On a Random Sum Formula for the Busy Period of the M|G|Infinity Queue with Applications
Makowski, Armand M.
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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.