Queuing theory have wide range of applications that helps a person in making right decision in complex queuing system encountered in daily life. Queuing theory deals with the study of queues that occurs in real world situations and arise when the rate of arrival exceeds the rate of service. The capacity of a particular system can be determined by queueing theory based on the probability idea. A method of optimization cannot be used to describe the application of queueing theory. It aids in making the best possible use of the currently available staff and other resources to enhance the service. As a result of the unfavorable experiences of waiting for service, customers become dissatisfied and may migrate to other service providers. The cost of waiting is both psychological and financial, because waiting time implies the loss of a valuable resources. Customer dissatisfaction increases as the wait time increases.This book provides a stochastic analysis of a priority bi-tandem queue network of two parallel biserial subsystems commonly connected to a single server. This analytical study is not limited to a specific situation, but has numerous applications in networking system, supermarket, administrations, industries etc. This study is useful to increase customer's satisfaction and optimum utilizations of the serving facilities. Numerical and Graphical analysis of the study is helpful to those, who are interested to analyze the complex Priority queue system in stochastic environment.