# On Optimal Cell Flashing for Reducing Delay and Saving Energy in Wireless Networks
## 2 System Model  
We assume a basic small cell wireless network where each base station is equipped with an omnidirectional antenna. For analytical tractability, we consider small cell hexagonal networks, but our model can be further extended to randomly deployed small cells using stochastic geometry, which is beyond the scope of this paper. We consider a region \(\mathcal{L}\subset\mathbb{R}^{2}\) that is served by a set of base stations \(\mathcal{B}\). Let \(x\in\mathcal{L}\) denote a location and \(i\in\mathcal{B}\) be a BS index. Note that we use the BS index \(i\) for cell index because BS and cell refer to the same object with slightly different purposes, which can be understood in the context. Let \(k\subset\mathcal{B}\) be a _cluster_, which consists of a set of adjacent cells that may orthogonally use a time-domain resource. Even though the number of the BSs in a cluster can be two or more, _three_ is meaningful in a practical system because too many BSs in a cluster sacrifice the benefit of frequency reuse. Thus, we consider three BSs in a cluster hereafter. We assume that file transfer or web page download requests, i.e., flow arrivals follow a Poisson point process with arrival rate per unit area \(\lambda(x)\) and file sizes that are independently distributed with mean \(1/\mu(x)\) at location \(x\in\mathcal{L}\), so the traffic load density is defined by \(\gamma(x):=\frac{\lambda(x)}{\mu(x)}\); we assume \(\gamma(x)<\infty\) for \(x\in\mathcal{L}\). This captures spatial traffic variability. For example, a hot spot can be characterized by a high arrival rate and/or possibly large file sizes [23; 24; 25]. Figure 1 depicts the hexagonal cellular networks operated by cell flashing. Figure 0(a) shows the case when time-domain resources are divided into four partitions. In partition 0, all three BSs transmit while in partition \(i\). Only BS \(i\) transmits and other BSs remain silent. Figure 0(b) shows the coverage based on signal-to-interference-plus-noise ratio (SINR) in each partition. For example, during partition 0, each cell serves its own coverage, while during partition \(i\), only BS \(i\) is activated and serves its own coverage. Let \(\beta\) denote a fraction of time that cells flash, i.e., the fraction of time for partitions 1, 2, and 3. Thus, with a ratio of \(1-\beta\), all BSs are on (partition 0), and with a ratio of \(\beta\), only one BS \(i\in\{1,2,3\}\) is on as shown in Figure 0(b). Thus, the inter-cell interference can be decreased just like frequency reuse 3, and capacity seen by cell edge users can be improved. One may want to consider load balancing where radio resource, either time or frequency, is allocated depending on traffic variation in space. For example, our previous work of [25] proposed adaptively changing the spectrum bandwidth of each BS in accordance with the loads of BSs. In this work, however, we do not consider load balancing because when partition time is not orthogonalized among adjacent clusters, inter-cluster interferences from adjacent clusters may become severe. This makes complicated dynamic inter-cell interference unavoidable, and the analysis of flow-level dynamics is not applicable [24; 25; 27]. In this regard, we consider the case where all cells have the equal partition length. The study on cell flashing with load balancing remains for further study. This paper focuses on scenarios where users see (a roughly) static interference from neighboring cells, which was also assumed in [23; 24; 25]. Static interference assumption makes sense when interfering cells independently operate with the interfered cell and also interferences are not severe by using, for example, FFR or enhanced inter-cell interference coordination (elCIC). Then, the summation of interference can be considered as static Gaussian-like noise [23; 24; 25].