State-Dependent System Residence times for time Shared Queues

In this paper we obtain the Laplace-Stieltjes transform of the time an arriving customer spends in an FB_N queueing system until completion of service at the kth level (1 ≦ k ≦ N) given that at least k levels of service are required. The results are conditioned upon the state of the system at the time of arrival of the customer.