Performance analysis of mobile users in Poisson wireless networks

Stochastic geometry is a widely accepted mathematical tool used to analyze cellular networks, where the location of base stations are modeled by spatial point processes. It is used to derive closed-form or semi-closed-form expressions for the SINR or for the functions of the SINR which determine various network performance metrics such as coverage probability, "edge" capacity, 90% quantile rate, spectral efficiency, and connectivity without resorting to complicated simulation methods. Predominantly, it is used in deriving marginal distributions of SINR by considering a typical user assumed to be located anywhere on the plane. Models beyond the typical user approach have been proposed with the aim of analyzing QoS metrics of a population of users, and not just a single user. Most of which include considering networks at certain times by representing instances or snapshots of active users as realizations of spatial (usually Poisson) processes or users occurring at random locations that last for some random duration. Analyzing the performance of a typical mobile user on the move or that of a population of such mobile users is complicated since it requires studying not just the marginal but the spatial stochastic fields associated with wireless networks. In this thesis, we model and analyze the fields associated with wireless networks where the locations of base stations are distributed according to a homogeneous Poisson point process. We focus on characterizing the level crossings, extremes, and variability of the Shannon rate fields in noise limited (SNR based) environment by establishing a connection to queueing theory. In interference limited (SIR based) environments, we rely on the theory of Gaussian random fields which arise as natural limits of standardized interference under densification. Using this, we characterize the spatial correlations, and variability of the Shannon rate fields in the limiting regime. We leverage the spatial characterization of the fields to study the temporal variations and various Quality of Service (QoS) metrics seen by the users on the move. The quantification of such metrics as a function of a small number of network parameters, e.g., the density of base stations, path loss, should allow network operators to appropriately tune the density of the base stations to meet the demands of mobile users for a required performance level. In noise limited environments, we study the performance of mobile users in dense networks by incorporating the cost of handovers along with the temporal variability in the Shannon rate. We study the tradeoff between the cost of handover and the Shannon rate by proposing a new class of association policies. Associating with a base station that is farthest in the known users' direction of motion leads to fewer handovers but may lead to a decrease in the rate. Thus, we attribute a local association region to the mobile user to restrict the greediness in the association, which also models the constraint on the available information about the locations of the base stations. We propose a class of greedy association policies and once again leverage stochastic geometry to characterize the performance of such policies. We then optimize the shape and size of the association region by establishing a connection to the theory of Markov processes and compare the performance of this policy to traditional association policies