In lossless interconnection networks such as InfiniBand, congestion control (CC) can be an effective mechanism to achieve high performance and good utilization of network resources. The InfiniBand standard describes CC functionality for detecting and resolving congestion, but the design decisions on how to implement this functionallity is left to the hardware designer. One must be cautious when making these design decisions not to introduce fairness problems, as our study shows.In this paper we study the relationship between congestion control, switch arbitration, and fairness. Specifically, we look at fairness among different traffic flows arriving at a hot spot switch on different input ports, as CC is turned on. In addition we study the fairness among traffic flows at a switch where some flows are exclusive users of their input ports while other flows are sharing an input port (the parking lot problem).Our results show that the implementation of congestion control in a switch is vulnerable to unfairness if care is not taken. In detail, we found that a threshold hysteresis of more than one MTU is needed to resolve arbitration unfairness. Furthermore, to fully solve the parking lot problem, proper configuration of the CC parameters are required.