# On Optimal Cell Flashing for Reducing Delay and Saving Energy in Wireless Networks
## 1 Introduction
One may think that cell flashing may not be practical, at least at this moment, because turning base stations on and off may take significant time, either base station (BS) goes to sleep mode or returns back to active mode, or uplink signals cannot be continuously received. When BS goes to deep-sleep mode, which consumes very low power, it takes a long time and uplink signals cannot be continuously received. However, when fast discontinuous transmission (DTX) is used [19], the transition period between sleep mode and active mode is similar to the case of state on/off change in time division duplexing (TDD) system, and subframes for uplink signals can be continuously received at the expense of energy consumption [20; 21]. According to [22], it is possible to switch on/off states in the order of 17 \(\upmu\)s. This is a much shorter time than long term evolution advanced (LTE-A) scheduling period of 0.5 ms, and thus cell flashing can be viable. Of course, energy saving of DTX cannot be as much as that of deep-sleep mode. To better understand energy saving and the user-perceived performance, we consider stochastic traffic loads where new file transfers, or equivalently flows, are initiated at random and leave the system after being served. This is usually referred to as flow-level dynamics [23; 24; 25]. Unlike the previous works of FTR [5; 6] where energy efficiency was ignored, and static population (or infinitely backlogged users) was assumed, our work is unique in the sense that it captures the impact of dynamic user population on energy efficiency and the long term average performance, which is closer to user-perceived performance, e.g., file download time (or called delay hereafter). Note that user experience is based on the time-averaged performance rather than instantaneous capacity. Analyzing such systems is, however, more challenging because of the dynamic nature of the system, and its analysis is hardly tractable in general [24]. When cell flashing is employed in a dynamic system, we consider the user-perceived performance, i.e., the average delay measured by file download time and the energy consumption of base stations and formulate an optimization problem. Based on flow-level dynamics, we prove that cell flashing can improve both total energy saving and the average delay in the interference-limited regime, which is typically the case of small cells. This can be achieved because large average delay is mainly incurred by cell edge users' poor performances, and thus improved cell edge user performances make the average delay lower. Thus, cell flashing has three advantages: higher energy efficiency, improved cell edge user performances, and lower average delay in small cells. These benefits are promising because cell densification is essential to achieve higher network-level capacity [2] and lower energy consumption [26]. However, as the cell radius increases, there is a tradeoff between energy saving and reducing delay. Our extensive simulations show that when noise power is negligibly small compared to transmit power, energy consumption of the base stations can be reduced by 25%, and at the same time, the overall average delay is reduced by up to 75% compared to the case of non-flashing. Furthermore, the performance improvement for cell edge users is also noticeable, e.g., the conditional average delay at cell edge is reduced by 80%. We would like to emphasize that previous papers mainly focused on deep-sleep mode on a long-term scale, but our work analyzes the impact of turning BSs on and off rapidly while receiving uplink signals continuously. Thus, the time scales of energy saving are different, and cell flashing can be implemented independently of deep-sleep mode; even if the BS decides to remain on because traffic volume is moderate, the BS still can be turned on/off rapidly for extra energy saving. In addition, cell flashing can reduce both energy and delay simultaneously in small cells (see Proposition 1). The rest of paper is organized as follows.