SENSITIVITY TO SERVICE TIMES IN INFINITE-SERVER SYSTEMS

Abstract

The stationary distribution of the number of customers in the infinite-server system with non- Poissonian arrivals is dependent on the form of the service time distribution. In particular, when the interarrival time is a hyperexponential random variable that is more variable than an exponential random variable, the stationary state distribution becomes stochastically less variable, as the service time becomes more variable. On the other hand, when the interarrival time is an Erlang random variable that is less variable than an exponential random variable, the more variable service time yields the more variable stationary state distribution.