Geo/Geo/1 Optional Working Vacation Queueing System With Negative Customers And N-policy

In recent years,queueing theory obtained the rapid development in the field of communication natworks.In the ATM network,fixed length of the cell is the basic unit of the data transmission and any business after processing can be divided into a set of cell,all the information transmission time is the duration of an ATM cell integer times.Using discrete-time queueing model is to analyze the data transmission is an ideal tool.Compared with the normal signal transimission,considering the interference signal of the system appear is an important part of the study the queueing model.At the same time in the computer information processing,we set the N threshold to reduce the number of busy period and vacation period frequent transformation,when the information in the system accumulated to a certain amount and then swich to busy period to process information.This paper improves the queue models based on the existing literature and makes detailed analysis.The main work of this paper is as follow:Considering a discrete-time Geo/Geo/1 multiple vacations queueing system with optional working vacation.Using the quasi birth and death chain and matrix-geometric solution method,we gain the state transition probability matrix of the model,then,the distribution of systems reliability and the number of customers and waiting time of a customer in the system in steady state are researched.Furthermore,some numerical examples are given for analyzing the effect of parameters on the performance of the system by matlab.Lastly empirical analysis.We present a discrete time Geo/Geo/1 multiple vacations queueing with negative customers,N-policy and optional working vacation.Using the method of quasi birth and death chain,we establish a two-dimensional Markov chain and a state transition probability partitioned matrix,and we get the distribution of systems reliability and the number of customers and waiting time of a customer in the system in steady state by matlab and method of matrix-geometric solution.At last,we use the chart depicting the effects of related parameters on the performance indicators.