A queuing system with variable parameters (Q1123490)

The authors consider a queueing system consisting of n servers with state-dependent Markovian input of rate \(\lambda_ m\) if m customers are in the system. The required amount of work for a customer has a general probability density depending on the number of customers in the system at the beginning of his service. The service is accomplished with a service rate depending again on the number of customers in the system. For the distribution of the queue length, of the amount of work serving all customers present in the queue at time t and of the duration of the busy period the Laplace transform is obtained.