A note on characterizing service interruptions with phase type distribution

In this article, we model an interrupted service scheme that has applications in practice using phase-type distribution. Services are subject to interruptions that occur according to a Poisson process. An interrupted service is either resumed from where left or repeated from the beginning based on a timer (referred to as a threshold clock) set at the epoch of an interruption. A service can have at most a fixed number of interruptions. Further, a super-clock will be set at the epoch of the first interruption and will be frozen whenever the service resumes from an interruption. However, if this super-clock expires before an interrupted service resumes, no further interruptions for this service can occur. Assuming all interruptions, threshold, and the super clocks as well as the service time to be of phase type (independent of each other), we show that the effective service time can be modeled as a phase-type distribution. Some illustrative numerical examples are presented