Performance Analysis Of M/G/1 Queueing System With Delayed Uninterrupted Vacation Under N-policy Control

In this dissertation,based on the actual situation,we propose to establish two new M/G/1 queueing models with delayed and uninterrupted vacation under N-policy con-trol by combining the uninterrupted vacation mechanism and the N-policy,and analyze the queueing performance of the two systems.It is divided into two parts as follows:1)In the first chapter of this dissertation,by combining the uninterrupted single vacation mechanism and the N-policy,we propose to establish an M/G/1 queueing model with delayed and uninterrupted single vacation,in which the system starts the service under the control of N-policy.Applying some mathematical theories and tools such as the renewal process the-ory,the total probability decomposition technique and the Laplace transform tool,we study the queueing performance of this system.Firstly,we discuss the transient and equilibrium properties of the queue length starting from any initial state.The expressions of the Laplace transform of the transient queue-length distribution with respect to time t are obtained.And then using the L'Hospital's rule and some algebraic operations,some important performance indicators,such as the recursive formulas of the steady queue-length distribution,the analytical expressions of the probability generating function of the steady queue-length distribution and the expected size,and the stochastic decomposition structure of the steady queue size and the analytical expressions of the additional queue-length distribution,are presented.Furthermore,some special cases such as Y=0,or Y??,or V=0,are also discussed.Secondly,based on a given cost structure,the explicit expression of the long-run expected cost per unit is derived by renewal reward theorem.Through a numerical example,the optimal control policy N*which minimizes the long-run expected cost per unit time is determined.2)In the second chapter of this dissertation,by combining the uninterrupted multiple va-cations and the N-policy,we propose to establish an M/G/1 queueing model with delayed and uninterrupted multiple vacations,in which the system starts the service under the control of N-policy.Employing the same arguments used in the first chapter,the transient and equilibrium properties of the queue size are studied,and some corresponding important queueing perfor-mance indicators of this model,for example,the expressions of the Laplace transform of the transient queue-length distribution with respect to time t,the recursive formulas of the steady queue-length distribution,and so on,are obtained.Meanwhile,some special circumstances are also discussed.Finally,by renewal reward theorem,the explicit expression of the long-run expected cost per unit is derived under a given cost structure.With the help of MATLAB soft-ware,the optimal control policy N*that minimizes the system cost is obtained by a numerical example.