The Elbow of Death!
The trap of perfectionism and operating at maximum capacity!
Have you ever entered a bank or a department store to see a huge queue in front of you and started wondering how many extra agents do they need to add to make this queue vanish?
The answer may not be what you expect!
You are probably viewing the problem at a specific point in time rather than seeing the bigger picture.
Let’s take an example, if you have a queue of X number of customers served by one agent, where the waiting time for the last customer in the queue is — God Forbids! —around five hours! By how much do you think this waiting time will drop if you add another agent?
Let me guess, you’re thinking that it will drop by half, right? Well, you’re not mistaken, if you add that agent at this specific moment in time, then the waiting time will drop by half, but if you added the agent at the beginning of the day, you should expect that waiting time to drop by 90-ish%! Why? Simply because that single agent was operating at full capacity, or past the “Elbow of Death”!
Allow me to explain to you why.
When your customers arrive at a rate which is lower than the time you need to serve them, you assume you can handle the load, but that is only true if your customers are arriving in a spaced fashion like clockwork. But the fact is that there is a high variance in the rate at which they arrive.. Elaborating on the example above, assume that you can manage six customers per hour, 10 minutes per customer. The worst case scenario is that you may spend most of the hour idle and have all of your customers arrive at the last minute. This means that the waiting time for the last in queue is 50 minutes, and even worse, 60-ish minutes for the one arriving at the first minutes of the second hour. Expand that over the full day, that’s how you get the five-hour wait time..
When a system is operating at a point close to full capacity the variance in incoming traffic chokes it, and it would rarely be able to catch its breath beyond that!
If our agents are busy serving the customers 100% of the time, this means that the inflow is higher than what that team can handle, and this can result in INFINITE waiting times!
When considering queues, the two most important things to think about are:
- Arrival rate
- Service Time (aka. the average handling time — AHT)
From the management point of view, that extra added agent would not be doing much for most of the time, but when the spike comes, s/he will be critical in catching-up, otherwise the business may never have the chance to get back on track. This idleness is exactly what is saving the day!
We always strive to achieve maximum productivity and efficiency throughout our organizations, but if we push it too far, that can be at the expense of our customers waiting time and service level.
What can we do to improve the case?
I would love to tell you that just adding another agent to that horrible queue would do the trick, It will certainly help, but the problem has a lot of other nuts and bolts to tighten, from people switching between queues, to multi-tasking and balancing the load with the capacity of your team. This is a field of research that has been under study for the past five decades, if you’re interested in more information about it, you can search for “Queueing Theory”.
One take-away for personal productivity
Plan for 80% of your time throughout a day and leave the other 20% to the variance in the time each task will take or to the unpredictable tasks that will pop-up throughout the day and demand your attention. Otherwise you will always be overwhelmed and feel that you will never be able to catch up.
Reflection
It always fascinates me how much we can learn about our social interaction from the technical challenges we face with systems and data. I try to capture these snippets along with some of my perspective around them in a series of articles, mostly they are abstractions from different readings and resources that I refer to at the end of each article. Consider following for similar articles.
You can read more stories like this from the links below:
This article was based on Episode Two of “Algorithms at Work” by Brian Christian and Tom Griffiths.
