The risk of vehicle collisions significantly increases when drivers are overloaded with information from in-vehicle systems. One of the solutions to this problem is developing adaptive workload management systems (AWMSs) to dynamically control the rate of messages from these in-vehicle systems. However, existing AWMSs do not use a model of the driver cognitive system to estimate workload and only suppress or redirect in-vehicle system messages, without changing their rate based on driver workload. In this paper, we propose a prototype of a new queueing network-model human processor AWMS (QN-MHP AWMS), which includes a queueing network model of driver workload that estimates the driver workload in several driving situations and a message controller that determines the optimal delay times between messages and dynamically controls the rate of messages presented to drivers. Given the task information of a secondary task, the QN-MHP AWMS adapted the rate of messages to the driving conditions (i.e., speeds and curvatures) and driver characteristics (i.e., age). A corresponding experimental study was conducted to validate the potential effectiveness of this system in reducing driver workload and improving driver performance. Further development of the QN-MHP AWMS, including its use in in-vehicle system design and possible implementation in vehicles, is discussed.