M^{λ 1, λ 2}/G/1 Queuing System With Variable Arrival Rate And Multiple Vacations Under Control Of The Min（N,V）-policy

In this thesis we introduce "variable arrival rate" into M/G/1 queueing system with multiple vacations under control of the Min(N,V)-policy, in which the customers have different arriva l rate when the server is busy or on vacation. Using the total probability decomposition technique and the Laplace transform tool, we study the transient distribution of the queue length which is started from an arbitrary initial in this system. Then we obtain the expression of the Laplace transform of the transient distribution, and the recursion expression of the steady state queue length as well. On this basis, we further discuss some special cases. Secondly, the optimal capacity design of the system is discussed by using the recursion expression of the distribution of system length in steady state. Finally, we establish the cost structure function to discuss the optimal control threshold N?, and give the numerical solutions of optimal control threshold N? under two special cases.