Recurrence and decay properties of a star-typed queueing model with refusal

We consider a multiclass service system with refusal and bulk-arrival. The properties regarding recurrence, ergodicity, and decay properties of such model are discussed. The explicit criteria regarding recurrence and ergodicity are obtained. The stationary distribution is given in the ergodic case. Then, the exact value of the decay parameter, denoted by λ_E, is obtained in the transient case. The criteria for the λ_E-recurrence are also obtained. Finally, the corresponding λ_E-invariant vector/measure is considered.