Let L n be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L n and L n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL n = 1 for all n. We also show that L n is increasing in the convex sense when the mean service time equals the mean interarrival time, and it is increasing in the increasing convex sense when the mean service time is less than the mean interarrival time.
