1 2 3 0 10 20 30 40 50 60 70 80 90 100 Load Points Percentage Gains meanUA 5pcUA meanOSPA 5pcOSPA 1 2 3 0 20 40 60 80 100 120 Load Points Percentage Gains meanUA 5pcUA meanOSPA 5pcOSPA Fig. 5. Out-band scenario: pico and macro cells share different bands. Fig. 4. In-band scenario: pico and macro cells share same band. some m = 2 , · · · , N$_{b}$ + 1 , then each user u whose corresponding ratio R$_{u,}$$_{1}$ R$_{u,b}$ is smaller than µ$_{m,b}$ is assigned resource only in TP b whereas each user u whose corresponding ratio R$_{u,}$$_{1}$ R$_{u,b}$ is equal or greater than µ$_{m,b}$ is assigned resource only by the Macro. The total load imposed by users associated to TP b on the Macro in this case is given by N$_{b}$ λ − m − 1 λ . Then, note that irrespective of whether λ ∈ S A b or λ ∈ S B b , upon increasing (decreasing) λ the total load imposed on the Macro by users of TP b decreases (increases), which establishes that the unique λ that fully uses all the Macro resource can be determined using bi-section search to solve relation in (20). REFERENCES [1] J. Andrews, et.al., “An overview of load balancing in HetNets: Old myths and open problems,” in IEEE commun. mag. , May 2014 [2] K. Son, et.al., “Dynamic association for load balancing and interference avoidance in multi-cell networks,” in IEEE Trans. Wireless Comm. , 2009. [3] K. Shen and W. Yu, “Distributed pricing-based user association for downlink heterogeneous cellular networks,” in IEEE Journal Sel. Areas. Commun. , Jun. 2014. [4] N. Prasad, et.al., “Exploiting dual connectivity in Heterogeneous Cellular Networks,” in IEEE WiOpt. , May. 2017. [5] N. Prasad, et.al., “Exploiting cell dormancy and load balancing in LTE hetnets: Optimizing the proportional fairness utility,” in IEEE Trans. on Commun. , Oct. 2014. [6] E. Altman, et.al., “Spatial sinr games of base station placement and mobile association,” IEEE Infocom. , 2009. [7] A. Bedekar and R. Agrawal, “Optimal muting and load balancing for eICIC,” Proc. IEEE WiOPT , May 2013. [8] Q. Ye, et. al., “On/Off Macrocells and Load Balancing in Heterogeneous Cellular Networks”, in IEEE Globe. , Dec. 2013