# Matching of Energy Provisions in Multihop Wireless Infra-Structures
## 1 Introduction  
Wireless Multihop Infrastructure (WMI) networks facilitate flexible and quick deployment of communication networks. Multi-hop relay between low-cost base-stations in WMI can greatly extend the network coverage. Access to external networks through gateways can support access to the Internet, smart city networks, IoT and emergency networks [1; 2; 3]. Therefore, the WMI networks play an important role as a temporary alternative of conventional network infrastructures in the emergency situations, as well as other temporary networks such as low-cost IoT infrastructures. A key issue affecting the operation of WMIs is resource constraints such as limited energy supply in the no-charging periods of emergency situations or the no-charging period of solar power supplies at night. Emergency situations may involve failure of network power supplies due to natural disasters such as earthquakes, hurricanes or floods [4; 5]. A disaster hit area may be without grid power supply from several days to several weeks. Moreover, the re-charging or replacementof batteries may be delayed for long times in remote locations or large-scale disaster situations. Consequently, the sustainability of WMI networks with such energy constraints is a serious concern. Furthermore, with the recent advances in green energy sources and portable energy storage, the supply of energy to wireless base stations (BS) has been experiencing a change from traditional electricity power grid to renewable energy supplies and distributed energy storage [6; 7; 8; 9; 10]. This change facilitates the deployment of BSs and operation of sustainable WMI networks in off-grid locations. On the other hand, the supply of energy from renewable energy sources may be intermittent. For example, the no-charging period of solar panels at right time results in the energy constraint that the network should operate a long as possible with limited initial energy power. Optimizing the energy supply and the operation of the WMI network requires consideration of the wireless activity and energy consumption in the whole network. Failure of any one node due to energy depletion could affect the connectivity of the network and disrupt the operation of the whole network. To date, many studies have been made on energy efficiency of networks with a focus on improving local energy efficiency at nodes, links and routes [11; 12; 13; 14; 15; 16]. In many cases, local energy efficiency may lead to global energy efficiency, especially in hierarchical networks or hierarchical node functions such as data aggregation in sensor networks [15; 17; 18]. On the other hand, there are gaps between local and global energy efficiency. For example, unavoidable uneven energy consumption occurs in multihop networks [19]. This may cause some nodes to fail earlier than others, depending on their position in the network. A challenging problem in WMIs in the no-charging period is the energy consumption differentiation among BSs in the network. If total energy resources are limited, then in order to optimize the lifetime of the network it is necessary to provide the BS with energy resources according to their differences of energy consumption. We call this the matched energy provision problem. In this paper, we address this problem of matched energy provision in WMI. First we present a general mathematical formulation of the energy provisioning problem. In particular, we describe the principle of Energy Provision Matching (Matching-EP). Next, we propose a practical method for implementing Matching-EP in WMI based on estimation of position-dependent differentiation of energy consumption among BSs in a WMI. Finally, we validate the effectiveness of the proposed method by conducting packet-level simulation using standard Medial Access Control (MAC) and routing protocols.The evaluation results show that Matching-EP with 4%-34% improvement in energy matching degree enables 10%-40% improvement of the network lifetime, and 5%-40% improvement of packet delivery compared with conventional WMI networks.