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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 discretedoi:10.1155/s0161171294000827 fatcat:bmpze532dbebfhiuduhoj4h67m