We consider the definition of the expedited forwarding per-hop behavior (EF PHB) as given in RFC 2598 and its impact on worst case end-to-end delay jitter. On the one hand, the definition in RFC 2598 can be used to predict extremely low end-to-end delay jitter, independent of the network scale. On the other hand, the worst case delay jitter can be made arbitrarily large, while each flow traverses at most a specified number of hops, if we allow networks to become arbitrarily large; this is in contradiction with the previous statement. We analyze where the contradiction originates and find the explanation. It resides in the fact that the definition in RFC 2598 is not easily implementable in known schedulers, mainly because it is not formal enough and also because it does not contain an error term. We propose a new definition for the EF PHB, called "packet scale rate guarantee" (PSRG) that preserves the spirit of RFC 2598 while allowing a number of reasonable implementations and has very useful properties for per-node and end-to-end network engineering. We show that this definition implies a rate-latency service curve property. We also show that it is equivalent, in some sense, to the stronger concept of "adaptive service guarantee". Then we propose some proven bounds on delay jitter for networks implementing this new definition in cases without loss and with loss.

We consider the definition of the expedited forwarding per-hop behaviour (EF PHB) as given in RFC 2598 (Jacobsen et al. 1999), and its impact on worst case end-to-end delay jitter. On one hand, the definition in RFC 2598 can be used to predict extremely low end-to-end delay jitter, independent of the network scale. On the other hand, we find that the worst case delay jitter can be made arbitrarily large, while each flow traverses at most a specified number of hops, if we allow networks to become arbitrarily large; this is in contradiction with the previous statement. We analyze where the contradiction originates, and find the explanation. It resides in the fact that the definition in RFC 2598 is not easily implementable in schedulers we know of, mainly because it is not formal enough, and also because it does not contain an error term. We propose a new definition for the EF PHB, called "packet scale rate guarantee", which preserves the spirit of RFC 2598, while allowing a number of reasonable implementations, and has very useful properties for per-node and end-to-end network engineering. We show that this definition implies the rate-latency service curve guarantee. Then we propose some proven bounds on delay jitter for networks implementing this new definition, both in cases without loss and with loss.

The fluid generalized processor sharing (GPS) algorithm has desirable properties for integrated services networks and many packet fair queueing (PFQ) algorithms have been proposed to approximate GPS. However, there have been few high-speed implementations of PFQ algorithms that can support a large number of sessions with diverse rate requirements and at the same time maintain all the important properties of GPS. The implementation cost of a PFQ algorithm is determined by: (1) computation of the system virtual time function; (2) maintenance of the relative ordering of the packets via their timestamps (scheduling); and (3) regulation of packets based on eligibility time, in some algorithms. While most of the recently proposed PFQ algorithms reduce the complexity of computing the system virtual time function, the complexity of scheduling and traffic regulation is still a function of the number of active sessions. In addition, while reducing the algorithmic or asymptotic complexity has been the focus of most analysis, it is also important to reduce the complexity of basic operations in order for the algorithm to run at high speed. We develop techniques to reduce both types of complexities for networks of both fixed and variable size packets. Regulation and scheduling are implemented in an integrated architecture that can be viewed as logically performing sorting in two dimensions simultaneously. By using a novel grouping architecture, we are able to perform this with an algorithmic complexity independent of the number of sessions in the system at the cost of a small controllable amount of relative error. To reduce the cost of basic operations, we propose a hardware-implementation framework and several novel techniques that reduce the on-chip memory size, off-chip memory bandwidth, and off-chip access latency. The proposed implementation techniques have been incorporated into commercial ATM switch and IP router products.

It is a widely held belief that packet reordering in the Internet is a pathological behavior, or more precisely, that it is an uncommon behavior caused by incorrect or malfunctioning network components. Some studies of Internet traffic have reported seeing occasional packet reordering events and ascribed these events to "route fluttering", router "pauses" or simply to broken equipment. We have found, however, that parallelism in Internet components and links is causing packet reordering under normal operation and that the incidence of packet reordering appears to be substantially higher than previously reported. More importantly, we observe that in the presence of massive packet reordering transmission control protocol (TCP) performance can be profoundly effected. Perhaps the most disturbing observation about TCP's behavior is that large scale and largely random reordering on the part of the network can lead to self-reinforcingly poor performance from TCP.

The fluid generalized processor sharing (GPS) algorithm has desirable properties for integrated services networks and many packet fair queueing (PFQ) algorithms have been proposed to approximate GPS. However, there have been few high speed implementations of PFQ algorithms that can support large number of sessions with diverse rate requirements and at the same time maintain all the important properties of GPS. The implementation cost of a PFQ algorithm is determined by two components: (1) computation of the system virtual time function and (2) maintaining the relative ordering of the packets via their timestamps in a priority queue mechanism. While most of the recently proposed PFQ algorithms reduce the complexity of computing the system virtual time function, the complexity of maintaining the priority queue, and therefore the overall complexity of implementing PFQ, is still a function of the number of active sessions. In addition, while reducing the algorithmic or asymptotic complexity has been the focus of most analysis, to run at high speed, it is also important to reduce the complexity of basic operations. In this paper, we develop techniques to reduce both types of complexities. In particular, we present a novel grouping architecture for implementing PFQ with an algorithmic complexity that is a function of the number of distinct rates supported, but independent of the number of sessions in the system.

We propose to use the idealized hierarchical generalized processor sharing (H-GPS) model to simultaneously support guaranteed real-time, rate-adaptive best-effort, and controlled link-sharing services. We design hierarchical packet fair queueing (H-PFQ) algorithms to approximate H-GPS by using one-level variable-rate PFQ servers as basic building blocks. By computing the system virtual time and per packet virtual start/finish times in unit of bits instead of seconds, most of the PFQ algorithms in the literature can be properly defined as variable-rate servers. We develop techniques to analyze delay and fairness properties of variable-rate and hierarchical PFQ servers. We demonstrate that in order to provide tight delay bounds with an H-PFQ server, it is essential for the one-level PFQ servers to have small worst-case fair indices (WFI). We propose a new PFQ algorithm called WF/sup 2/Q+ that is the first to have all the following three properties: (1) providing the tightest delay bound among all PFQ algorithms; (2) having the smallest WFI among all PFQ algorithms; and (3) having a relatively low asymptotic complexity of O(log N). Simulation results are presented to evaluate the delay and link-sharing properties of H-WF/sup 2/Q+, H-WFQ, H-SFQ, and H-SCFQ.

The generalized processor sharing (GPS) discipline is proven to have two desirable properties: (a) it can provide an end-to-end bounded-delay service to a session whose traffic is constrained by a leaky bucket; (b) it can ensure fair allocation of bandwidth among all back logged sessions regardless of whether or not their traffic is constrained. The former property is the basis for supporting guaranteed service traffic while the later property is important for supporting best-effort service traffic. Since GPS uses an idealized fluid model which cannot be realized in the real world, various packet approximation algorithms of the GPS have been proposed. Among these, weighted fair queueing (WFQ) also known as packet generalized processor sharing (PGPS) has been considered to be the best one in terms of accuracy. In particular, it has been proven that the delay bound provided by WFQ is within one packet transmission time of that provided by GPS. We show that, contrary to popular belief there could be large discrepancies between the services provided by the packet WFQ system and the fluid GPS system. We argue that such a discrepancy will adversely effect many congestion control algorithms that rely on services similar to those provided by GPS. A new packet approximation algorithm of GPS called worst-case fair weighted fair queueing (WF/sup 2/Q) is proposed. The service provided by WF/sup 2/Q is almost identical to that of GPS, differing no more than one maximum size packet.

Hierarchical Packet Fair Queueing (H-PFQ) algorithms have the potential to simultaneously support guaranteed real-time service, rate-adaptive best-effort, and controlled link-sharing service. In this paper, we design practical H-PFQ algorithms by using one-level Packet Fair Queueing (PFQ) servers as basic building blocks, and develop techniques to analyze delay and fairness properties of the resulted H-PFQ servers. We demonstrate that, in order to provide tight delay bounds in a H-PFQ server, it is essential for the one-level PFQ servers to have small Worst-case Fair Indices (WFI). We propose a new one-level PFQ algorithm called WF2Q+ that is the first to have all the following three properties: (a) providing the tightest delay bound among all PFQ algorithms; (b) having the smallest WFI among all PFQ algorithms; and (c) having a relatively low implementation complexity of O(log N). We show that practical H-PFQ algorithms can be implemented by using WF2Q+ as the basic building block and prove that the resulting H-WF2Q+ algorithms provide similar delay bounds and bandwidth distribution as those provided by a H-GPS server. Simulation experiments are presented to evaluate the proposed algorithm.