An analysis method of open queueing networks with a degradable structure and instantaneous repair times of systems

An unreliable open queueing network with Poisson arrivals is considered. For each queueing system the service and failures times are exponentially distributed random variables. The failures of systems lead to changes in the structure of the network and corresponding changes in the performance measures of the queueing network. It is assumed that the times between changes in the network structure are sufficient for the steady-state regime. The main measure of the quality for the network at each structure constancy interval is the average response time. Repairs of all queueing systems occur immediately when the average response time becomes greater than the threshold value. This article presents a method of the network analysis using continuous time Markov chains. It is shown that the steady-state probability distribution of the unreliable queueing network has a product form solution. Expressions for the stationary performance measures of queueing systems and the network including the average of system repair time intervals are obtained. A numerical example to investigate the dependence of the performance measures on some network parameters is demonstrated.