Delay Analysis of a Place Reservation Queue

Modern communication networks have to support an increasingly diverse range of applications, each bearing their own particular set of Quality of Service (QoS) requirements. Realtime applications (e.g. multimedia streaming, telephony, gaming, ...) are characterized by hard delay requirements: the mean delay and the delay jitter of the data packets should typically be kept minimal. For non-real-time applications (e.g. www, ftp, e-mail, ...) on the other hand, delay requirements are typically less stringent, but packet loss should be (very) low. In short, the network should differentiate between the various types of traffic, in order to meet up with the traffic types’ QoS requirements. Over the last decades, many solutions have been proposed, varying in complexity and effect. A common method of supporting differentiated QoS, is the use of priority scheduling in the network nodes, opposed to standard First-In First-Out (FIFO) scheduling. In what follows, we will divide all network traffic in two separate classes: class 1 will cover delay-sensitive traffic, class 2 consists of delaytolerant traffic. In FIFO, all packets are treated equally, regardless of their requirements. The other extreme is posed by the Absolute Priority (AP) scheduling mechanism, where different traffic types are mapped to different priority levels, and transmission priority is always given to packets of the highest priority level. In this particular case, we will consider class-1 traffic to be high-priority and class-2 traffic to be low-priority. When the server of an AP system becomes available, the first class-1 packet, present in the queue, if any, is served first. Class-2 packets can then only enter the server in the absence of class-1 packets. AP has been studied extensively for various cases. It has been shown that AP does indeed decrease highpriority packet delay at the expense of lowpriority traffic. This may lead to excessive lowpriority packet delays or so-called starvation. To counter the problem of packet starvation, a new priority scheduling mechanism was proposed in [1], called the Reservation Discipline (RD). With RD, a dummy packet, the reserved place R, is inserted in the queue, to act as a placeholder for future class-1 packets. As a class-1 packet arrives at the system, it is inserted at R’s position and R gets reinserted at the end of the queue. Class-2 packets are simply inserted at the end of the queue, just as they would have been under FIFO scheduling. If multiple packets arrive at the system during the same time slot, first the class-1 packets are inserted one by one and then the class-2 packets are appended in arrival order. This way, class-1 packets are favoured twice: not only are they inserted before the class-2 packets that arrived during the same slot; the first class-1 packet of each slot is inserted at R’s position, allowing the packet to jump over some class-2 packets. Since any class-2 packet can be jumped over only once, there is a limit to the disadvantage sustained. Research has been done before for service times of exactly one slot, see [2]. We have studied RD in case of geometric and general service times, see [3] and [4] respectively.