The paper modifies the model M/G/1 by (a) providing pioneer customers (initiators of a busy period) with exceptional service; and (b) by having an exceptional arrival rate when the server idles. The regimen is FCFS (first come first served) and exhaustive (a busy server turns idle if and only if the load is exhausted). It derives so-called omni-equations for virtual and true delay and expresses them in terms of a delay in M/G/1 and a model-specific variable. The paper derives the queue size from the delay using the Poisson operator, as it is called. P.D. Welch allows exceptional service but no exceptional arrivals, and derives no compositions. It is thought that the present treatment is simpler and easier to extend once the hurdle of new notation is overcome. The special arrival rate of pioneers forces careful distinguishing of virtual from true delays.
