Analysis of multi-level queueing systems with servers breakdown by using recursive solution technique

In this paper we construct a multi-level queueing model that alternates between three modes of an operation system. The service times have followed an Erlang type K distribution with parameter μ. Customers arrive in batches according to a time-homogeneous compound Poisson process with mean rate λ for the batches. Our aim is to give a recursive scheme for the solution of the steady state equations. Next we derive some important measures of performance which may affect the efficiency of the system under consideration such as the expected waiting time per customer, the expected number of customers who arrive to a full system. The expected number of customers will also be calculated. Finally, we can also calculate the efficiency measures of the system by using the recursive results through an example.