The main objective of this sequel is to solve the out-of-sequence problem that occurs in the load balanced Birkhoff-von Neumann switch with one-stage buffering. We do this by adding a load-balancing buffer in front of the first stage and a resequencing-and-output buffer after the second stage. Moreover, packets are distributed at the first stage according to their flows, instead of their arrival times in Part I. In this paper, we consider multicasting ows with two types of scheduling policies: the First Come First Served (FCFS) policy and the Earliest Deadline First (EDF) policy. The FCFS policy requires a jitter control mechanism in front of the second stage to ensure proper ordering of the traffic entering the second stage. For the EDF scheme, there is no need for jitter control. It uses the departure times of the corresponding FCFS output-buffered switch as deadlines and schedules packets according to their deadlines. For both policies, we show that the end-to-end delay through our multistage switch is bounded above by the sum of the delay from the corresponding FCFS output-buffered switch and a constant that only depends on the size of the switch and the number of multicasting flows supported by the switch.

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.

High performance packet switches frequently use a centralized scheduler (also known as an arbiter) to determine the configuration of a non-blocking crossbar. The scheduler often limits the scalability of the system because of the frequency and complexity of its decisions. A recent paper by C.-S. Chang et al. introduces an interesting two-stage switch, in which each stage uses a trivial deterministic sequence of configurations. The switch is simple to implement at high speed and has been proved to provide 100% throughput for a broad class of traffic. Furthermore, there is a bound between the average delay of the two-stage switch and that of an ideal output-queued switch. However, in its simplest form, the switch mis-sequences packets by an arbitrary amount. In this paper, building on the two-stage switch, we present an algorithm called Full Frames First (FFF), that prevents mis-sequencing while maintaining the performance benefits (in terms of throughput and delay) of the basic two-stage switch. FFF comes at some additional cost, which we evaluate in this paper.

Continuous-media traffic (i.e., audio and video) can tolerate some loss but has rigid delay constraints. A natural QoS requirement for a continuous-media connection is a prescribed limit on the fraction of traffic that exceeds an end-to-end delay constraint. We propose and analyze a framework that provides such a statistical QoS guarantee to traffic in a packet-switched network. Providing statistical guarantees in a network is a notoriously difficult problem because traffic flows lose their original statistical characterizations at the outputs of queues. Our scheme uses bufferless statistical multiplexing combined with cascaded leaky-buckets for smoothing and traffic contracting. This scheme along with a novel method for bounding the loss probability gives a tractable framework for providing end-to-end statistical QoS. Using MPE(] video traces, we present numerical resuits that compare the connection-carrying capacity of our scheme with that of guaranteed service schemes (i.e., no loss) using (]PS and RCS. Our numerical work indicates that our scheme can support significantly more connections without introducing significant traffic loss.

The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows. A drawback of the deterministic network calculus is that it only provides worst-case bounds. Here we present a network calculus for statistical service guarantees, which can exploit the statistical multiplexing gain of sources. We introduce the notion of an effective service curve as a probabilistic bound on the service received by an individual flw, and construct an effective service curve for a network where capacities are provisioned exclusively to aggregates of flows. Numerical examples demonstrate that the calculus is able to extract a significant amount of multiplexing gain in networks with a large number of flows.

We consider the problem of scheduling packets over a number of channels with time varying connectivity. Policies proposed for this problem either stabilize the system when the arrival rates are within the stability region, or optimize an objective function under the assumption that all channel queues are saturated. We address the realistic situation where it is not known apriori whether the channel queues are saturated or not, and provide a scheduling policy that maximizes the weighted sum of channel throughputs. We employ a burstiness-constrained channel model that allows us to dispense of statistical assumptions and simplifies the proofs.

We give a representation of the packet-level dynamical be- havior of the Reno and Tahoe variants of TCP over a sin- gle end-to-end connection. This representation allows one to consider the case when the connection involves a net- work made of several, possibly heterogeneous, deterministic or random routers in series. It is shown that the key features of the protocol and of the network can be expressed via a linear dynamical system in the so called max-plus algebra. This opens new ways of both analytical evaluation and fast simulation based on products of matrices in this algebra. This also leads to closed form formulas for the throughput allowed by TCP under natural assumptions on the behavior of the routers and on the detection of losses and timeouts; these new formulas are shown to refine those obtained from earlier models which either assume that the network could be reduced to a single bottleneck router and/or approximate the packets by a fluid.

A novel algorithm for buffer management and rate allocation is presented for providing loss and delay differentiation for traffic classes at a network router. The algorithm, called JoBS, provides delay and loss differentiation independently at each node, without assuming admission control or policing. Contrary to most existing algorithms, scheduling and buffer management decisions are performed in a single step. Both relative

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).

Providing quality of service (QoS) guarantees over wireless links requires thorough understanding and quantification of the interactions among the traffic source, the wireless channel, and the underlying link-layer error control mechanisms. In this paper, we account for such interactions in an analytical model that we use to investigate the delay distribution and the packet discard rate over a wireless link. In contrast to previous studies, our analysis accommodates the inherent autocorrelations in both the traffic source as well as the channel error characteristics. An on/off fluid process is used to model the arrival of packets at the transmitter. These packets are temporarily stored in a FIFO buffer before being transmitted over a channel with a time-varying and autocorrelated service rate. Using fluid analysis, we first derive the distribution for the queueing delay at the transmitter. As part of this analysis, we solve a fundamental fluid problem, namely, the probability distribut...