Performance Analysis Of Queueing System With Balking, State-Dependent And Hyper-Exponential Service

With the quick development of the communication systems and computer techniques, there are many kinds of complicated queuing systems. The queuing systems are widely applied in the manufacture system, computer system and communication network, especially those with balking, state-dependent and vacations, so they have more practical significance.In this paper, we mainly analyze three queuing systems with balking, state-dependent, hyper-exponential service and multiple vacations. They are expansions of other models in the documents. The main result of this paper has three parts.Firstly, we investigate a finite waiting room M/H_k/1/L queuing system with balking and state-dependent. By writing the transition rate matrix as block matrix, we get the very simple iterative computation formula of the steady-state probabilities, which process is succinct and computation load is small. In addition, we established the cost model, and analyze the influence of the parameters of the system to the optimal cost and critical value.Secondly, we investigate an infinite M/H_k/1 queuing system with balking and state-dependent. By the quasi-birth-death process and the matrix geometric solution, we obtain the equilibrium condition of the system and the steady-state probability distribution. In ordinary situation, we get the iterative computation formula of matrix R, and also get the explicit expression of matrix R in special situation. In addition, we get some explicit computation formula of performance measures of the system.Finally, we deal with an infinite waiting room M/H_k/1 queuing system with balking, N-policy and multiple vacations. By using the quasi-birth-death process and the matrix geometric solution, we obtain the equilibrium condition of the system and the steady-state probability distribution. In ordinary situation, we get the iterative computation formula of matrix R, and also get the explicit expression of matrix R in special situation. In addition, we get the explicit expression of system performance measures and develop a cost model, the numerical analysis is also presented.