  In the upcoming 6G era, vehicular networks are shifting from simple
Vehicle-to-Vehicle (V2V) communication to the more complex
Vehicle-to-Everything (V2X) connectivity. At the forefront of this shift is the
incorporation of Large Language Models (LLMs) into vehicles. Known for their
sophisticated natural language processing abilities, LLMs change how users
interact with their vehicles. This integration facilitates voice-driven
commands and interactions, departing from the conventional manual control
systems. However, integrating LLMs into vehicular systems presents notable
challenges. The substantial computational demands and energy requirements of
LLMs pose significant challenges, especially in the constrained environment of
a vehicle. Additionally, the time-sensitive nature of tasks in vehicular
networks adds another layer of complexity. In this paper, we consider an edge
computing system where vehicles process the initial layers of LLM computations
locally, and offload the remaining LLM computation tasks to the Roadside Units
(RSUs), envisioning a vehicular ecosystem where LLM computations seamlessly
interact with the ultra-low latency and high-bandwidth capabilities of 6G
networks. To balance the trade-off between completion time and energy
consumption, we formulate a multi-objective optimization problem to minimize
the total cost of the vehicles and RSUs. The problem is then decomposed into
two sub-problems, which are solved by sequential quadratic programming (SQP)
method and fractional programming technique. The simulation results clearly
indicate that the algorithm we have proposed is highly effective in reducing
both the completion time and energy consumption of the system.
