The proportional differentiation model provides the network operator with the `tuning knobs' for adjusting the per-hop quality-of-service (QoS) ratios between classes, independent of the class loads. This paper applies the proportional model in the differentiation of queueing delays, and investigates appropriate packet scheduling mechanisms. Starting from the proportional delay differentiation (PDD) model, we derive the average queueing delay in each class, show the dynamics of the class delays under the PDD constraints, and state the conditions in which the PDD model is feasible. The feasibility model of the model can be determined from the average delays that result with the strict priorities scheduler. We then focus on scheduling mechanisms that can implement the PDD model, when it is feasible to do so. The proportional average delay (PAD) scheduler meets the PDD constraints, when they are feasible, but it exhibits a pathological behavior in short timescales. The waiting time priority (WTP) scheduler, on the other hand, approximates the PDD model closely, even in the short timescales of a few packet departures, but only in heavy load conditions. PAD and WTP serve as motivation for the third scheduler, called hybrid proportional delay (HPD). HPD approximates the PDD model closely, when the model is feasible, independent of the class load distribution. Also, HPD provides predictable delay differentiation even in short timescales.

The proportional differentiation model was proposed in [1] as a target for controllable and predictable relative differentiated services. [1] considered only the delay differentiation aspect of the model, and focused on packet scheduling mechanisms. In this paper, we extend the proportional differentiation model in the direction of loss rate differentiation. Severalprevious mechanisms for buffer management and packet dropping, such as complete buffer partitioning, partial buffer sharing, or multiclass RED, are not suitable for relative differentiated services. We proposeand evaluate two dropping mechanisms that closely approximate the proportional loss rate differentiation model. The two droppers, PLR(1) and PLR(M), differ in the time interval over which the loss rates are measured and proportionally adjusted. This difference results in several trade-offs, in terms of implementation complexity, accuracy, and ability to deal with nonstationary traffic loads. We also re-evaluate the dela...

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The relative differentiation architecture does not require per-flow state at the network core or edges, nor admission control, but it can only provide higher classes with better service than lower classes. A central premise in the relative differentiation architecture is that users with an absolute QoS requirement can dynamically search for a class which provides the desired QoS level. In the first part of this paper, we investigate this Dynamic Class Selection (DCS) framework in the context of Proportional Delay Differentiation (PDD). We illustrate that, under certain conditions, DCS-capable users can meet absolute QoS requirements, even though the network only offers relative differentiation. For a simple link model, we give an algorithm that checks whether it is feasible to satisfy all users, and if this is the case, computes the minimum acceptable class selection for each user. Users converge in a distributed manner to this minimum acceptable class, if the DCS equilibrium is unique. However, suboptimal and even unacceptable DCS equilibria may also exist. Simulations of an end-to-end DCS algorithm provide further insight in the dynamic behavior of DCS, show the relation between DCS and the network Delay Differentiation Parameters, and demonstrate how to control the trade-off between a flow's performance and cost using DCS.

We consider the problem of link provisioning in a di#erentiated services network that o#ers N classes of service. At the provisioning phase, the network manager con#gures the link to support the requirements of M distinct tra#c types. Each tra#c type is speci#ed by an expected arrival rate and an average delay requirement. The objective of the provisioning phase is to jointly determine: the minimum link capacity needed to support the M given tra#c types, the nominal class of service for each tra#c type, and the appropriate resourceallocation between classes.