## 1 Introduction  
Energy consumption of core networks is constantly increasing due to constantly increasing traffic demands and despite the improving energy-efficiency in terms of power required to provide certain capacity (Watt/bps). One of the most promising approaches to reduce energy consumption of Internet Protocol (IP)-over-Wavelength Division Multiplexing (WDM) networks is the application of Sleep Mode (SM) to network devices (see, e.g., the surveys [1; 2]). The main idea of this approach is to dynamically deactivate network resources when they are unused and activate them again when needed. However, the application of SM has an impact on the devices lifetime (i.e., the time between one failure and the following one) [3]. Specifically, the authors have shown in [3] that the lifetime of network devices is heavily influenced by HardWare (HW) parameters of the devices as well as by the strategy used to put devices into SM or Active Mode (AM). Therefore, a core network experiences energy and lifetime variations as a consequence of the activation/deactivation of its resources. The choice whether a subset of devices shall be put into SM is highly dependent on the evolution of traffic over time. More precisely, networks are dimensioned to satisfy peak traffic demands. However, traffic varies both in time and space. At night few users generate traffic, resulting in a low utilization of network devices. Moreover, if the network spans across different time zones, the periods of low utilization will not occur at the same time in all regions of the network, but will be shifted across the time zones. In this context, several questions arise, like: How to model temporal and spatial traffic variations in a core network? What is the influence of both temporal and spatial traffic variations on the energy savings and on the devices lifetime? How does the difference across time zones affect the results? The goal of this paper is to provide answers to such questions. More in depth, we first propose a simple traffic model that captures temporal and spatial traffic variation. We then focus on a network scenario adopting a realistic network topology, as well as the traffic variations derived from our model. Moreover, a sophisticated Mixed-Integer Linear Programming (MILP) model with realistic parameters is used to design the network, i.e., choose which devices to install and how to configure them. The designed network is then taken as input for dynamic operation over time, i.e., selection which devices to put into SM as a consequence of the traffic variation while ensuring Quality of Service (QoS) constraints. Specifically, we exploit a heuristic approach to dynamically find the set of active LCs versus time. Finally, we compute the achieved energy savings as well as the effect on devices lifetime and profitability, showing the influence of the proposed traffic model on these evaluation metrics. Previous works in the literature mainly investigated the impact of temporal variations of traffic on the energy savings (see particularly [4; 5]). In the work [6] we went two steps further by: (i) considering the devices lifetime; and (ii) considering the impact of spatial traffic distribution on both lifetime and energy savings. We extend [6] by (i) explicitly considering the impact of temporal traffic variation on lifetime and energy savings; (ii) performing a sensitivity analysis of lifetime variation as a consequence of different combinations of input HW parameters; and (iii) estimating the total profitability of the network as the difference between electricity savings and reparation costs triggered by lifetime variation. In addition, the presented MILP formulation used to design the input topology enforces single-shortest-path routing of IP traffic demands over the IP topology in the reference network, which is an aspect in general not considered by any related work in energy-efficient multilayer core networks.