Performance And Optimal Control Strategy Of M/G/1 Queueing System Based On N-Policy And Single Vacation

This dissertation studies the performance and optimal control strategy of M/G/1 queueing system,in which the server takes single server vacation and the system adopts N—policy control.It is divided into two parts as follows:In the first chapter of this dissertation,we consider two types of M/G/1 queueing systems with N-policy and single server vacation,one of which is uninterruptible on vacation and the other is of interruptible on vacation.Using the stochastic decomposition property of the system'queue-length in steady state,the probability generating function of the steady-state solution of the queue-length distribution is derived.By numerical examples,the sensitivity,and comparison of the system'idle rate and the additional average queue-length towards some system parameters are discussed.Furthermore,under the given cost structure,by the renewal reward theorem,the analytical expressions of the objective function of the expected cost per unit time of the long-term operation of the system in the stable state are derived.Moreover,with the help of MAT LAB software,and by numerical examples,we determine the control strategy N*of one-dimensional decision variable for minimizing the system cost as well as the optimal strategy(N*,T*)of two-dimensional decision variables when the random variable V is fixed duration T,In the second chapter of this dissertation,we propose to establish a new M/G/1 queueing model in which the server takes a single vacation and interrupts the vacation with a probability?(0 ???1)according to the importance of the work and N-control policy.Employing the total probability decomposition formula in Probability Theory,Laplace transform and probability generating function,the distribution of the queue length at any time t,i.e.the transient solution of the queue length is discussed.The expressions of the Laplace transformation of the transient queue-length distribution with respect to time t are obtained.Moreover,by some algebraic manipulations,we also obtain the recurrence expressions of the steady queue length,the expression of the probability generating function of the steady queue length distribution and the analytical expression of the average queue length of the system in the steady state.Further-more,the stochastic decomposition structure of the steady-state queue length of the system,the analytical expression of the additional queue length distribution caused by the systematic control strategy and vacation mechanism for server are derived.At the end of this chapter,we give a cost structure model and use the renewal reward theorem to present the analytical expression of the expected cost per unit time when the system reaches a stable state and runs for a long time.With the help of MATL AB software,the optimal value N*of one-dimensional decision variable which makes the cost objective function minimum is determined in the form of a numerical example.In addition,when the random variable V is fixed as T,the objective function expressed by two-dimensional decision variable is obtained.Similarly,the optimal value(N*,T*)of two-dimensional decision variable is also given by another numerical example.