Expected queue length of a Poisson process while service time is based on an unknown distribution with known expected value $\beta$

Question

Suppose we have a service provider with an in-process task queue in which tasks arrive based on a Poisson distribution with parameter $\lambda$. Moreover, the service time of each task is based on an unknown distribution with a known expected value $\beta$. Let $Q(t)$ be the size of the task queue at a specific time $t$. What is the expected number of in-process tasks at a specific time $t$? in other words, what is $E[Q(t)]$ or generally $E[Q]$?