Joint Resource Partitioning and Offloading in Heterogeneous Cellular Networks

In heterogeneous cellular networks (HCNs), it is desirable to offload mobile users to small cells, which are typically significantly less congested than the macrocells. To achieve sufficient load balancing, the offloaded users often have much lower SINR than they would on the macrocell. This SINR degradation can be partially alleviated through interference avoidance, for example time or frequency resource partitioning, whereby the macrocell turns off in some fraction of such resources. Naturally, the optimal offloading strategy is tightly coupled with resource partitioning; the optimal amount of which in turn depends on how many users have been offloaded. In this paper, we propose a general and tractable framework for modeling and analyzing joint resource partitioning and offloading in a two-tier cellular network. With it, we are able to derive the downlink rate distribution over the entire network, and an optimal strategy for joint resource partitioning and offloading. We show that load balancing, by itself, is insufficient, and resource partitioning is required in conjunction with offloading to improve the rate of cell edge users in co-channel heterogeneous networks

On Association Cells in Random Heterogeneous Networks

Characterizing user to access point (AP) association strategies in heterogeneous cellular networks (HetNets) is critical for their performance analysis, as it directly influences the load across the network. In this letter, we introduce and analyze a class of association strategies, which we term stationary association, and the resulting association cells. For random HetNets, where APs are distributed according to a stationary point process, the area of the resulting association cells are shown to be the marks of the corresponding point process. Addressing the need of quantifying the load experienced by a typical user, a "Feller-paradox" like relationship is established between the area of the association cell containing origin and that of a typical association cell. For the specific case of Poisson point process and max power/SINR association, the mean association area of each tier is derived and shown to increase with channel gain variance and decrease in the path loss exponents of the corresponding tier

A constitutive model for simple shear of dense frictional suspensions

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $\phi$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $\phi$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of shear rate. Recent studies have related shear thickening to a transition between mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over a wide range of the dimensionless parameters $(\phi,\tilde{\sigma}$, and $\mu)$, with $\tilde{\sigma} = \sigma/\sigma_0$ the dimensionless shear stress and $\mu$ the coefficient of interparticle friction: the dimensional stress is $\sigma$, and $\sigma_0 \propto F_0/ a^2$, where $F_0$ is the magnitude of repulsive force at contact and $a$ is the particle radius. The data have been used to populate the model of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev. Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity divergences or \textquotedblleft jamming\textquotedblright\ points at volume fraction $\phi_{\rm J}^0 = \phi_{\rm rcp}$ (random close packing) for the low-stress lubricated state, and at $\phi_{\rm J} (\mu) < \phi_{\rm J}^0$ for any nonzero $\mu$ in the frictional state; a generalization provides the normal stress response as well as the shear stress. A flow state map of this material is developed based on the simulation results.Comment: 12 pages, 10 figure