  In this paper, we consider fair assignment of complex requests for
Mobility-On-Demand systems. We model the transportation requests as temporal
logic formulas that must be satisfied by a fleet of vehicles. We require that
the assignment of requests to vehicles is performed in a distributed manner
based only on communication between vehicles while ensuring fair allocation.
Our approach to the vehicle-request assignment problem is based on a
distributed auction scheme with no centralized bidding that leverages utility
history correction of bids to improve fairness. Complementarily, we propose a
rebalancing scheme that employs rerouting vehicles to more rewarding areas to
increase the potential future utility and ensure a fairer utility distribution.
We adopt the max-min and deviation of utility as the two criteria for fairness.
We demonstrate the methods in the mid-Manhattan map with a large number of
requests generated in different probability settings. We show that we increase
the fairness between vehicles based on the fairness criteria without
degenerating the servicing quality.
