This paper analyzes the impact of user mobility in multi-tier heterogeneousnetworks. We begin by obtaining the handoff rate for a mobile user in anirregular cellular network with the access point locations modeled as ahomogeneous Poisson point process. The received signal-to-interference-ratio(SIR) distribution along with a chosen SIR threshold is then used to obtain theprobability of coverage. To capture potential connection failures due tomobility, we assume that a fraction of handoffs result in such failures.Considering a multi-tier network with orthogonal spectrum allocation amongtiers and the maximum biased average received power as the tier associationmetric, we derive the probability of coverage for two cases: 1) the user isstationary (i.e., handoffs do not occur, or the system is not sensitive tohandoffs); 2) the user is mobile, and the system is sensitive to handoffs. Wederive the optimal bias factors to maximize the coverage. We show that when theuser is mobile, and the network is sensitive to handoffs, both the optimum tierassociation and the probability of coverage depend on the user's speed; aspeed-dependent bias factor can then adjust the tier association to effectivelyimprove the coverage, and hence system performance, in a fully-loaded network.
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