The authors consider two models of the M/MaÅ,b/c queueing system with servers’ vacation. In model I, any server on completion of a service batch of size k (a•k•b), who finds less than or equal to (a-1) customers in the waiting line, leaves for an exponential vacation. If any server finds β (0•β•a-1) customers on returning to the main system, immediately takes another vacation. Model II discusses the case of any server taking only a single vacation at a time. When any server returns to the main system after vacation, he begins service if there are x (x≥a) customers waiting in the queue. If the queue size is β (0•β•a-1), the server awaits until the queue size becomes ‘a’. The authors present the steady state probability of the number of customers in the queue.
