ANALYSIS AND PERFORMANCE OPTIMIZATION OF A GEOM/G/1 QUEUE WITH GENERAL LIMITED SERVICE AND MULTIPLE ADAPTIVE VACATIONS

In this paper, we first present an analysis for a general limited service Geom/G/1 queueing model with multiple adaptive vacations (MAVs). Then we give the Probability Generating Function (P.G.F.) of the queue length by using the embedded Markov chain method and the regeneration cycle approach. The P.G.F. of the waiting time is derived based on the independence between the arrival process and the waiting time. The probabilities of various states (such as "busy", "idle" and "vacation") are also derived in the system. We can explicitly calculate their averages and higher moments by differentiating these P.G.Fs. to numerically compare different system cases. Furthermore, we present an analysis of the cost model for this general limited service Geom/G/1 queueing model with multiple adaptive vacations to determine the optimal management policy by minimum cost. We can obtain the optimal values of service rate and the optimal expected traffic intensity in the system. Finally, based on numerical results, the relations of performance measures and the optimal expected traffic intensity are discussed.