Analysis And Optimization Of The Age Of Information In Spatial Stochastic Networks

Nowadays,people's life style has been greatly changed because of the development of wireless communications.On the one hand,in the actual large scale wireless communication systems,the spatial distribution of access points is not regular.Since the spatial positions of all the interfering transmitters greatly decide the interference of each transmitter,modeling the network geometry is vitally important to analyze the performance of wireless networks.Here,we tried to utilize some existing mathematical tools to model the wireless network we study,and simulate the spatial positions of the nodes as accurate as possible.From the previous relevant papers,they showed that traditional network models performed poorly in modeling the spatial randomness of wireless network,but the use of stochastic geometry(especially the point process theory)can do this more accurately.On the other hand,as the development of wireless networks,numerous applications in networks require the transmission of information about the real-time state between a source and a destination.Hence,a theory of age of information(AoI)has been recently proposed to characterize the freshness of the information at the receiver.As a novelty,the age of information has been extensively studied in recent years.The content of this thesis can be classified into two parts:(1)In this part,we investigated the AoI of a static Poisson bipolar network.We adopt a discrete-time random access system with transmitters and receivers distributed as a Poisson bipolar network.We assume that the locations of all the transmitter-receiver pairs keep unchanged during all time slots once generated at the beginning,i.e.,the network is static,and we define the average age in this section.Assuming that each transmitter in this network possesses an independent queue to store the packets it generated(or randomly arrived).Each packet length is the same and each queue has a total capacity of two packets(including the packet in transmission),i.e.,there is a transmitting packet and a packet waiting for transmission at most at the same time.We take the use of the point process theory and queueing theory and introduced the auxiliary systems to study the age of information of this network.We analyzed the numerical relationship between the average age and the success probability,and we obtained the lower and upper bounds for the cumulative distribution function(cdf)of the success probability.Then,we derived the lower and upper bounds for the cdf of the average age.Our simulation results showed us that there is a small difference between the lower bound and upper bound,which revealed the reasonability of using the auxiliary systems.And we also found the numerical relationship between the average age and transmitter intensities or packet arrival rates.In fact,this is the first time to study the age of information in the static Poisson network.This work extends the analysis of the age of information to large scale wireless network,which is good reference for the analysis of the age of information in various wireless networks in the future.(2)In this part,we investigated the AoI of a static Poisson bipolar network with deadline.We analyzed the AoI in a static Poisson network,and then does some optimizing works:adding deadline.In this section,we focused on the analysis of the age of information with deadline in a static Poisson network and the discussion about the influence of deadline to the age of information.We introduce two kinds of deadline policy here.In essence,this two kinds of deadline policy can only affect the packets waiting in the queue and the packets in service,respectively,and try to make the average age decrease.We employed the existing mathematic tools and conclusions to introduce a time averaging approach to deal with the problems because of the deadline.Then,we derived the lower and upper bounds for the cdf of the average age with deadline(A)and(B),respectively.The numerical results showed that the use of an appropriate packet deadline,which constrains the packets in the queue,can make the average age decrease.On the other hand,the lower and upper bounds for the cdf of the average age with deadline(A)and(B)are different because they affect different packets in the queue.By comparing the lower and upper bounds for the cdf of the average age with deadline(A)and(B),we found that different kinds of deadline caused different optimization.Thus,we should choose appropriate kind of deadline according to the system model we study.Different from the existing works,we studied the age of information in the static Poisson network with deadline and compare different optimization caused by different kinds of deadline for the first time.