# How to teach steady state in queueing (if at all?)

I am teaching an undergraduate course in Operations Research to business students (they are not: maths students). I want to check, if and how teaching the steady state makes any sense.

As in the semesters before, the challenge of this term was to make the concept of "steady state" plausible. Thus we wrote a very simple M/M/1 queueing simulation, repeated it, produced histograms of the queue lengths of the repeated simulation over time, analysed time-regions, where these histograms did not change very much and finally calculated the "ideal steady-state histogram" by solving simple systems of linear equations.

This made the concept of "steady state" clearer and brought in more joy as an exploratory task than just a calculation task or formula. However, the question came up: where in the real world would a real planner in a real application (and by "real" the students mean: real-real) put that much focus on what is the steady state of a queue?

Some ideas from my side (counterarguments in brackets):

*the planner would try to discover, at which time his system stabilises - the supermarket opens, 20 people waiting outside, when will the cashpoints be in their "normal"/average state? (well, wouldn't a simple measure like variance in the simulation suffice to just explore, when a system swang in?)

*the planner could use the steady state for more strategic tasks - what happens e.g. if the incoming behaviour of the queue changes e.g. during night shifts? (But still: the planner could just simulate that, calculate averages and never touch his operations-research-concept steady state again, right?).

Someone's up for more realistic ideas - and how to teach these? Or should we rather defocus the concept of steady state when teaching a few weeks of basic queueing theory?

• Also posted at StatsSE. May 7, 2015 at 1:15