Performance Analysis Of Finite Buffer M/M/1/N Queueing System With Multiple Working Vacations

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, reneging and multiple working vacations, so they have more practical significance.In this paper, two finite buffer queuing systems with balking, reneging, and multiple working vacations are analyzed. They are expansions of other models in the documents. The main result of this paper has two parts.Firstly, we investigate a finite buffer M/M/1/N queuing system with multiple working vacations. First, we derive the steady-state equations by the Markov process method .By writing the transition rate matrix as block matrix, we get the matrix form solution of the steady-state probabilities and present a algorithm for calculating the steady-state probabilities. In addition, using the symbol function of Matlab, we get the explicit expression of the steady-state probabilities for the special case of N=3. Finally, we analyze the influence of the parameters of the system to the system performance measures .Secondly, we investigate a finite buffer M/M/1/N queuing system with balking, reneging and multiple working vacations. First, by writing the transition rate matrix as block matrix, we get the matrix form solution of the steady-state probabilities . In addition, we develop a steady-state cost model where the busy service rateμb is the control variable. However, the expression of the cost function is too complex to get the explicit expression of the optimal service rate, so we use the numerical method to get the optimal service rate and the optimal cost. Finally, we investigate the effect of the parameters of the system on the optimal service rate, the optimal cost and the system performance measures by several numerical examples.