In this paper, the problem of joint power and resource allocation for ultra reliable low latency communication (URLLC) in vehicular networks is studied. The key goal is to minimize the networkwide power consumption of vehicular users (VUEs) subject to high reliability in terms of probabilistic queuing delays. In particular, using extreme value theory (EVT), a new reliability measure is defined to characterize extreme events pertaining to vehicles' queue lengths exceeding a predefined threshold with non-negligible probability. In order to learn these extreme events in a dynamic vehicular network, a novel distributed approach based on federated learning (FL) is proposed to estimate the tail distribution of the queues. Taking into account the communication delays incurred by FL over wireless links, Lyapunov optimization is used to derive the joint transmit power and resource allocation policies enabling URLLC for each VUE in a distributed manner. The proposed solution is then validated via extensive simulations using a Manhattan mobility model. Simulation results show that FL enables the proposed distributed method to estimate the tail distribution of queues with an accuracy that is very close to a centralized solution with up to 79% reductions in the amount of data that need to be exchanged. Furthermore, the proposed method yields up to 60% reductions of VUEs with large queue lengths, while reducing the average power consumption by two folds, compared to an average queue-based baseline. For the VUEs with large queue lengths, the proposed method reduces their average queue lengths and fluctuations therein by about 30% compared to the aforementioned baseline. arXiv:1807.08127v2 [cs.IT] 1 Aug 2018 Index Terms V2V communication, Lyapunov optimization, extreme value theory, federated learning, URLLC, 5G. I. INTRODUCTION Providing efficient vehicle-to-vehicle (V2V) communications is a necessary stepping stone for enabling autonomous and intelligent transportation systems (ITS) [1]-[5]. V2V communications can extend drivers' field of view, thus enhancing traffic safety and driving experience, while enabling new transportation features such as platooning, real-time navigation, collision avoidance, and autonomous driving [1], [4]. However, the performance of emerging transportation applications heavily rely on the availability of V2V communication links with extremely low errors and delays. In this regard, achieving ultra-reliable low-latency communication (URLLC) for V2V networks is necessary for realizing the vision of intelligent transportation [1]. Since over-the-air latency and queuing latency are coupled, ensuring low queuing latency is required to achieve the much coveted target end-to-end latency of 1 ms. This, in turn, necessitates efficient radio resource management (RRM) techniques [5]-[7]. Furthermore, the increased energy consumption and its negative impact on the environment due to the large number of vehicles in modern transportation system, and improving energy-efficiency/energy savings need to be addressed ...