Performance Analysis Of Queuing Systems With Multiple Stages Of Vacation Or Failur

Queueing system with vacation or breakdown policy has become a research hotspot nowadays,and it has been widely used in computer communication network,manufacturing system and so on.In this thesis,the GI~X/M/1 queuing system with two-stage vacation policy is studied by using the shift operator,and then the fluid model with two-stage breakdown policy is studied by using the Uniformization Technique.These two types of systems are analyzed,and the important performance indicators of the corresponding systems are obtained.Firstly,this thesis analyzes the GI~X/M/1 queueing system with two-stage vacation policy.The two-stage vacation policy can be described as follows:If the system is empty at the end of the regular busy period,the service will enter a working vacation during which the service rate decreases.If the system is non-empty at the end of the working vacation,the service will enter the regular busy period,otherwise the service will enter the vacation,until the system is non-empty after the end of a vacation,the service will enter the regular busy period.The differential equations satisfied by the model are constructed.By solving these equations,the queue length distribution at pre-arrival and arbitrary time is obtained.The average sojourn time of any customer in the system is obtained,and the effectiveness of this method is verified by numerical examples and the influence of system parameters on the system performance is shown.Secondly,the fluid model with two-stage breakdown policy is analyzed.The two-stage breakdown policy can be described as follows:During the normal working period,if the breakdown occurs,the system will enter partial breakdown period,during which the buffer continues to provide services for the fluid but at a lower service rate.If the breakdown occurs again during the partial breakdown period,the system will stop completely.The recursive expression of the tail distribution function of the buffer content of the fluid model is obtained,and the calculation method of truncation step under the given error limit is given.Meanwhile,the expression of each order moment of the buffer content is given and a numerical example is given to show the trend of tail distribution function.Finally,an example analysis is presented.The fluid model with two-stage breakdown policy is used to simulate the queuing phenomenon in cloud computing services.It is found that the buffer content decreases with the increase of output rate,increases with the increase of breakdown rate,and decreases with the decrease of maintenance time.The system operator can control the system parameters reasonably so as to realize the optimal control of the system.