Before revision:  We focus on the setting where the service rates \mu are unknown , and are interested in the holding-cost regret -- the difference in the expected holding-costs between that induced by a learning-based rule (that learns \mu) and that from the c \mu rule (which has knowledge of the service rates) over any fixed time horizon.
After revision:  We focus on the setting where the service rates \mu are unknown , and are interested in the holding-cost regret (regret against the c \mu rule (which has knowledge of the service rates) over any fixed time horizon.