We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated services, and streaming media playback delays. We also present mechanisms and architecture for scalable support of guaranteed services in the Internet, based on the concept of a stateless core. Methods for scalable control operations are also briefly discussed. We then turn our attention to statistical performance guarantees, and describe several new probabilistic results that can be used for a statistical dimensioning of differentiated services. Lastly, we review recent proposals and results in supporting performance guarantees in a best effort context. These include models for elastic throughput guarantees based on TCP performance modeling, techniques for some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support.

Abstract. Part II continues the development of policy synthesis techniques for multiclass queueing networks based upon a linear fluid model. The following are shown: (i) A relaxation of the fluid model based on workload leads to an optimization problem of lower dimension. An analogous workload-relaxation is introduced for the stochastic model. These relaxed control problems admit pointwise optimal solutions in many instances. (ii) A translation to the original fluid model is almost optimal, with vanishing relative error as the networkload ρ approaches one. It is pointwise optimal after a short transient period, provided a pointwise optimal solution exists for the relaxed control problem. (iii) A translation of the optimal policy for the fluid model provides a policy for the stochastic networkmodel that is almost optimal in heavy traffic, over all solutions to the relaxed stochastic model, again with vanishing relative error. The regret is of order | log(1 − ρ)|.

We present a statistical network calculus in a setting where both arrivals and service are specified interms of probabilistic bounds. We provide explicit bounds on delay, backlog, and output burstiness in a network. By formulating well-known effective bandwidth expressions in terms of envelope functions,we are able to apply our calculus to a wide range of traffic source models, including Fractional Brownian Motion. We present probabilistic lower bounds on the service for three scheduling algorithms: Static Priority (SP), Earliest Deadline First (EDF), and Generalized Processor Sharing (GPS).

We consider stochastic guarantees for networks with aggregate scheduling, in particular, Expedited Forwarding (EF). Our approach is based on the assumption that a node can be abstracted by a service curve, and the input flows are regulated individually at the network ingress. Both of these assumptions are inline with EF [1], [2]. For a service curve node, we derive bounds on the complementary distributions of the steady-state backlog and backlog as seen by packet arrivals. We also give a bound on the long-run loss ratio for a service curve node where the buffer size is too small to guarantee loss-free operation. For a Packet Scale Rate Guarantee node [3], [1], we use the delay from backlog bound to obtain a probabilistic bound on the delay. Our analysis is exact under the given assumptions. Our results should help us to understand the performance of networks with aggregate scheduling, and provide the basis for dimensioning such networks. Keywords--- Expedited Forwarding, Differentiated Services, Aggregate Scheduling, Statistical Multiplexing, Stochastic QoS, Service Curve, Packet Scale Rate Guarantee, Queueing, Loss Ratio, Network Calculus I.

The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by O (H log H), where H is the number of nodes traversed by a flow. Using currently available techniques that compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by O(H³).

We consider the problem of bounding the probability of buffer overflow in a network node fed with independent arrival processes that are each constrained by arrival curves, but that are served as an aggregate. Existing results (for example [1] and [2]) assume that the node is a constant rate server. However, in practice, one finds complex network nodes that do not provide a constant service rate, and thus to which the existing bounds do not apply. Now many nodes can be adequately abstracted by a service curve property. We extend the results in [1] and [2] to such cases. As a by-product, we also provide a slight improvement to the bound in [2]. Our bounds are valid for both discrete and continuous time models. Index Terms---Statistical multiplexing, scheduling, queuing analysis I.

Scalability concerns of QoS implementations have stipulated service architectures where QoS is not provisioned separately to each flow, but instead to aggregates of flows. This paper determines stochastic bounds for the service experienced by a single flow when resources are managed for aggregates of flows and when the scheduling algorithms used in the network are not known. Using a recently developed statistical network calculus, per-flow bounds can be calculated for backlog, delay, and the burstiness of output traffic.

While utilization bound based schedulability test is simple and effective, it is often difficult to derive the bound itself. For its analytical complexity, utilization bound results are usually obtained on a case-by-case basis. In this paper, we develop a general framework that allows one to effectively derive schedulability bounds for a wide range of real-time systems with different workload patterns and schedulers. Our analytical model is capable of describing a wide range of tasks and schedulers ’ behaviors. We propose a new definition of utilization, called workload rate. While similar to utilization, workload rate enables flexible representation of different scheduling and workload scenarios and leads to uniform derivation of schedulability bounds. We derive a parameterized schedulability bound for static priority schedulers with arbitrary priority assignment. Existing utilization bounds for different priority assignments and task releasing patterns can be derived from our closed-form formula by simple assignments of proper parameters. 1.

The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that end-to-end performance measures computed with a network service curve are bounded by @ �� � A, where is the number of nodes traversed by a flow. Using currently available techniques, which compute end-to-end bounds by adding single node results, the corresponding performance measures are bounded by Q A.

Recently, a mathematical framework has been developed for the provision of deterministic quality of service guarantees in integrated services networks. This framework, or so-called "network calculus," involves the concepts of traffic envelopes, service curves, and convolution in the min-plus alegebra. Traffic envelopes constrain arrival processes, while service curves constrain the input-output behavior of network elements. Upper bounds on network delay are implied by the distance between a traffic envelope and service curve. In this paper, we develop a somewhat parallel framework for the provision of deterministic quality of service guarantees to adaptive applications. Adaptive applications generate a traffic load that is dependent on network utilization, and thus characterizing the traffic generated from an adaptive application with an envelope is problematic. We introduce an adaptive service definition, through which upper bounds on network delay can be derived without using a traff...