Rare-event analysis of mixed Poisson random variables, and applications in staffing

The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of PN(a), we focus on the asymptotics of the probability that the number of clients in the system exceeds Na. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable.