In Chapter One, we see some basic definitions and review of literature related to Retrial Queueing System. Chapter Two deals with a single server retrial queueing model. The server operates under two vacation mechanisms. During service the server may go for vacation to attend an emergency call and after completing the vacation, the server continues the service for the same customer. Upon completion of a service, with a certain probability the server takes multiple vacations depending on the orbit size. In Chapter Three, an bulk arrival retrial queue with two phases of service is analyzed. Customers may balk or renege at particular times. The server is subject to breakdown with repairs. When the server fails it is not repaired immediately. The system has to wait for the repair to start. While the server is in breakdown, the customer in service can remain in the service position or leave and return. Immediately after completing the service of a customer, the server searches for customers in the orbit or remains idle. In Chapter Four Bulk arrival and orbital search retrial queueing models with server vacations - Emergency and multiple vacation are analyzed.