enotes the queuing time for the tagged packet. W denotes the total time the tagged packet spends in the system. It is the sum of the queuing time and the service time B of a packet. 6 Dimensioning for Single ATM-Based lub Tagged low priority packet Queue lengths just after the start of B High priority tagged Low priority packet Partial service time U Residual service time V Ongoing service time B High priority packet Low priority packet Figure 6.49: Basic idea to study the delay distribution of a priority queue [HZ05] Firstly consider a high priority tagged packet. As shown in Figure 6.49, this packet sees the server busy with some packets queuing (the queue could also be empty). Since it is a high priority packet, it can only see the high priority packets which are queuing ahead of it, if there are any. Low priority packets, even any that came earlier, are transparent to the tagged packet. In this case, the queuing delay of this tagged packet consists of three parts: (1) the first part is the time for the server to serve all the high priority packets that were already in the queue at the time the on-going service began; (2) the second part comes from serving those high priority packets that enter the system during the partial service time U; (3) the third part is the residual period V. For a low priority packet, its queuing delay is the sum of four parts, as shown in Figure 6.49. (1) the first part is the sum of the high-priority busy periods generated by all the packets (A) in the queue at the time the on-going service began; (2) the second part comes from the sum of the busy periods generated by all the packets (X) that enter the system during the partial service time U; (3) the third part arises from the busy periods generated by the high priority packets that arrive during V ; (4) the fourth part is the residual period V. In this thesis, the dimensioning is according to the performance of the low priority queue, as it is found that in all investigated cases the high priority traffic can overachieve its QoS d