Abstract : In this paper we study base station sleep modes that, by reducing power consumption in periods of low traffic, improve the energy efficiency of cellular access networks. We assume that when some base stations enter sleep mode, radio coverage and service provisioning are provided by the base stations that remain active, so as to guarantee that service is available over the whole area at all times. This may be an optimistic assumption in the case of the sparse base station layouts typical of rural areas, but is, on the contrary, a realistic hypothesis for the dense layouts of urban areas, which consume most of the network energy. We consider the possibility of either just one sleep mode scheme per day (bringing the network from a high-power, fully-operational configuration, to a low-power reduced configuration), or several sleep mode schemes per day, with progressively fewer active base stations. For both contexts, we develop a simple analytical framework to identify optimal base station sleep times as a function of the daily traffic pattern. We start by considering homogeneous networks, in which all cells carry the same amount of traffic and cover areas of equal size. Considering both synthetic traffic patterns and real traffic traces, collected from cells of an operational network, we show that the energy saving achieved with base station sleep modes can be quite significant, the actual value strongly depending on the traffic pattern. Our results also show that most of the energy saving is already achieved with one sleep mode scheme per day. Some additional saving can be achieved with multiple sleep mode schemes, at the price of a significant increase in complexity. We then consider heterogeneous networks in which cells with different coverage areas and different amounts of traffic coexist. In particular, we focus on the common case in which some micro-cells provide additional capacity in a region covered by an umbrella macro-cell, and we prove that the optimal scheduling of micro-cell sleep times is in increasing order of load, from the least loaded to the most loaded. This provides a valuable guideline for the scheduling of sleep modes (i.e., of low-power configurations) in complex heterogeneous networks.