Usually arrival is a Poisson distribution and work time is an exponential distribution, IIRC. But I’ll admit I’m rusty on the stats since it’s been nearly 15 years since I was in college, and professionally I haven’t had to use it much.

To be more precise, the mathematical models usually assume that people arrive at one rate regardless of how recently someone arrived, and work finishes at another rate regardless of how long you have been working.

This makes the time between arrivals, and the time to complete a job both exponential distributions. It also makes the number of arrivals while a job is being worked on into a Poisson distribution.

For a computer simulation you can simplify this even further by forgetting about time and focusing on events. If the worker is busy, the next event is either a new arrival or a job completion with a probability based on the rates.

One of the simplest and most common approximations is to assume a Poisson process for arrivals, which corresponds to exponential distribution of the inter-arrival times.

It's tempting to model work time with an exponential distribution too, and there's a lot of theory for this case. Unfortunately, exponential distribution has a mode = 0, so it's not a good choice for real life process times. It's more common to see distributions like lognormal, gamma, Weibull, loglogistic, beta, or others with a mode > 0.

I tried an exponential distribution with its mean equal to the rate work is processed and got the same result.

Edit: same qualitative result (substantially sublinear). Didn’t try to fit it to a distribution.