studying operations. And today’s topic is managing queues.

Managing queues is particularly interesting as we all experience, and generally dislike, queues.

The average wait time in a queue is given by the following formula:


To break down each of the parts of this formula in simple terms (with an analogy of a queue at an ice cream stand):

  • Mean service time is the amount of time taken by the person serving the queue
  • Utilization is the amount of time he/she spends serving out of his/her total time on the job
  • Variability (more on this later) is a measure of how steady the demand is. If people enter the queue steadily through the day, it is much easier to deal with demand versus random fluctuations

Things get interesting when we study the effect of utilization on increasing waiting time. This graph, from HBR, illustrates it beautifully:


What this graph is saying is that waiting times more than double when your solitary ice cream server is working 80% of the time. It doubles again when he finds himself working 90% of the time. Why? Because delays are caused by sudden fluctuations in the queue, e.g., a mass of tourists that come in to buy ice cream in the midst of their city tour. And since our solitary server has no spare capacity, it is inevitable that waiting times go up.

So, if you are staffing your restaurant, for example, and if you find yourself running at 100% capacity all the time, that may not be the best thing for your customers since it is inevitable that waiting time goes up (If you are an exclusive restaurant, it may not be a bad thing, but that’s a different matter.).

The insight in managing our personal lives is pretty profound. If we organize ourselves such that we always find ourselves running at 100% capacity, it is inevitable that queues will build up on our plate. That’s because work doesn’t arrive at a constant rate. An emergency project is bound to show up and, if we’re running with no safety capacity, that could be a problem. Additionally, we’ll never have the bandwidth to deal with other sorts of fluctuations that may occur outside work, like a family member that gets sick or a friend who needs help. So it is a good idea to maintain safety capacity.

And how do you do that?

Learn how to scope projects well. I had a manager who was a master at making sure we needed no late nights to get to the finish line on our projects. He believed our best work was done when we were relaxed. He reiterated that he’d rather we build models slowly, but accurately, rather than fast and requiring multiple revisions. He also believed we should always be able to deal with issues that come up with minimal stress. And of course, he consciously developed this single skill that, in my opinion, distinguishes great managers from bad ones.

In short, he understood the importance of safety capacity. We should, too.

Rohan Rajiv is a first-year student in Kellogg’s Full-Time Two-Year Program. Prior to Kellogg he worked at a-connect serving clients on consulting projects across 14 countries in Europe, Asia, Australia and South America. He blogs a learning every day, including his MBA Learnings series, on