Makowski, Armand M.A random sum formula is derived for the forward recurrence time associated with the busy period length of the M|G|infinity queue. This result is then used to (1) provide a necessary and sufficient condition for the subexponentiality of this forward recurrence time, and (2) establish a stochastic comparison in the convex increasing (variability) ordering betweenthe busy periods in two M|G|infinity queues with service times comparablein the convex increasing ordering.en-USGlobal Communication SystemsTechnical Report