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.

We examine a proportional-delay model for Internet differentiated services. Under this model, an ISP can control the waiting time "spacings" between di erent classes of traffic. Specifically, the ISP tries to ensure that the average waiting time of class i traffic relative to that of class i 1 traffic is kept at a constant specified ratio. If the waiting time ratio of class i 1 to class i is greater than one, the ISP can legitimately charge users of class i traffic a higher tariff rate (compared to the rate for class i 1 traffic), since class i users consistently enjoy better performance than class i 1 users. To realize such proportional delay differentiated services, we use the time-dependent priority scheduling algorithm. We formally characterize the feasible regions in which given delay ratios can be achieved. Moreover, a set of control parameters for obtaining the desired delay ratios can be determined by an efficient iterative algorithm. We also use an adaptive control algorithm to maintain the correctness of these parameters in response to changing system load. Experiments are carried out to illustrate the short-term, medium-term and long-term relative waiting time performances for different service classes under Poisson, Pareto, MMPP and mixed traffic workloads. We also carry out experiments to evaluate the achieved end-to-end accumulative waiting times for different classes of traffic which traverse multiple hops under our service model.

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 this context is that users with absolute QoS requirements should dynamically search for an appropriate class. We investigate this Dynamic Class Selection (DCS) framework, and illustrate that, under certain conditions, DCS-capable users can meet absolute QoS requirements, even though the network only offers relative differentiation. For a single link model, we can examine whether it is feasible to satisfy all users, and when this is the case, compute 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 DCS equilibria may also exist. Simulations of a delay-based DCS algorithm show the relation between class differentiation and DCS, and demonstrate how to control the trade-off between the performance and cost of a flow.

ii Acknowledgements iv Acronyms xiii 1

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.

Recent results on the proportional differentiation model show that waiting time priority scheduling can be applied to implement proportional delay differentiatied services reasonably well under limited conditions. While earlier research focused on heavy load conditions only, more recent results provide insights into waiting time priority scheduling under moderate load conditions also, but the applicability of the algorithm has been limited to a two-service-class solution for numerical reasons. In this paper, in contrast, a dynamic adjustment of a waiting time priority scheduler is suggested to meet the differentiation requirements for any finite number of traffic classes. Our newly introduced approach is based on genetic algorithms. The dynamically optimized scheduling parameters can be determined with high accuracy. We apply an interpolation function to yield a continuum of parameters rather than discrete values and propose a simple look-up table for a dynamic adjustment of the scheduling parameters. We also focus on feasibility and implementation issues related to the suggested algorithm. Suitability of other time-dependent priority functions for proportional delay differentiation is also investigated.

Class-based service differentiation can be realized without resource reservation, admission control and traffic policing. However, the resulting service guarantees are only relative, in the sense that guarantees given to a flow class at any time are expressed with reference to the service given to other flow classes. While it is, in principle, not feasible to provision for absolute guarantees (i.e., to assure lower bounds on service metrics at all times) without admission control and/or traffic policing, we will show in this paper that such a service can be reasonably well emulated using adaptive rate allocation and dropping mechanisms at the link schedulers of routers. We name the resulting type of guarantees best-effort bounds. We propose mechanisms for link schedulers of routers that achieve these and other guarantees by adjusting the drop rates and the service rate allocations of traffic classes to current load conditions.

Abstract — The DiffServ architecture provides a scalable mechanism for QoS introduction in a TCP/IP network. The idea of DiffServ is based on the aggregation of traffic flows at an ingress (or egress) point of a network and the IP packet marking for different priority flows, according to several classification criteria. Two approaches exist in the DiffServ architecture: the absolute and the relative. In absolute DiffServ, an admission control scheme is used to provide QoS guarantees as absolute bounds of specific QoS parameters. The relative DiffServ model provides QoS guarantees per class expressed with reference to guarantees given to the other classes defined. Our study targets at providing relative proportional delay differentiation service based on Class Based Queue (CBQ) scheduler. The main idea is to frequently adjust the service rates allocated to classes of a CBQ scheduler in order to achieve relative delay spacing among classes. The simulation experiments conducted show that our model can attain relative delay, provided that the required Delay Differentiation Parameters (DDPs) are feasible.