Although many multiprocessor resource sharing protocols have been proposed, their impacts on the schedulability of real-time tasks are largely ignored in most of the existing literature. Recently, work has been done to integrate queue locks (FIFO-queue-based non-preemptive spin locks) with multiprocessor schedulability analysis but the techniques used introduce a substantial amount of pessimism. For global fixed task priority preemptive multiprocessor systems, this pessimism impacts low priority tasks, greatly reducing the number of tasksets that can be recognised as schedulable. We develop a new schedulability analysis lp-CDW to target this issue specifically. By combing lp-CDW with existing techniques, we significantly increase the number of tasksets that can be recognised as schedulable.