I am preparing for an exam and understand why the mean service time $E[B]$ equals $\frac{1}{\mu}$ for an $M/M/1$ queue but I fail to intuitively understand why the mean remaining service time is the same in this case, i.e $E[R] = E[B]$. Why is this so?
I am also unsure what $E[R]$ and $E[B]$ become when there are more servers, i.e. for an $M/M/2$ or $M/M/3$.
EDIT
I am using Kendall notation for my queues: $M/M/2$ means Poisson arrivals,
Poisson service times with 2 servers. $\mu$ is the service rate.