[drewhk]

I am a bit worried of the overuse of Little's formula, especially in these catchy educational presentations. In reality queue sizes will dictate your consumer observable latency profile, which is in turn is dictated by the actual distribution of the service time - it is not a constant.

If you think about it, if you have an ideal system that serves users like a clockwork, every X ms with no jitter, while your arrival is also completely regular, every Y ms (Y < X), then basically a queue length of 1 is sufficient. In reality, just like we all observe in real-life queues, service time is far from constant, and outliers result in queue buildup. This is why often cutting the tail of service-time latency results in better overall latency than simply reducing average service-time.

Little's formula of course holds also in the above scenario, but it handles long-time averages and does not give you any indication what extreme behavior is lurking under the mask of these averages.

[kqr]

> ...the actual distribution of the service time - it is not a constant.

I'm concerned by the number of misunderstandings expressed in short time here.

1. Nobody claims service time is constant.

2. Little's law is one of the few parts of queueing theory that remarkably does not depend on service time distribution.

3. Many results for typical simplified M/M/c systems apply well also to any other service time distribution provided (a) arrivals are Poisson, and (b) the server uses time slicing multiprocessing. These are not very severe requirements, fortunately!

Long-term average sounds restrictive but it really just means a period long enough to exhibit some statistical stability. Most systems I see sit mainly in those regimes.

[drewhk]

> I'm concerned by the number of misunderstandings expressed in short time here.

I have a feeling you misread my comment completely, and the misunderstandings are on your part?

> Nobody claims service time is constant.

Neither did I. Neither did I claimed that Little's Formula requires a constant service time.

> Little's law is one of the few parts of queueing theory that remarkably does not depend on service time distribution.

I did not say otherwise either. My point is that it is way less useful and enlightening than these edutainment posts make it. Two systems with the exact same parameters and results by Little's Formula might behave completely differently, and in many cases, counterintuitively.

> Many results for typical simplified M/M/c systems apply well also to any other service time distribution provided (a) arrivals are Poisson, and (b) the server uses time slicing multiprocessing. These are not very severe requirements, fortunately!

This was not my point. Or do you claim that queue size distributions DO NOT depend on service time distribution? Because that WAS my point. Averages do not tell the story you are most interested in. The whole point of queues is that service and arrival times have distributions with deviation. I personally think queues and buffers are very-very important and I am a huge proponent of predictable user-observable latencies as they improve general system health and resiliency under load.

> Long-term average sounds restrictive but it really just means a period long enough to exhibit some statistical stability. Most systems I see sit mainly in those regimes.

Long-term averages do not talk about pathological transient behavior, do not help you with queue sizing - or setting ideal timeouts. Also, statistical stability is misleading, the convergence time to the given statistic might be arbitrarily slow. Also, if we talk about real-world systems (which you do), they exhibit feedback do to clients retrying, throwing off the formula and potential ergodicity.

[kqr]

With these clarifications I realise we are in violent agreement and indeed the misunderstandings were on my part. I apologise, and an grateful you took the time to expand!