It's not given that the queue backlog is staying even, but you would also have to factor the externalities of better or worse performing offices into the queueing analysis. Slower government workers have consequences like the public giving up and bothering to add to the queue, and occasionally, lawsuits due to failure to perform a required task, legal cases being a less desirable budget spend than bureaucratic staffing.
Parents point is that there must be slack in a system in order to have a stable queue size.
But slack can also be perceived as waste, which can be cut.
And if your budget is cut, you are likely to see that slack as "first thing on the copping block" with the consequence that the queue begins to expand. But most systems have natural buffers which delay catastrophic failure. By that point there have been elections, you have retired, etc. and someone else is left holding the bag.
At that point you can blame the organisation for being "slow", or "inefficient", and then you can cut it's funding further, or destroy it outright or maybe outsource it to the private sector.
Then the private sector can drive profits by asset stripping and cutting safety or vital maintenance work, then when the whole system collapses, you can hold the taxpayer hostage by demanding a bailout of the, presumably vital, service (or you can renationalise it), and the whole cycle starts again.
Welcome to our planet, enjoy your stay, it's likely to be a brief one :)
Ah, if that was their only point, then I should have pointed out that a better operating department can achieve a lower waiting time with the same degree of slack. I understand the utilization rate tradeoff and that's not the issue.
I'm glad you've enjoyed writing your comments--like your style. :)
Ah sorry, slightly misinterpreted, my understanding was that without slack you cannot stabilize queue sizes which makes OP incorrect(?)
Yeah, more efficient nodes can delay that effect, but it seems that in real world system the existence of buffers means that consequences are delayed in ways that have significance (across careers, elections, etc) and those factors tend to dominate.
yw, nice that anyone reads it, without that i'd just be another mad shouty bloke on the internet, maybe i still am :)
