Another look at the transient behavior of the M/G/1 workload process

We use Palm measures, along with a simple approximation technique to derive new explicit expressions for all of the transient moments of the workload process of an M/G/1 queue. These expressions can also be used to derive a closed-form expression for the nth moment of the stationary workload, which solves the well-known Takács recursion that generates the waiting time moments of an M/G/1 queue that serves customers in a first-come-first-serve manner.