Analysis of Packet Delay in a GI-G-1 Queue with Non-preemptive Priority Scheduling Joris Walraevens, Bart Steyaert, and Herwig Bruneel SMACS Research Group Ghent University, Vakgroep TELIN (TW07V) Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium. Phone: 0032-9-2648902 Fax: 0032-9-2644295 {jw,bs,hb}@telin.rug.ac.be Abstract. Priority scheduling for packets is becoming a hot topic, as attemps are being made to integrate voice services in existing IP data networks. In this paper, we consider a discrete-time queueing system with head-of-line (HOL) non-preemptive priority scheduling. Two classes of traffic will be considered, i.e., high priority and low priority traffic, which both generate variable-length packets. We will derive expressions for the Probability Generating Function (pgf) of the packet delay of the high priority tra ffic and the low priority traffic. From these, some performance measures (such as the mean value) will be derived. These will be used to illustrate the significance of priority scheduling and the effect of non- preemptive scheduling on the high priority traffic. 1 Introduction In recent years, there has been much interest devoted to incorporating multi- media applications in IP networks. Different types of traffic need different QoS standards. For real-time applications, it is important that mean delay and delay- jitter are bounded, while for non real-time applications, the Loss Ratio (LR) is the restrictive quantity. In general, one can distinguish two priority strategies, which will be referred to as Time Priority and Space Priority. Time priority schemes attempt to guar- antee acceptable delay boundaries to delay-sensitive traffic (such as voice/video). This is achieved by giving it HOL priority over non-delay-sensitive traffic, and/or by sharing access to the server among the various traffic classes in such a way so that each can meet its own specific delay requirements. Several types of Time priority (or scheduling) s chemes (such as Weighted-Round-Robin (WRR), Weighted-Fair-Queueing(WFQ)) have been proposed and analyzed, each with their own specific algorithmic and computational complexity (see e.g. [6] and the references therein). On the other hand, Space Priority schemes attempt to minimize the packet loss of loss-sensitive traffic (such as data). Again, vari- ous types of Space Priority (or discarding) strategies (such as Push-Out Buffer (POB), Partial Buffer Sharing (PBS)) have been presented in the literature (see G. Pujolle et al. (Eds.): NETWORKING 2000, LNCS 1815, pp. 433–445, 2000. c  Springer-Verlag Berlin Heidelberg 2000