Controller area network (CAN) enables communication of electronic control units (ECUs) via messages using priority-based arbitration, which requires the implementation of priority queues (PQs) in the ECU device driver. Nevertheless, it is possible that not all ECUs on a CAN support PQs but use FIFO queues (FQs) instead. In this case, the classical CAN scheduling model with PQs is not suitable for the computation of message worst-case responsetimes (WCRTs) that are essential for verifying the correct vehicle operation. This paper considers an existing scheduling model for CAN with both PQs and FQs. First, an improved algorithm for speeding up the WCRT computation is proposed. Second, the practical case where an existing CAN message set is extended by new messages is addressed. An original algorithm for assigning priorities to new messages while keeping the priority order of existing messages is developed. Both algorithms are evaluated by computational experiments.