Branching‐type polling systems with large setups

The present paper considers the class of polling systems that allow a multi‐type branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times tend to infinity. The motivation to study these setup time asymptotics in polling systems is based on the specific application area of base‐stock policies in inventory control. Our analysis provides new and more general insights into the behavior of polling systems with large setup times.