Usually, cellular networks are modeled by placing each tier (e.g macro, pico and relay nodes) deterministically on a grid. When calculating the metric performances such as coverage probability, these networks are idealized for not considering the interference. Overcoming such limitation by realistic models is much appreciated. This paper considered two- tier twohop cellular network, each tier is consisting of two-hop relay transmission, relay nodes are relaying the message to the users that are in the cell edge. In addition, the locations of the relays, base stations (BSs), and users nodes are modeled as a point process on the plane to study the two hop downlink performance. Then, we obtain a tractable model for the k-coverage probability for the heterogeneous network consisting of the two-tier network. Stochastic geometry and point process theory have deployed to investigate the proposed two-hop scheme. The obtained results demonstrate the effectiveness and analytical tractability to study the heterogeneous performance.
This study aims at identifying determinants of health related quality of life in Poland, and in particular at verifying whether health domains are complements or substitutes and what the impact of heterogeneity of population on the health state valuation is. The paper uses data in panel structure coming from a survey conducted in Poland and consisting of 6700 valuations (after data cleaning) of EQ-5D health states with time trade-off method. Several econometric models are built in order to detect the impact of complementarity and heterogeneity. Random effects models as well as random parameters models estimated using Bayesian approach are used. The results show that health domains are complementary goods. Especially the lack of pain/discomfort is a complement to other health domains. Demographic factors influence how health state change impacts utility. These factors encompass sex, education, respondent’s health state and even belief in life after death.