With Balking, Reneging And The M/m/1 Multiple Work Vacation Queuing System

In this paper,we consider queueing systems with balking,regening and multiple working vacation.Each arriving customer either decides to enter the queue with a probability b or balk with a probability 1 - b.The impatient customer in the queue may leave the system if it has not been served after a period of waiting time.The sever takes multiple working vacations imediately when it becomes idle at a service completion instant.The sever works at a lower rate rather than completely stops during a working vacations period.In Chapter 2,we study an M/M/1/N queueing systems with balking,regening and nmltiple working vacation.The purpose of this chapter is to derive the probability distribution of steady-state waiting time based on the steady-state probability. By introducing different probability analysis for the different cases that the customers in the system may renege,we obtain the distribution of the steady state waiting time of the customers that enter the system and acquire the service under the condition that the server is busy and on working vacation,respectively.In Chapter 3,we study an M/M/1/N queueing systems with balking,regening,multiple working vacation and infinite waiting space.First,we obtain the steady-state probability equation by the Markov process method.Second,we derive the steady-state probability by the probability generating function method.Finally,we derive some performance measures of the system,such as,the expected number of the customers in the system and the average rate of the custom lost.