# A Statistical Performance Analysis of Named Data Ultra Dense Networks
## 1 Introduction
However, if the PIT entry does not exist, it checks the CS for the desired content and may respond with the data packet on the interface from where the interest arrives. If desired content is absent from the CS, the router forwards the interest towards the producer using longest prefix matching on the FIB. The FIB data structure can have more than one interface for a single name prefix. Once the interest packet reaches the producer node, it may respond with the data packet, which comprises the name of content, the content itself, and optional fields. When the data packet arrives at the routers, it searches the corresponding PIT entry and forwards the data to all downstream face IDs. Finally, it stores the data in the CS and removes the PIT entry. It is to be noted that in pure ICN and most of the literature, the CS lookup is the very first operation after the arrival of an interest packet. However, NDN follows the PIT operations first. The main reason behind this logic is to minimize the CS lookup delay because the PIT is considered to be significantly smaller than the CS. The initial implementation of NDN, which was Content Centric-Networking (CCN) also follows the CS lookup operation first. However, the CCN was then extended to the NDN architecture, and NDN is slightly different from CCN in the architectural perspective in a way that in CCN when a content request is received on a content router, then the very first operation is to check the CS. However, NDN checks the PIT at first, and then, the CS is checked [13; 14; 15; 16]. Figure 1 presents the NDN communication process in a network. NDN routers cache the incoming data based on the name of the content to satisfy future requests with low latency. Thus, they mitigate the backhaul traffic on a single provider. However, in the case of congestion, cache management is a challenging task [17]. Despite the use of caching in the network, a bottleneck may still occur in highly-crowded areas, such as shopping malls, concerts, or stadiums, where thousands of users and IoT devices are requesting information that may change over time (such as dynamic content) [18]. Thus, end users or devices may suffer from a poor packet delivery ratio (PDR). To overcome issues such as cache management, bottleneck mitigation, and congestion, statistical modeling of an ultra-dense network can be utilized to provide a broader view of the network topology and its characteristics. In this paper, we provide an analysis of content delivery in terms of the interest satisfaction rate (ISR) in ultra-dense network traffic situations. Extensive simulation is carried out in two phases. In the first phase, we ran the simulations in order to select appropriate parameters for our statistical analysis. In the second phase, a four-way factorial design method was employed to generate the dataset for statistical analysis. The rationale of choosing the four-way design method is the higher-level models can be used to reveal the non-linearity of the data, unlike the two- or three-level models, which are used to present the first or second polynomial models. The primary statistical analysis started with the evaluation of the main and interaction effects of predictors and their influence on ISR. A multiple comparison test was conducted to analyze the difference in mean ISR according to the levels of each predictor. In our regression analysis, the initial model includes the candidate predictors with four levels, and their interactions are chosen from the mean plots, interaction plots, and multiple comparison tests. Finally, the best model is selected based on the AIC. Moreover, to validate the accuracy of the final model, residual graphs are employed. Figure 1: Named data networking (NDN) communication process. CS, content store; PIT, pending interest table; FIB, forwarding information base. In summary, the contributions of this paper are discussed as follows:  
1. We present a four-way factorial design method, which is applied to generate the dataset, including various network parameters, in the ndnSIM simulator. 2.