This article deals with a general single-server bulk queueing system with a server waiting until the queue will reach levelrbefore it starts processing customers. If at leastrcustomers are available the server takes a batch of the fixed sizerof units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time.The authors evaluate the steady state probabilities of the queueing processes with discrete

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... ses with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. The authors use the recent results on the first excess level processes to explicitly find all characteristics of the named processes. Some characteristics of the input process, service cycle, intensity of the system, and both idle and busy periods are also found. The results obtained in the article are illustrated by numerous examples.