Stationary Analysis And Its Application Of D-type Multi-server Working Vacation Queueing System

With the continuous development of wireless communication technology and the continuous improvement of the communication quality requirements of customers,there are more and more models that apply queueing theory to wireless communication networks.With the limited communication resources and the uncertain number of customers,there is a need to improve customers' satisfaction and reduce the waste of communication resources,so,the rational allocation of resources has become an urgent problem to be solved.On this basis,the d-type working vacation queue model is established,we obtained the steady-state distribution,and the application of the model in the communication network is given.Firstly,the M/M/c queue model with d-type multiple working vacation is established.Let d servers start a multiple working vacation while there are d servers idled.During the working vacation,if the number of customer in the system is more than c-d,a customer leaved may be served by normal service rate or low service rate.According to the method of quasi-birth and death process and matrix geometric solution,the model is analyzed and the steady-state distribution is obtained.The model is applied to the wireless communication network,and the numerical analysis of the indexes that affect the system performance is made.Secondly,this paper studies the M/M/c queue model with d-type single working vacation.Use the quasi-birth and death process and matrix geometry solution,we got the distribution of steady state.In the wireless communication system,the d idled channels are transformed into overflow pool,which can provide channels both for two cellular layers,and the numerical analysis is made.Finally,in order to avoid the frequent transition between working vacation and normal working,we introduce N policy into d-type multiple working vacation,the queueing model with d-type and N policy working vacation is studied.The transition process is analyzed and the stationary queue length is obtained.In the end,through the change of the parameters,the numerical analysis of the influence on the system performance is given.