The development of autonomous ground and aerial vehicles has driven the requirement for radio access technologies (RATs) to support low latency applications. While onboard sensors such as Light Detection and Ranging (LIDAR), Radio Detection and Ranging (RADAR), and cameras can sense and assess the immediate space around the vehicle, RATs are crucial for the exchange of information on critical events, such as accidents and changes in trajectory, with other vehicles and surrounding infrastructure in a timely manner. Simulations and analytical models are critical in modelling and designing efficient networks. In this dissertation, we focus on (a) proposing and developing algorithms to improve the performance of decentralized vehicular communications in safety critical situations and (b) supporting these proposals with simulation and analysis of the two most popular RAT standards, the Dedicated Short Range Communications (DSRC) standard, and the Cellular vehicle-to-everything (C-V2X) standard. In our first contribution, we propose a risk based protocol for vehicles using the DSRC standard. The protocol allows a higher beacon transmission rate for vehicles that are at a higher risk of collision. We verify the benefits of the risk based protocol over conventional DSRC using ns-3 simulations. Two risk based beacon rate protocols are evaluated in our ns-3 simulator, one that adapts the beacon rate between 1 and 10 Hz, and another between 1 and 20 Hz. Our results show that both protocols improve the packet delivery ratio (PDR) performance by up to 45% in congested environments using the 1-10 Hz adaptive beacon rate protocol and by 38% using the 1-20 Hz adaptive scheme. The two adaptive beacon rate protocol simulation results also show that the likelihood of a vehicle collision due to missed packets decreases by up to 41% and 77% respectively, in a three lane dense highway scenario with 160 vehicles operating at different speeds. In our second contribution, we study the performance of a distance based transmission protocol for vehicular ad hoc network (VANET) using tools from stochastic geometry. We consider a risk based transmission protocol where vehicles transmit more frequently depending on the distance to adjacent vehicles. We evaluate two transmission policies, a listen more policy, in which the transmission rate of vehicles decreases as the inter-vehicular distance decreases, and a talk more policy, in which the transmission rate of vehicles increases as the distance to the vehicle ahead of it decreases. We model the layout of a highway using a 1-D Poisson Point process (PPP) and analyze the performance of a typical receiver in this highway setting. We characterize the success probability of a typical link assuming slotted ALOHA as the channel access scheme. We study the trends in success probability as a function of system parameters. Our third contribution includes improvements to the 3rd Generation Partnership Project (3GPP) Release 14 C-V2X standard, evaluated using a modified collision framework. In C-V2X basic safety messages (BSMs) are transmitted through Mode-4 communications, introduced in Release 14. Mode-4 communications operate under the principle of sensing-based semi-persistent scheduling (SPS), where vehicles sense and schedule transmissions without a base station present. We propose an improved adaptive semi-persistent scheduling, termed Ch-RRI SPS, for Mode-4 C-V2X networks. Specifically, Ch-RRI SPS allows each vehicle to dynamically adjust in real-time the BSM rate, referred to in the LTE standard as the resource reservation interval (RRI). Our study based on system level simulations demonstrates that Ch-RRI SPS greatly outperforms SPS in terms of both on-road safety performance, measured as collision risk, and network performance, measured as packet delivery ratio, in all considered C-V2X scenarios. In high density scenarios, e.g., 80 vehicles/km, Ch-RRI SPS shows a collision risk reduction of 51.27%, 51.20% and 75.41% when compared with SPS with 20 ms, 50 ms, and 100 ms RRI respectively. In our fourth and final contribution, we look at the tracking error and age-of-information (AoI) of the latest 3GPP Release 16 NR-V2X standard, which includes enhancements to the 3GPP Release 14 C-V2X standard. The successor to Mode-4 C-V2X, known as Mode-2a NR-V2X, makes slight changes to sensing-based semi-persistent scheduling (SPS), though vehicles can still sense and schedule transmissions without a base station present. We use AoI and tracking error, which is the freshness of the information at the receiver and the difference in estimated vs actual location of a transmitting vehicle respectively, to measure the impact of lost and outdated BSMs on a vehicle's ability to localize neighboring vehicles. In this work, we again show that such BSM scheduling (with a fixed RRI) suffers from severe under- and over- utilization of radio resources, which severely compromises timely dissemination of BSMs and increases the system AoI and tracking error. To address this, we propose an RRI selection algorithm that measures the age or freshness of messages from neighboring vehicles to select an RRI, termed Age of Information (AoI)-aware RRI (AoI-RRI) selection. Specifically, AoI-aware SPS (i) measures the neighborhood AoI (as opposed to channel availability) to select an age-optimal RRI and (ii) uses a modified SPS procedure with the chosen RRI to select BSM transmission opportunities that minimize the overall system AoI. We compare AoI-RRI SPS to Ch-RRI SPS and fixed RRI SPS for NR-V2X. Our experiments based on the Mode-2a NR-V2X standard implemented using system level simulations show both Ch-RRI SPS and AoI-RRI SPS outperform SPS in high density scenarios in terms of tracking error and age-of-information. / Doctor of Philosophy / An increasing number of vehicles are equipped with a large set of on-board sensors that enable and support autonomous capabilities. Such sensors, which include Light Detection and Ranging (LIDAR), Radio Detection and Ranging (RADAR), and cameras, are meant to increase passenger and driver safety. However, similar to humans, these sensors are limited to line-of-sight (LOS) visibility, meaning they cannot see beyond other vehicles, corners, and buildings. For this reason, efficient vehicular communications are essential to the next generation of vehicles and could significantly improve road safety. In addition, vehicular communications enable the timely exchange of critical information with other vehicles, cellular and roadside infrastructure, and pedestrians. However, unlike typical wireless and cellular networks, vehicular networks are expected to operate in a distributed manner, as there is no guarantee of the presence of cellular infrastructure. Accurate simulations and analytical models are critical in improving and guaranteeing the performance of the next generation of vehicular networks. In this dissertation, we propose and develop novel and practical distributed algorithms to enhance the performance of decentralized vehicular communications. We support these algorithms with computer simulations and analytical tools from the field of stochastic geometry.