  We study the impact of service-time distributions on the distribution of the
maximum queue length during a busy period for the M^X/G/1 queue. The maximum
queue length is an important random variable to understand when designing the
buffer size for finite buffer (M/G/1/n) systems. We show the somewhat
surprising result that for three variations of the preemptive LCFS discipline,
the maximum queue length during a busy period is smaller when service times are
more variable (in the convex sense).
