Parallel service with vacations

We study a system with unlimited service potential where all service requests are served in parallel. The entire system itself becomes unavailable for a random period of time at the first instance that the system becomes idle. A queue builds up while the system is unavailable, and then all waiting customers enter the system simultaneously – each to its own processor – when the system becomes available again. All customers who arrive to find the system in operation proceed directly into service. The analysis of this system entails finding the distribution of the delayed busy period of an M/G/∞ queue. The steady-state distribution of the number of customers in the system is obtained for the special cases of exponential and deterministic service times. Among other applications, our results enable us to analyze and solve for the optimal N-policy for the systems with unlimited service potential. We also study a multiclass model of a polling system with exhaustive service.