Wireless communications systems are by nature and by regulations limited in bandwidth and hence capacity. Services with high demands on Quality of Service (QoS) will enforce high demands on the available capacity. This observation motivates the development of schedulers that can deliver the required QoS as well as being resource efficient. In this paper, we provide expressions of the worst case delivery time for schedulers based on the First In First Out (FIFO) and the Earliest Due-Date (EDD) principles which are applied to the HiperAccess point-to-multipoint radio communication system. Further, we propose modifications of the schedulers which are more resource efficient at the expense modified scheduling algorithms can still provide an average of rare deadline misses. Despite the deadline misses, the delivery time well within the required deadline.