An integrated heuristic for best effort scheduling of (m,k)-firm streams in point-to-point networks

In point-to-point networks, real-time services are supported by sending real-time streams over guaranteed or best-effort channels [1]. A stream consists of packets moving across individual links on the point-topoint network from a given source to destination. For each link, a scheduler is responsible for determining which packets shall be transmitted according the queue of packets stored. For streams that can allow the occasional dropped packets, a (m,k)-firm guarantee may be used that states that for every k packets, the delay requirements of at least m packets have to be satisfied. When a stream fails to meet this (m,k)-firm guarantee, a condition known as dynamic end-to-end failure occurs, thus vastly reducing the usability of the data. For real-time scheduling, the use of schemes such as Earliest Deadline First (EDF) and Least Laxity First (LLF) do not provide adequate support for the (m,k)firm guarantee method. For scheduling (m,k)-firm streams, best-effort schemes [3, 4] have been proposed in the literature with the objective of minimizing the dynamic failure. Initially in [3], Hamadaoui and Ramanathan proposed a scheduling policy named DBP (Distance Based Priority) which introduced the notion of an (m,k) state diagram to the scheduling scheme. In short, an (m,k) stream was given a priority based on its distance from failing, in terms of the number of transitions necessary to reach a failing state. The lower the distance from a failing state, the higher the priority. However, this initial DBP algorithm dealt with only single hop connections. To improve upon this, Lindsay and Ramanathan in [4] proposed DBP-M, a method for implementing DBP across point-to-point networks. DBP-M directly confronts the problem proposed by point-to-point networks by having packets transmitted onward until they have missed their overall deadline. Thus, although a packet may miss its local deadline, it may still have a chance of meeting its overall deadline across the pointto-point network. DBP and DBP-M assume a per flow queue at every node along the path of connections. This poses many problems when the number of connections increases, a large overhead is introduced to the scheduler and processor requirements can greatly increase. Suppose a given link has N streams flowing across it but only M queues available. If M >= N, DBP-M is applicable. Otherwise, if N > M, streams must be multiplexed onto queues thus undermining the primary assumption in DBP & DBP-M that each queue has a specific DBP state. This drawback is the principal motivation for this paper; in it, an integrated heuristic is proposed which will allow multiplexing of streams into queues.