Duration of a Countdown when Considered as an Interrupted Service Process

A countdown (and other kinds of service processes) could be interrupted by several kinds of problems, and, following each interruption, it could continue according to one of several policies, seven such policies are considered in this paper. The problem addressed is that of accounting for the randomly occurring problems and the time required to deal with them when estimating the distribution of interrupted countdown durations. The countdown is considered as an interrupted service process, and expressions are derived from which the moments of the interrupted countdown duration distribution can be obtained. The first two moments are derived explicitly. Although the results are derived in a countdown context, they appear applicable to other kinds of service processes that are subject to randomly occurring interruptions.