Markovian queueing model with multiple working vacation and catastrophe with restoration

Our model deals with single server queuing model, multiple working vacation and catastrophe with restoration. Client gets in to the organization with parameter λ comes off Poisson process. Service time throughout working vacation epoch, normal service epoch and vacation epoch with parameters µ₁ and µ₂ (µ₁˂µ₂) and γ are all exponentially distributed respectively. If queue length increases throughout a multiple working vacation epoch, the server goes to ordinary busy epoch. In this paper also dispute about catastrophe and restoration throughout service an unforeseen event that causes distress or damage organizationtakes time to restart in regular function, called restoration with rate β. The catastrophe occurswith parameter ζcomes off Poisson process. This type of model is examined by using Matrix Geometric Approach to derive probability vectors. From that we also obtain some numerical performance measurements.