An optimal stopping problem for software rejuvenation in a job processing system

In this paper, we derive the optimal policy for deciding software rejuvenation trigger in a job processing system when observing a performance degradation of the system. At the detection of service degradation, we assume that the system enters a digesting phase where newly arrival jobs are rejected and queued jobs are processed with decreased service rate. The service can be modeled as a pure death process, and both of the delayed jobs due to decreased service rate, the dropped jobs caused by rejuvenation, and the rejected arrival jobs are counted as the cost components. We formulate the decision problem of software rejuvenation, which trade-offs the costs associated with the decisions, as an optimal stopping problem. Our analysis on the optimality equation clarifies the conditions to switch the optimal policy for triggering software rejuvenation to minimize the expected cost.