## 1 Introduction  
Ever increasing energy consumption is one of the important issues related to the problem of global warming [1] and reducing the energy consumption of mobile communication networks has gained significant attentions since it takes a major part of the total energy consumption of information and communication technology (ICT). In future, the effect of the energy consumption of the mobile communication network will be more serious since more traffic load will be expected in forthcoming 5G networks [2; 3]. Reference [4] considers the base station (BS) to be the major source of energy consumption of mobile communication networks and the energy consumption of the BS depends on the traffic load which varies depending on the geographical location. To reduce the energy consumption of mobile communication networks, significant work has been carried out regarding the energy saving of a BS. The basic principle of the work to reduce the energy consumption of a BS is to turn off the components of the BS as much as possible, when they are no longer needed [4]. For example, the BS can be put into sleep mode by shutting down the energy to most of its components when they are not being actively used. Figure 1 shows that, furthermore,the BS can be turned off to save energy more significantly, if there is little traffic of a BS and the traffic of the BS can be covered by neighbor BSs. Since user equipments (UEs) covered by the center BS can be also covered by neighbor BSs with overlapping coverage, the center BS can be turned off to save energy and the UEs are served by neighbor BSs [5]. The _on_/_off_ state of BS is determined based on the context information such as the traffic demand and channel state in an environment where connections between the BS and UE are changing dynamically. In [6], greedy-on and greedy-off schemes were proposed, where the state of a BS is changed to either _on_ or _off_ state when a certain condition is met, and it was concluded that greedy-on scheme was more efficient in terms of energy efficiency. In [7], various ways of reducing the number of BSs with _on_ state was introduced and a traffic-intensity-aware multi-cell cooperation scheme was introduced, where the state of a BS is changed to _off_ state based on its traffic density, which is classified into peak hour traffic and off-peak traffic, depending on the traffic demand of the UE. Also, coverage hole is accommodated by neighbor BSs with on state. In contrast to the activation and deactivation schemes of BSs [4; 5; 6; 7], the cell zooming scheme was introduced in [8], where cells are zooming-in and zooming-out depending on the traffic load and channel condition of BSs by controlling the coverage area of BSs, as shown in Figure 2. In cell zooming, if a BS has a higher traffic load and is congested, the BS zooms in, while neighbor BSs zoom out to avoid any possible coverage hole. On the other hand, if a BS has a lower traffic load and is not congested, the BS zooms out, while neighbor BSs zoom in. In cell zooming, the zoomed-in BS can sleep in order to save energy and then neighbor BSs should cover the area that was previously covered by the sleeping BS. In the cell zooming scheme, the main objective is to balance the traffic load and increase the energy efficiency of the total network by reducing the energy consumption of BSs. Therefore, BSs with _on_ state should accommodate the coverage hole and cooperate with nearby BSs to deal with the traffic of the turned off BSs [9]. In [10], as an extension of the original cell zooming scheme, the authors proposed an efficient energy saving scheme for BSs, where BSs are turned off when traffic load is very low and active BSs extend the cell coverage by increasing the transmission power. In [11], the authors proposed three cell zooming schemes, i.e., continuous, discrete, and fuzzy schemes. In continuous cell zooming scheme, a BS controls transmit power to cover its farthest user. In discrete cell zooming scheme, only discrete values of transmit power are allowed.