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?


1 Answer 1


This is a stretch as it is far from my area, but my understanding is that steady-state histograms play a "real" role in Internet packet traffic analyses. Here is one suggestive figure from a paper cited below (the blue histogram is steady-state buffer distribution).

The OP would know better than I if one could make a case for packet queues that would be more resistant to counterarguments.

Hernández-Orallo, Enrique, and Joan Vila-Carbó. "Network performance analysis based on histogram workload models." Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, 2007. MASCOTS'07. 15th International Symposium on. IEEE, 2007.

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    $\begingroup$ thanks, Joseph, this application brings two ideas to me: (1) using the steady state histogram as the "expected core" of the behaviour --- and visualising the results of the simulations as fluctuations around this core. This would still sharpen the conceptual part of the lectures (2) in large networks of interacting queues the theory-based calculation outperforms simulations $\endgroup$
    – Statos
    May 7, 2015 at 6:32

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