On the k nearest-neighbor path distance from the typical intersection in the Manhattan Poisson line Cox process

In this paper, we consider a Cox point process driven by the Manhattan Poisson line process. We calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the $k$-th nearest node of the Cox process. The CDF is expressed as a sum over the integer partition function $p\!\left(k\right)$, which allows us to numerically evaluate the CDF in a simple manner for practical values of $k$. These distance distributions can be used to study the $k$-coverage of broadcast signals transmitted from a \ac{RSU} located at an intersection in intelligent transport systems (ITS). Also, they can be insightful for network dimensioning in vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the \ac{RSU} is placed at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting. We corroborate the applicability of our distance distribution model using the map of an urban area

Shortest Path Distance in Manhattan Poisson Line Cox Process

While the Euclidean distance characteristics of the Poisson line Cox process (PLCP) have been investigated in the literature, the analytical characterization of the path distances is still an open problem. In this paper, we solve this problem for the stationary Manhattan Poisson line Cox process (MPLCP), which is a variant of the PLCP. Specifically, we derive the exact cumulative distribution function (CDF) for the length of the shortest path to the nearest point of the MPLCP in the sense of path distance measured from two reference points: (i) the typical intersection of the Manhattan Poisson line process (MPLP), and (ii) the typical point of the MPLCP. We also discuss the application of these results in infrastructure planning, wireless communication, and transportation networks

Stochastic Geometry for Mobility-Aware Performance Modeling in 6G Multi-band Wireless Networks

Using tools from stochastic geometry, I develop a stochastic geometry-based tractable framework to analyze the performance of a mobile user in a two-tier wireless network operating on sub-6GHz and terahertz (THz) transmission frequencies. Specifically, using an equivalence distance approach, I characterize the overall handoff (HO) rate in terms of the horizontal and vertical HO probability. In addition, I characterize novel coverage probability expressions for THz network in the presence of molecular absorption noise and highlight its significant impact on the users' performance. Specifically, I derive a novel closed-form expression for the Laplace Transform of the cumulative interference in the presence of molecular noise observed by a mobile user in a hybrid RF-THz network. Furthermore, I provide a novel approach to derive the conditional distance distributions of a typical user in a hybrid RF-THz network. Finally, using the overall HO rate and coverage probability expressions, the mobility-aware probability of coverage has been derived in a hybrid RF-THz network. The mathematical results validate the correctness of the derived expressions using Monte-Carlo simulations. The results offer insights into the adverse impact of users' mobility and molecular noise in THz transmissions on the probability of coverage of mobile users. The results demonstrate that a small increase in the intensity of THz base-station (TBSs) (about 5 times) can increase the HO probability much more compared to the case when the intensity of RF base-station (RBSs) is increased by 100 times. Furthermore, I note that high molecular absorption can be beneficial (in terms of minimizing interference) for dense deployment of TBSs and the benefits can outweigh the drawbacks of signal degradation due to molecular absorption

Quality-Driven Cross-Layer Protocols for Video Streaming over Vehicular Ad-Hoc Networks

The emerging vehicular ad-hoc networks (VANETs) offer a variety of applications and new potential markets related to safety, convenience and entertainment, however, they suffer from a number of challenges not shared so deeply by other types of existing networks, particularly, in terms of mobility of nodes, and end-to-end quality of service (QoS) provision. Although several existing works in the literature have attempted to provide efficient protocols at different layers targeted mostly for safety applications, there remain many barriers to be overcome in order to constrain the widespread use of such networks for non-safety applications, specifically, for video streaming: 1) impact of high speed mobility of nodes on end-to-end QoS provision; 2) cross-layer protocol design while keeping low computational complexity; 3) considering customer-oriented QoS metrics in the design of protocols; and 4) maintaining seamless single-hop and multi-hop connection between the destination vehicle and the road side unit (RSU) while network is moving. This thesis addresses each of the above limitations in design of cross-layer protocols for video streaming application. 1) An adaptive MAC retransmission limit selection scheme is proposed to improve the performance of IEEE 802.11p standard MAC protocol for video streaming applications over VANETs. A multi-objective optimization framework, which jointly minimizes the probability of playback freezes and start-up delay of the streamed video at the destination vehicle by tuning the MAC retransmission limit with respect to channel statistics as well as packet transmission rate, is applied at road side unit (RSU). Two-hop transmission is applied in zones in which the destination vehicle is not within the transmission range of any RSU. In the multi-hop scenario, we discuss the computation of access probability used in the MAC adaptation scheme and propose a cross-layer path selection scheme; 2) We take advantage of similarity between multi-hop urban VANETs in dense traffic conditions and mesh connected networks. First, we investigate an application-centric routing scheme for video streaming over mesh connected overlays. Next, we introduce the challenges of urban VANETs compared to mesh networks and extend the proposed scheme in mesh network into a protocol for urban VANETs. A classification-based method is proposed to select an optimal path for video streaming over multi-hop mesh networks. The novelty is to translate the path selection over multi-hop networks to a standard classification problem. The classification is based on minimizing average video packet distortion at the receiving nodes. The classifiers are trained offline using a vast collection of video sequences and wireless channel conditions in order to yield optimal performance during real time path selection. Our method substantially reduces the complexity of conventional exhaustive optimization methods and results in high quality (low distortion). Next, we propose an application-centric routing scheme for real-time video transmission over urban multi-hop vehicular ad-hoc network (VANET) scenarios. Queuing based mobility model, spatial traffic distribution and prob- ability of connectivity for sparse and dense VANET scenarios are taken into consideration in designing the routing protocol. Numerical results demonstrate the gain achieved by the proposed routing scheme versus geographic greedy forwarding in terms of video frame distortion and streaming start-up delay in several urban communication scenarios for various vehicle entrance rate and traffic densities; and 3) finally, the proposed quality-driven routing scheme for delivering video streams is combined with a novel IP management scheme. The routing scheme aims to optimize the visual quality of the transmitted video frames by minimizing the distortion, the start-up delay, and the frequency of the streaming freezes. As the destination vehicle is in motion, it is unrealistic to assume that the vehicle will remain connected to the same access router (AR) for the whole trip. Mobile IP management schemes can benefit from the proposed multi-hop routing protocol in order to adapt proxy mobile IPv6 (PMIPv6) for multi-hop VANET for video streaming applications. The proposed cross-layer protocols can significantly improve the video streaming quality in terms of the number of streaming freezes and start-up delay over VANETs while achieving low computational complexity by using pattern classification methods for optimization