Queuing theory for measuring "change" delivery?

Question

In his presentation "Adopting Continuous Delivery" (http://www.infoq.com/presentations/Adopting-Continuous-Delivery), Jez Humble mentions (~6:50) that queuing theory proves that optimizing for resource utilisation and lower coast, actualy leads to the most inefficient procedures for pushing change out to production. He also quotes the book "The Principles of Product Development Flow" by Donald Reinertsen.

Is there any proof of that? I mean, I've learned some queuing theory at the university for telephony, and I cannot even imagine how this principle can be mathematically proved.

Answer 1

Agner Erlang originated queueing theory in 1909 in telephony. In a completely deterministic system, no delays are present until we exceed 100 percent utilization. Erlang showed that because phone calls arrive at unpredictable times and have unpredictable durations, delays rise exponentially BEFORE we reach 100 percent utilization. This math does not only apply to telephony -- we use it for highway design, manufacturing systems, supermarket lines, etc. Whenever there is 1) variability in arrival times or durations, and 2) a cost of delay, then one can "prove" that loading to 100 percent utilization is not economically optimal. It leads to infinite queues, and the queues cost money. It's not a "proof" in the Maths PhD sense, but we'd throw away a lot of useful engineering ideas if we required this level of axiomatic rigor. Alternatively, one could ask what conditions would make 100 percent utilization optimal: no variability or no cost of delay. Then, try to determine if one of these conditions exist on your project. If they do, maximize resource utilization. Hope this helps.

Answer 2

optimizing for resource utilisation and lower coast, actualy leads to the most inefficient procedures for pushing change out to production.

I have not read any study which might prove the above scientifically, but in defence of the writer it might be true in certain aspects.

If the effort required to optimize a resource utilization and the output from the resource post optimization are not proportionate (with positive bias) then the above statement holds true. The queue length may also play an important part in it.

If the effort put in optimization outweights the output it gives, then its not worth optimizing it. This will be true in activities which are not business critical. I am tempted to say that one might want to tune the resources enough so that they keep delivering at profitable levels.