On pseudo-conversation laws for the cyclic server system with compound Poisson arrivals

Boxma and Groenendijk obtain the pseudo-conservation laws for cyclic server systems, for both the continuous-time system with simple Poisson arrivals, and for the discrete-time system. The authors extend these laws to the continuous-time cyclic server system with compound poisson arrivals. In the process they identify an error in Boxma and Groenendijk’s analysis of the semi-exhaustive service strategy in the discrete-time cyclic server system.