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Yes, that is a very basic point, one basic reason to do queuing is that queues are buffers for uncertainty. If things are perfectly predictable, as you see on some robots, you allocate exactly what you need and no extra. The uncertainty exists in two places though... It's not just the events coming in but also the time to process each queued event, is another source of uncertainty in the same system that can have the same effect. The author mentions “M/M/1,” this quantifies that there is only one queue-handling process, that events come in with the sort of randomness that raindrops have (no periodicity), and that handling an event does not have any “timeouts” nor any “long tails” where once a handler has been occupied for 3 or 4 T (where T is the average time to resolve) then the prediction for how much time is remaining for them either drops to 0 (timeout) or escalates dramatically (long tail)... The exponential distribution is used, kind of to be nicely in between these, it is a model where over a time dt the handler is asked to pick a random number with success rate p=dt/T, if they pick the right random number then the event is handled, otherwise a new random number is generated, repeat ad nauseam. The basic lessons are surprisingly transferable though. So for example traffic on the highway does not have this raindrop sort of randomness because cars kind of repel each other, they space out much more uniformly than you would have predicted on short term scales... The handling time is also nothing like this model of random guessing. Nevertheless, traffic jams still form at high utilization! And they form for a really interesting reason which is that the n handlers—lanes, we call them—have correlations between them. All these queuing models optimistically assume that a handler never stops another handler, “hey have you ever seen anything like this? where can I find that password?” etc. But in traffic, a car can only lane change from one lane to another if both lanes synchronize speed. With a fixed ability to accelerate, this depends the amount of space between you and the next car, and the amount of space in the lane you want to switch to: as utilization increases both of these spaces drop and synchronization becomes a massive source of inefficiency. Same happens at a company too, it is possible that an employee might spend more time waiting for meetings, and finding convenient times to schedule them, in order to synchronize two streams of work, than the work itself takes. Can be very frustrating! |