SEMIREGENERATIVE ANALYSIS OF CONTROLLED BULK QUEUING-SYSTEMS WITH A BILEVEL SERVICE DELAY DISCIPLINE AND SOME ERGODIC-THEOREMS

The authors consider a class of bulk queueing systems with a compound Poisson input modulated by a semi-Markov process, multilevel control service time and a queue length dependent service delay discipline. According to this discipline, the server starts the next service act if the queue length is at least r; in this case, all available units, or R (server capacity) of them, whichever is less, are taken for service. Otherwise, the server delays the service act until the number of units in the queue reaches or exceeds level r. The stationary distribution of the queueing process with continuous time parameter is obtained by using semi-regenerative techniques. The authors establish some ergodic theorems for functionals of input and output processes and present an optimization problem.