Head-of-the-Line priority with Random Assignment Mohamed Salah Aguir * , G´ erard H´ ebuterne † , Yves Dallery ‡ July 13, 2004 Abstract The well known Head-of-the-Line mechanism can lead to overprovisioning , as the con- straint brought by one of the flows imposes the server speed, while the other flows would require a lower level of resources. We propose and analyse a mechanism, which added to the basic HoL, allows an optimal usage of the server capacity. We derive the conditions under which the optimal behavior can be reached, and we discuss several aspects of the dimensioning. Keywords: Priority, Head of the Line, Optimization. 1 Introduction In multiservices networks, the Quality of Service (QoS) offered to the various applications is de- scribed in terms of loss, delay, reliability, etc. Fulfilling each criterion relies on specific mechanisms, and a goal of traffic engineering is to provision resources so as to provide the QoS level optimally (in terms of resource usage). In this paper, we focus on delay constraints (either the absolute delay or its variation – the so-called jitter). Various priority queueing mechanisms have been proposed, and we restrict the analysis here on the classical Head of the Line (HoL) discipline, assuming the non preemptive version of HoL. However, HoL leads most of the time to a non-optimal use of the resource, as discussed in Section 2. This is related to the fact that the delay constraints of all the services cannot be simultaneously fulfilled: the most severe one serves as the dimensioning criterion, and all the other ones are provided a better QoS level. This observation holds for numerous applications of the HoL mechanism. The present paper is devoted to the multiplexing of several flows in a packet network (the analysis is restricted to n = 2 flows, although the extension to larger values would be possible following exactly the same arguments). Note that another application has been studied, which concerns the dimensioning of a call center serving customers with different priorities (see ref. [1]). The observation leads to introducing a mechanism, termed HoL with Random Assignment, which allows, under certain conditions, an optimal use of the bandwidth resource. * Ecole Centrale de Paris, salah@lgi.ecp.fr † Institut National des T´ el´ ecommunications, gerard.hebuterne@int-evry.fr ‡ Ecole Centrale de Paris, dallery@lgi.ecp.fr P11/1