A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.