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This book is an attempt to analyze the bi-serial queue network models with Priority discipline. The proposed Queuing Models have been analyzed in Stochastic Environment. The Chapman- Kolmogorov equations (CKE) are used to define the joint probability distributions with associated probabilities and satisfied all required conditions for the existence of time - independent solutions in stochastic process. The present study is useful to reduce congestions and idle period of service systems. The applicability of the study finds in banking sectors, medical, registrations and administrations and many other fields with assumptions of high priority visitors gets special treatment over the common (low priority) visitors.