We propose a novel distributed approach for the problem of scheduling a fleet of autonomous vehicles. Our distributed system avoids a single point of failure, is scalable, fault tolerant and robust. We describe an agent-based distributed system to conduct a set of procurement auctions. The vehicles are the "sellers" and the passengers are the "buyers" in the auction. Each vehicle bids for the passengers with a bid value which is an inverse function of the time it would take the vehicle to reach the passenger. In our agent based architecture, the various software agents reside on different systems and we describe distributed algorithms for their communication. We have performed simulations of a vehicle fleet in two different locations (Bangalore, India and Tyson's Corner, Virginia, USA) and compare the maximum and average waiting times of the passenger of our algorithm with a FIFO algorithm. We also compute the ratio of the time in which the vehicle is servicing a passenger to the total time, to compute the fuel wastage. The results show that our system improves the maximum and average waiting times of the passengers, as well as the fuel costs for the vehicle fleet. Furthermore, we show that such a distributed system reduces the time it would take on average to respond to customer requests, as compared to a system which is not distributed.