The M/D/1+D queue has the minimum loss probability among M/G/1+G queues

We consider the loss probability Ploss in the stationary M/G/1 queue with generally distributed impatience times (M/G/1+G queue). Recently, it was shown that Ploss increases with service times in the convex order. In this paper, we show that Ploss also increases with impatience times in the excess wealth order. With these results, we show that Ploss in the M/D/1+D queue is smallest among all M/G/1+G queues with the same and finite arrival rate, mean service time, and mean impatience time.