To maximize the energy efficiency of packet networks, energy use in network equipment should scale rigorously with the traffic load. Rate adaptation is gaining popularity as a promising framework for achieving energy proportionality in the data-path components of routers and switches, but a thorough characterization of its energy-saving capabilities and impact on network performance is still lacking. In this paper, we present novel rate-adaptation schemes that are easy to implement, amenable to incremental deployment in packet switches and routers, and whose negative effect on end-to-end packet delays is bounded. We derive tight lower and upper bounds on energy consumption that we use to further refine the design of our schemes. Our analysis indicates that large-scale deployments of rate adaptation can enable substantial energy savings, as large gains can be attained in individual data-path devices under parametric configurations that do not compromise the end-to-end delay performance of the network.

Input-queued switches are used extensively in the design of high-speed routers. As switch speeds and sizes increase, the design of the switch scheduler becomes a primary challenge, because the time interval for the matching computations needed for determining switch configurations becomes very small. Possible alternatives in scheduler design include increasing the scheduling interval by using envelopes , and using a frame-based scheduler that guarantees fixed rates between input-output pairs. However, both these alternatives have significant jitter drawbacks: the jitter increases with the envelope size in the first alternative, and previously-known methods do not guarantee tight jitter bounds in the second. In this paper, we propose a hybrid approach to switch scheduling. Traffic with tight jitter constraints is first scheduled using a frame-based scheduler that achieves low jitter bounds. Jitter-insensitive traffic is later scheduled using an envelope-based scheduler. The main contribution of this paper is a scheduler design for generating low-jitter schedules. The scheduler uses a rate matrix decomposition designed for low jitter and different from the minimum-bandwidth Birkhoff-Von Neumann (BV) decomposition. In addition to generating low-jitter schedules, this decomposition in the worst case yields fewer switch configuration matrices (O(n)) than the BV decomposition (O(n/sup 2/)), and so requires far less high-speed switch memory. We develop an efficient algorithm for decomposing the rate matrix and for scheduling the permutation matrices. We prove that our low-jitter algorithm has an O(logn) factor bound on its bandwidth consumption in comparison to the minimum-bandwidth BV decomposition. Experimentally, we find that the bandwidth increase in practice is much lower than the theoretical bound. We also prove several related performance bounds for our scheduler. Finally, we propose a practical algorithm for bandwidth-guaranteed algorithm, and show how our findings could even be extended to systems with large tuning time.

Input-queued switches are used extensively in the design of high-speed routers. As switch speeds and sizes increase, the design of the switch scheduler becomes a primary challenge, because the time interval for the matching computations needed for determining switch configurations becomes very small. Possible alternatives in scheduler design include increasing the scheduling interval by using envelopes, and using a frame-based scheduler that guarantees fixed rates between input-output pairs. However, both these alternatives have significant jitter drawbacks: the jitter increases with the envelope size in the first alternative, and previously-known methods do not guarantee tight jitter bounds in the second. In this paper, we propose a hybrid approach to switch scheduling. Traffic with tight jitter constraints is first scheduled using a frame-based scheduler that achieves low jitter bounds. Jitter-insensitive traffic is later scheduled using an envelope-based scheduler. The main contribution of this paper is a scheduler design for generating low-jitter schedules. The scheduler uses a rate matrix decomposition designed for low jitter and different from the minimum-bandwidth Birkhoff-Von Neumann (BV) decomposition. In addition to generating low-jitter schedules, this decomposition yields fewer switch configuration matrices (O(n)) than the BV decomposition (O(n/sup 2/)), and so uses far less high-speed switch memory. We develop an efficient algorithm for decomposing the rate matrix and for scheduling the permutation matrices. We prove that our low-jitter algorithm has an O(log n) factor bound on its bandwidth consumption in comparison to the minimum-bandwidth BV decomposition. Experimentally, we find that the bandwidth increase in practice is much lower than the theoretical bound. We also prove several related performance bounds for our scheduler. Finally, we propose a practical bandwidth-guaranteed algorithm, and show how our findings could even be extended to systems with large tuning time.

Utilizing optical technologies to build packet fabrics for high-capacity switches and routers has several advantages in terms of scalability, power consumption, and cost. However, several technology related problems have to be overcome to be able to use such an approach. The reconfiguration times of optical crossbars are longer than those of electronic fabrics and end-to-end clock recovery in such systems add to the reconfiguration overheads. Both these problems can limit the efficiency of optical packet fabrics. In addition, existing work on input-buffered switches mostly assumes fixed size packets (referred as envelopes in this paper). When fixed size switching is used for Internet protocol networks where packets are of variable size, the incoming packets need to be fragmented to fit the fixed size envelopes. This fragmentation can lead to, possibly large loss of bandwidth and even instability. This paper addresses all of the above issues by presenting packetization and scheduling techniques that allow optical packet fabrics to be used within switches and routers. The proposed scheme aggregates multiple packets in a single envelope and when used in combination with proper scheduling algorithms, it can provide system stability as well as bandwidth and delay guarantees. As a result of the aggregation method, the reconfiguration frequency required from the optics is reduced, facilitating the use of optical technologies in implementing packet switch fabrics.

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.

Internet applications and users have very diverse service expectations, making the current same-service-to-all model inadequate and limiting. In the relative differentiated services approach, the network traffic is grouped in a small number of service classes which are ordered based on their packet forwarding quality, in terms of per-hop metrics for the queueing delays and packet losses. The users and applications, in this context, can adaptivelychoose the class that best meets their quality and pricing constraints, based on the assurance that higher classes will be better, or at least no worse, than lower classes. In this work, we propose the proportional differentiation model as a way to refine and quantify this basic premise of relative differentiated services. The proportional differentiation model aims to provide the network operator with the 'tuning knobs' for adjusting the quality spacing between classes, independent of the class loads; this cannot be achieved with other relative differentiation models, such as strict prioritization or capacity differentiation. We apply the proportional model on queueing-delay differentiation only, leaving the problem of coupled delay and loss differentiation for future work. We discuss the dynamics of the proportional delay differentiation model and state the conditions under which it is feasible. Then, we identify and evaluate (using simulations) two packet schedulers that approximate the proportional differentiation model in heavy-load conditions, even in short timescales. Finally, we demonstrate that such per-hop and class-based mechanisms can provide consistent end-to-end differentiation to individual flows from different classes, independently of the network path and flow characteristics.

No abstract available.

There has been much interest in using active queue management in routers in order to protect users from connections that are not very responsive to congestion notification. An Internet draft recommends schemes based on random early detection for achieving these goals, to the extent that it is possible, in a system without "per-flow" state. However, a "stateless" system with first-in/first-out (FIFO) queueing is very much handicapped in the degree to which flow isolation and fairness can be achieved. Starting with the observation that a "stateless" system is but one extreme in a spectrum of design choices and that per-flow queueing for a large number of flows is possible, we present active queue management mechanisms that are tailored to provide a high degree of isolation and fairness for TCP connections in a gigabit IP router using per-flow queueing. We show that IP flow state in a router can be bounded if the scheduling discipline used has finite memory, and we investigate the performance implications of different buffer management strategies in such a system. We show that merely using per-flow scheduling is not sufficient to achieve effective isolation and fairness, and it must be combined with appropriate buffer management strategies.

The objective of research in fair queueing schemes has been to efficiently emulate a fluid-flow generalized (weighted) processor sharing (GPS) system as closely as possible. A primary motivation for the use of fair queueing has been its use as a means of providing bandwidth guarantees and as a consequence end-to-end delay bounds for traffic with bounded burstiness. The rate guarantees translate to scheduling weights which are set when admission control is done. A consequence of fair queueing systems closely emulating GPS is that when one or more connections are not back-logged, any "excess" bandwidth is distributed to back-logged connections in proportion to their weights. However weights are set based on the long-term requirements of traffic flows and not in any state-dependent manner that reflects instantaneous needs. We question the notion that the queueing system should closely emulate a GPS system. Instead of emulating GPS, we propose three modified scheduling schemes which preserve the rate guarantees of fair queueing (and hence preserve deterministic delay bounds) but adaptively redistribute the excess bandwidth such that either losses are reduced or delays equalized. We compare the performance of the proposed schemes to that of fair queueing using different traffic sources such as voice and video, as well as sources which have aggregate long-range dependent behavior. We find that the proposed schemes, in comparison to packet GPS (PGPS), reduce packet losses and curtail the tails of delay distributions for real-time traffic and hence permit the use of significantly smaller playout buffers for the same network load.

In this paper, we investigate the extent to which fair queueing (and its variants), in conjunction with appropriately tailored buffer management schemes, can be used to achieve the following goals for TCP traffic: (1) alleviate the inherent unfairness of TCP towards connections with long round-trip times, (2) provide isolation when connections using different TCP versions share a bottleneck link (3) provide protection from TCP-unfriendly traffic sources (which might include TCP ACKs since they are not loss-responsive) and misbehaving users, (4) alleviate the effects of ACK compression in the presence of two-way traffic, (5) prevent users experiencing ACK loss (which causes their traffic to be bursty) from significantly affecting other connections, (6) provide low latency to interactive connections which share a bottleneck with "greedy" connections without reducing overall link utilization. The paper proposes new buffer management schemes to be used in conjunction with fair queueing, so as to achieve the above goals for TCP, and compares the performance of the proposed schemes to the performance obtained using random early detection (RED) for packet dropping.

The ability to provide differentiated services to users with widely varying requirements is becoming increasingly important, and Internet Service Providers would like to provide these differentiated services using the same shared network infrastructure. The key mechanism, that enables differentiation in a connectionless network, is the packet classification function that parses the headers of the packets, and after determining their context, classifies them based on administrative policies or real-time reservation decisions. Packet classification, however, is a complex operation that can become the bottleneck in routers that try to support gigabit link capacities. Hence, many proposals for differentiated services only require classification at lower speed edge routers and also avoid classification based on multiple fields in the packet header even if it might be advantageous to service providers. In this paper, we present new packet classification schemes that, with a worst-case and trafficindependent performance metric, can classify packets, by checking amongst a few thousand filtering rules, at rates of a million packets per second using range matches on more than 4 packet header fields. For a special case of classification in two dimensions, we present an algorithm that can handle more than 128K rules at these speeds in a traffic independent manner. We emphasize worst-case performance over average case performance because providing differentiated services requires intelligent queueing and scheduling of packets that precludes any significant queueing before the differentiating step (i.e., before packet classification). The presented filtering or classification schemes can be used to classify packets for security policy enforcement, applying resource management decisions, flow identification for RSVP reservations, multicast look-ups, and for source-destination and policy based routing. The scalability and performance of the algorithms have been demonstrated by implementation and testing in a prototype system. 1

Generalized processor sharing (GPS) has been considered as an ideal scheduling discipline based on its end-to-end delay bounds and fairness properties. Until recently, emulation of GPS in a packet server has been regarded as the ideal means of designing a packet-level scheduling algorithm to obtain low delay bounds and bounded unfairness. Strict emulation of GPS, as required in the weighted fair queueing (WFQ) scheduler, however, incurs a time-complexity of O(N) where N is the number of sessions sharing the link. Efforts in the past to simplify the implementation of WFQ, such as self-clocked fair queueing (SCFQ), have resulted in degrading its isolation properties, thus affecting the delay bound. We present a methodology for the design of scheduling algorithms that provide the same end-to-end delay bound as that of WFQ and bounded unfairness without the complexity of GPS emulation. The resulting class of algorithms, called rate-proportional servers (RPSs), are based on isolating scheduler properties that give rise to ideal delay and fairness behavior. Network designers can use this methodology to construct efficient fair-queueing algorithms, balancing their fairness with implementation complexity.

Although weighted fair queueing (WFQ) has been regarded as an ideal scheduling algorithm in terms of its combined delay bound and proportional fairness properties, its asymptotic time complexity increases linearly with the number of sessions serviced by the scheduler, thus limiting its use in high-speed networks. An algorithm that combines the delay and fairness bounds of WFQ with O(1) timestamp computations had remained elusive so far. In this paper we present two novel scheduling algorithms that have O(1) complexity for timestamp computations and provide the same bounds on end-to-end delay and buffer requirements as those of WFQ. The first algorithm, frame-based fair queueing (FFQ), uses a framing mechanism to periodically recalibrate a global variable tracking the progress of work in the system, limiting any short-term unfairness to within a frame period. The second algorithm, starting potential based fair queueing (SPFQ), performs the recalibration at packet boundaries, resulting in improved fairness while still maintaining the O(1) timestamp computations. Both algorithms are based on the general framework of rate-proportional servers (RPSs) introduced by Stiliadis and Varma (see ibid., vol.6, no.2, p.164-74, 1998). The algorithms may be used in both general packet networks with variable packet sizes and in asynchronous transfer mode (ATM) networks.

We develop a general model, called latency-rate servers (/spl Lscr//spl Rscr/ servers), for the analysis of traffic scheduling algorithms in broadband packet networks. The behavior of an /spl Lscr//spl Rscr/ server is determined by two parameters-the latency and the allocated rate. Several well-known scheduling algorithms, such as weighted fair queueing, virtualclock, self-clocked fair queueing, weighted round robin, and deficit round robin, belong to the class of /spl Lscr//spl Rscr/ servers. We derive tight upper bounds on the end-to-end delay, internal burstiness, and buffer requirements of individual sessions in an arbitrary network of /spl Lscr//spl Rscr/ servers in terms of the latencies of the individual schedulers in the network, when the session traffic is shaped by a token bucket. The theory of /spl Lscr//spl Rscr/ servers enables computation of tight upper bounds on end-to-end delay and buffer requirements in a heterogeneous network, where individual servers may support different scheduling architectures and under different traffic models.

We introduce a general methodology for designing integrated shaping and scheduling algorithms for packet networks that provide fairness, low end-to-end delay, and low burstiness. The methodology is based on integrating a shaping mechanism with a scheduler from the class of rate-proportional servers (RPS) defined by Stiliadis and Varma (see Proceedings of ACM SIGMETRICS '96, p.104-15, 1996). The resulting algorithms provide an end-to-end delay bound identical to that of weighted fair queueing. Their worst-case fairness, in terms of minimizing the worst-case delay to empty the session backlog, is much superior to that of weighted fair queueing, and equal to the best known for any scheduling algorithm. In addition, the algorithms achieve a level of fairness in the distribution of free bandwidth among competing sessions better than that of weighted fair queueing. We show that, under this framework, even an unfair scheduling algorithm belonging to the RPS class, such as VirtualClock, can yield worst-case fairness identical to that obtained with weighted fair queueing. We also develop an integrated shaper-scheduler that provides optimal output burstiness and is attractive for use in both network adapters and in switches that support traffic re-shaping. We describe an efficient implementation of this integrated shaping and scheduling algorithm with log/sub 2/(V) complexity, where V is the number of sessions sharing the outgoing link.

Although direct-mapped caches suffer from higher miss ratios as compared to set-associative caches, they are attractive for today's high-speed pipelined processors that require very low access times. Victim caching was proposed by Jouppi (1990) as an approach to improve the miss rate of direct-mapped caches without affecting their access time. This approach augments the direct-mapped main cache with a small fully associate cache, called victim cache, that stores cache blocks evicted from the main cache as a result of replacements. We propose and evaluate an improvement of this scheme, called selective victim caching. In this scheme, incoming blocks into the first-level cache are placed selectively in the main cache or a small victim cache by the use of a prediction scheme based on their past history of use. In addition, interchanges of blocks between the main cache and the victim cache are also performed selectively. We show that the scheme results in significant improvements in miss rate as well as the average memory access time, for both small and large caches (4 Kbytes-128 Kbytes). For example, simulations with ten instruction traces from the SPEC '92 benchmark suite showed an average improvement of approximately 21 percent in miss rate over simple victim caching for a 16-Kbyte cache with a block size of 32 bytes; the number of blocks interchanged between the main and victim caches reduced by approximately 70 percent. Implementation alternatives for the scheme in an on-chip processor cache are also described.

In this paper, we develop a general model, called latency-rate servers (LR-servers), for the analysis of traffic scheduling algorithms in broadband packet networks. The behavior of an LR scheduler is determined by two parameters-the latency and the allocated rate. We show that several well-known scheduling algorithms, such as weighted fair queueing, virtualclock, self-clocked fair queueing, weighted round robin, and deficit round robin, belong to the class of LR-servers. We derive tight upper bounds on the end-to-end delay, internal burstiness, and buffer requirements of individual sessions in an arbitrary network of LR-servers in terms of the latencies of the individual schedulers in the network, when the session traffic is shaped by a leaky bucket. Thus, the theory of LR-servers enables computation of tight upper-bounds on end-to-end delay and buffer requirements in a network of servers in which the servers on a path may not all use the same scheduling algorithm. We also define a self-contained approach to evaluate the fairness of LR-servers and use it to compare the fairness of many well-known scheduling algorithms.

In this paper we introduce and analyze frame-based fair queueing, a novel traffic scheduling algorithm for packet-switched networks. The algorithm provides end-to-end delay bounds identical to those of PGPS (packet-level generalized processor sharing), without the complexity of simulating the fluid-model system in the background as required in PGPS. The algorithm is therefore ideally suited for implementation in packet switches supporting a large number of sessions. We present a simple implementation of the algorithm for a general packet switch. In addition, we prove that the algorithm is fair in the sense that sessions are not penalized for excess bandwidth they received while other sessions were idle. Frame-based fair queueing belongs to a general class of scheduling algorithms, which we call Rate-Proportional Servers. This class of algorithms provides the same end-to-end delay and burstiness bounds as PGPS, but allows more flexibility in the design and implementation of the algorithm. We provide a systematic analysis of this class of schedulers and obtain bounds on their fairness.