how queueing theory helped me with work-life balance

I find that mathematical models used to solve systems engineering problems are also useful for managing personal issues I face in everyday life. Stochastic processes and queueing theory helped me find and maintain a healthy work-life balance.

I was often wracked with guilt for taking personal time during graduate school and on the tenure track. Three things really helped.

1. Role models who are successful and who have balance made a big impact. I had an advisor in graduate school who talked about how I should take time off every week, and that was a help even though I often did not follow his advice. I am constantly inspired by colleagues I know who are OR rockstars and also have a healthy home life and engaging hobbies.

2. Having children helped me set healthy limits at work at a young age. I had my first child in graduate school, and in retrospect, that was probably the best thing for helping me find balance personally and professionally. My daughter needed me, and I needed to be there for her. I know the statistics indicate that maybe I am an anomaly, but I have had to balance the demands of work and motherhood throughout my professional life. Learning this early helped me later on.

Note: I am not suggesting that if you are really struggling with work-life balance issues you should have a child. I am certain I was predisposed to handle the transition to parenthood 🙂

3. Caretaking is not the same as taking time off from work; it’s a different kind of work. This is where stochastic processes and queueing theory helped.

I am a single server queue who works day after day. Work enters my queue with rate $\lambda$ and I finish tasks with rate $\mu$. If the arrival rate of new work exceeds my service rate (i.e., if $\lambda / \mu > 1$), the queue explodes and eventually becomes infinitely long. I can assure you that $\lambda / \mu > 1$.

One (unhealthy) way to frame this situation is to note that one way to reduce the length of the queue is to work all the time. But this is futile in the long run.

Another way to frame this situation is to note that I have some inefficiencies in how I work. Over time, I have become more efficient and have increased by $\mu$.

The third–and best–way to frame this is to accept that at some point, I can no longer improve my efficiency. And at that point, it’s still true that $\lambda / \mu > 1$. Queueing theory demonstrates that there is no systematic way to “catch up,” so I might as well take a break to run or go to the symphony or make cookies.

Having said that, I still struggle with guilt if I take breaks longer than one hour. I’m a work in progress 🙂

What helps you find balance?

5 responses to “how queueing theory helped me with work-life balance”

• Dom Cimafranca

In my old age, I’ve come to accept I can’t do it all so I pass on work to colleagues. In that sense, I’m more like an operating system kernel, acting more like a scheduler and interrupt handler: delegate to subsystems and process the result when they’re done.

• Mark L. Stone

Generate $n > \lambda /\mu$ i.i.d. copies of your server (you may need to travel to China to be cloned). The system service rate will then be $> \lambda$. Problem solved.

• Mark L. Stone

Generate $$n > \lambda /\mu$$ i.i.d. copies of your server (you may need to travel to China to be cloned). The system service rate will then be $$> \lambda$$. Problem solved.

• prubin73

Three slightly more advanced aspects of basic queuing theory work wonders for me. The first is using a priority queue (meaning stuff I actually want to do gets done first) rather than a FIFO queue. This enables the other two. The second is reneging. If I let work requested by someone else sit long enough, they eventually give up and move on (meaning the work effectively disappears from the queue). The third is balking: people looking to stick me with work see other people reneging, abandon any hope of a prompt response and never put the work in my queue in the first place.

Thus my mantra: never put off until tomorrow that which can be put off indefinitely.