An optimal repair approach for large-scale systems using queuing theory

An optimal repair approach for large‐scale systems is proposed based on queuing theory. In this approach, system steady states corresponding to the number of failed components are obtained by analysing the transition probabilities between states. Because the transition probabilities of two adjacent states are not zero, the transition process, as one of Markov processes, is further determined as the birth‐death process which is an important part of queuing theory. According to the queue theory, the long‐run expected number and probability distribution function of failed components are derived. On the basis of above analysis, a constrained optimisation problem in terms of cost utility is formulated. Finally, the numerical examples are given to demonstrate the effectiveness of our optimal model.