--- abstract: 'In the literature, the optimal strategy for online content delivery has been studied extensively by many researchers in the communication and networking community. These works consider a single server that serves online users in a real-time fashion, and therefore, these results may not be directly applicable to content delivery in a D2D-based multimedia network. In this paper, we propose a queueing model for content delivery in the downlink of a cellular-based cellular network with in-network caching and D2D communication between the base stations (BSs) and user devices (UDs). In addition, we propose a delivery strategy for this network, where a fraction of the files are stored in the BSs and the UDs, and this paper aims to derive the optimal fraction of the files to cache in the BSs and UDs. We also derive an upper bound on the average downlink data rate of the network under this proposed strategy.' author: - - - bibliography: - 'main.bib' title: 'Optimal Strategy for Offloading and Serving Content in a Cellular-Based Cellular Network with Downlink Caching' --- Introduction ============ Caching in the downlink of a cellular network is a promising technique to reduce the energy consumption of cellular base stations (BSs). One of the key challenges in a cellular network is the management of data traffic in the congested cellular access links. In order to overcome the data traffic congestion, caching can be performed at BSs. When files are requested by user devices (UDs), a part of the content can be provided from the BS caches. By prefetching the files and caching them at the BSs, cellular network operators can lower the BS load and save the energy of BSs. In addition, caching techniques have been widely studied in recent literature [@cache_survey]. While most of the works in the literature have been focusing on caching in the uplink, the potential of caching in the downlink is gaining much attention. In [@cache_dl], the effect of caching on the delay of content delivery and the energy consumption of cellular networks is considered. In this paper, we also focus on the energy savings of cellular networks, but rather than focusing on the latency of content delivery, we focus on the energy savings of cellular networks that benefit from caching at the BSs and UDs. The main motivation of the work in this paper comes from the fact that some recent works have considered content delivery in a D2D-based mobile ad hoc network (MANET). For instance, in [@adhoc_file_sharing], the authors have considered caching at UDs and an online content delivery strategy based on peer-to-peer (P2P) communication. P2P communication can increase the content availability in a network, and it also reduces energy consumption and signaling overhead. A related work is [@adhoc_cache], where the authors have considered P2P content delivery in MANETs, and they propose a heuristic strategy that finds the optimal fraction of data to be transmitted by D2D links and the optimal set of D2D link pairs that minimize the average delay of content delivery in the network. In [@femto_tactile_comm], the authors have proposed a distributed file delivery strategy with opportunistic caching for a tactile mobile network. They consider opportunistic D2D communications in the presence of mobile users and show that the optimal fraction of files can be reliably transmitted in a tactile fashion with negligible delay and very low energy consumption. Since all these works have proposed an optimal caching strategy in a D2D-based MANET, it is quite obvious that this strategy cannot be directly applied to a cellular-based network, since cellular communication is quite different than P2P communication. As can be observed, content delivery strategies in a cellular-based network and a D2D-based network have some similarities in terms of energy savings; however, there are several key differences as well. The major differences can be observed in terms of the cache memory, the UDs, and the data traffic in the network. In [@cache_dl], the authors have considered only a single BS to serve content. This case can be called the *one BS case*, and it can be observed that in this case, a P2P topology of cache-enabled UDs and one BS can be treated as a single cluster, which is quite similar to a D2D MANET. But in the downlink of a cellular-based network, the BSs are distributed in a cellular topology and they are all connected via wireless links to the core network. The second major difference in cellular networks and D2D networks is the existence of the core network. In addition, since users are moving in D2D networks, the UDs are mobile in nature and therefore, the core network has to track the location of UDs. On the other hand, in cellular networks, the cellular network has the knowledge of the location of each BSs and the location of UDs. In addition, when UDs visit the cells, the access of the UDs to the BSs is controlled, which allows some UDs to connect to the BSs directly. In addition, the BSs in cellular networks may be operated by different cellular operators. This is different from D2D networks, where all the UDs will be connected to the same network due to P2P communication. In this paper, we study the optimal strategy for D2D and in-network caching in cellular networks, in terms of a few key parameters, namely, the number of UDs, the number of BSs, the power model of cellular links, and the power model of cellular-U link transmission. We consider a cellular network with $K$ BSs and $U$ UDs. There are also $M$ files in the library of the network. Each BS and each UD have cache capacity $M_{BS}$ and $M_{UD}$, respectively, where $M_{BS}, M_{UD} \in \{0, 1, \cdots, M\}$, with $M_{BS}+M_{UD} \leq M$. Let $P_C$ be the capacity of the core network. The BSs can serve the UDs directly via wireless cellular links, and thus, the capacity of the BS-UD link is limited by the capacity of the core network. If a UD connects to the BS through a cellular-based cellular link, then it will be served by the BS directly, which means that its demand will be fulfilled in the cell coverage area. But in some cases, a UD may not be able to connect to the BS directly, because of the limited capacity of the BS-UD link. In this case, a D2D link can be used between the UD and the BS to serve its content demands. Therefore, when a UD is not connected to a BS through a wireless cellular link, the BS can still deliver its content by utilizing the D2D links of its neighboring UDs. We call this case as the *inter-cell caching case*. We also consider the *one BS case*, where there is only one BS that serves all of the UDs, which is quite similar to the D2D MANET model that has been considered in the literature. We also compare the two cases and show that in terms of the delay of content delivery, the delay of the inter-cell caching case is lower than the delay of the one BS case. We have also derived an analytical closed-form expression for this case in terms of the Laplace transform of the interference power of all the cellular links and the Laplace transform of the interference power of all cellular-UD links. As can be observed, the derived analytical expression for the one BS case is quite similar to that of the D2D MANET model that has been considered in the literature. In addition, we propose a delivery strategy for cellular networks with caching. For this strategy, a fraction of the files are stored in the BSs and the UDs, and this paper aims to derive the optimal fraction of the files to cache in the BSs and the UDs. It is interesting to compare our work with that of [@adhoc_cache], where a strategy has been proposed for a D2D-based MANET, which is quite similar to the optimal strategy for a cellular-based MANET in terms of communication between UDs and cellular network, but in the optimal strategy in [@adhoc_cache], we have also considered the interference to cellular network. Therefore, the strategy in [@adhoc_cache] is more restrictive than the strategy in this paper. In addition, the strategy in [@adhoc_cache] cannot be applied for cellular network, since the strategy in [@adhoc_cache] is a heuristic, while the strategy in this paper considers a system with $M$ files and a caching algorithm with $M$ BSs to satisfy the UDs’ demand. The rest of this paper is organized as follows: The system model is described in Section \[system\_model\]. The analysis of the energy consumption and delay of content delivery for different cases is provided in Section \[delay\_analysis\]. The simulation results for our analysis are provided in Section \[sim\_results\]. Finally, the paper is concluded in Section \[conclusions\]. System Model {#system_model} ============ As shown in Fig. \[system\_model\_downlink\], we consider a network with $K$ BSs and $U$ UDs. It is assumed that there are $M$ files in the library of the network, where $M_{BS}, M_{