# Non-stationary distribution of an M/M/infinity queue

1. Apr 26, 2014

### TaPaKaH

Suppose we have an M/M/$\infty$ queue with arrival rate $\lambda$ and service rate $\mu$ that is empty at time $0$.
(M/M/$\infty$ queue is a queue, in which the inter-arrival times are exponentially distributed, each job immediately gets its own dedicated server, in which it spends an exponentially distributed amount of time and then departs)

I'd like to compute the distribution for the number of jobs in the system if we run it for $t$ time units.