Efficient fair queueing algorithms for packet-switched networks

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     

提供端到端时延和时延抖动保障的QoS控制

 提出了一类具有最大速率控制的速率保障(Maximum Rate Control-Guaranteed Rate,MRC-GR)算法,可对流同时提供速率保障和最大速率控制.当网络各节点执行MRC-GR算法时,提供了确定网络端到端时延上限和下限的方法,针对服从令牌桶模型和同步单元模型的业务源给出了网络时延上限和下限.针对MRC-GR算法实例——具有最大速率控制的最差情形公平加权公平排队(worst-case fair weighted fair queueing with maximum rate control)调度算法进行仿真实验,仿真结果验证了理论分析.     

Rate-proportional servers: a design methodology for fair queueingalgorithms

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     

Solving the trade-off between fairness and throughput: Token bucket and leaky bucket-based weighted fair queueing schedulers

In this article, we present two efficient weighted fair queueing (WFQ) scheduling algorithms leaned on the well-known token bucket and leaky bucket shaping/policing algorithms. The performance of the presented algorithms is compared to those of the state-of-the-art WFQ approximations such as weighted round robin (WRR) and the recently proposed bin sort fair queueing (BSFQ). Our simulation results show that the proposed algorithms provide a better fairness at a lower implementation complexity while simultaneously achieving a comparable network utilization.     

Delay Analysis of All-Optical Packet-Switching Ring and Bus Communications Networks

We study the delay performance of all-optical packet communication networks configured as ring and bus topologies employing cross-connect switches (or wavelength routers). Under a cross-connect network implementation, a packet experiences no (or minimal) internal queueing delays. Thus, the network can be implemented by high speed all-optical components. We further assume a packet-switched network operation, such as that using a slotted ring or bus access methods. In this case, a packet's delay is known before it is fed into the network. This can be used to determine if a packet must be dropped (when its end-to-end delay requirement is not met) at the time it accesses the network. It also leads to better utilization of network capacity resources. We also derive the delay performance for networks under a store-and-forward network operation. We show these implementations to yield very close average end-to-end packet queueing delay performance. We note that a cross-connect network operation can yield a somewhat higher queueing delay variance levels. However, the mean queueing delay for all traffic flows are the same for a cross-connect network operation (under equal nodal traffic loading), while that in a store-and-forward network increases as the path length increases. For a ring network loaded by a uniform traffic matrix, the queueing delay incurred by 90% of the packets in a cross-connect network may be lower than that experienced in a store-and-forward network. We also study a store-and-forward network operation under a nodal round robin (fair queueing) scheduling policy. We show the variance performance of the packet queueing delay for such a network to be close to that exhibited by a cross-connect (all-optical) network.     

A Unified Architecture for the Design and Evaluation of Wireless Fair Queueing Algorithms

Fair queueing in the wireless domain poses significant challenges due to unique issues in the wireless channel such as location-dependent and bursty channel errors. In this paper, we present a wireless fair service model that captures the scheduling requirements of wireless scheduling algorithms, and present a unified wireless fair queueing architecture in which scheduling algorithms can be designed to achieve wireless fair service. We map seven recently proposed wireless fair scheduling algorithms to the unified architecture, and compare their properties through simulation and analysis. We conclude that some of these algorithms achieve the properties of wireless fair service including short-term and long-term fairness, short-term and long-term throughput bounds, and tight delay bounds for channel access.     

Fair scheduling with tunable latency: a round-robin approach

Weighted fair queueing (WFQ)-based packet scheduling schemes require processing at line speeds for tag computation and tag sorting. This requirement presents a bottleneck for their implementation at high transmission speeds. We propose an alternative and lower complexity approach to packet scheduling, based on modifications of the classical round-robin scheduler. Contrary to conventional belief, we show that appropriate modifications of the weighted round-robin (WRR) service discipline can, in fact, provide tight fairness properties and efficient delay guarantees to multiple sessions. Two such modifications are described: 1) list-based round robin, in which the server visits different sessions according to a precomputed list which is designed to obtain the desirable scheduling properties; 2) multiclass round robin, a version of hierarchical round robin with controls designed for good scheduling properties. The schemes considered are compared with well-known WFQ schemes and with deficit round robin (a credit-based WRR), on the basis of desirable properties such as bandwidth guarantees, fairness in excess bandwidth sharing, worst-case fairness, and efficiency of latency (delay guarantee) tuning. The scheduling schemes proposed and analyzed here operate with fixed packet sizes, and hence can be used in applications such as cell scheduling in ATM networks, time-slot scheduling on wireless links as in GPRS air interface, etc. A credit-based extension of the proposed schemes to handle variable packet sizes is also possible.     

A Modified Dynamic Weighted Round Robin Cell Scheduling Algorithm

In this paper, we propose the modified dynamic weighted round robin (MDWRR) cell scheduling algorithm, which guarantees the delay property of real‐time traffic and also efficiently transmits non‐real‐time traffic. The proposed scheduling algorithm is a variation of the dynamic weighted round robin (DWRR) algorithm and guarantees the delay property of real‐time traffic by adding a cell transmission procedure based on delay priority. It also uses a threshold to prevent the cell loss of non‐real‐time traffic that is due to the cell transmission procedure based on delay priority. Though the MDWRR scheduling algorithm may be more complex than the conventional DWRR scheme, considering delay priority minimizes cell delay and decreases the required size of the temporary buffer. The results of our performance study show that the proposed scheduling algorithm has better performance than the conventional DWRR scheme because of the delay guarantee of real‐time traffic.     

An Efficient Scheduling Discipline for Packet Switching Networks Using Earliest Deadline First Round Robin

This paper addresses a frame-oriented scheduling discipline, EDF-RR (earliest deadline first round robin), for OQ (output-queued) switch architecture and data traffic consisting of fixed-length cells. Bandwidth reservation for an active session is performed by holding a number of cell slots for the session in a repeatedly-transferred frame. Each cell that is going to be transferred in the frame is assigned a virtual release time and a virtual deadline according to the bandwidth reservation scheme. The transmitting order of the cells in the frame is determined by non-preemptive non-idling EDF algorithm so that cells of a backlogged session in the frame are distributed as uniformly as possible. Through the analysis applying real-time scheduling theory and network calculus as well as network simulation, EDF-RR takes the advantage of O(1) computational complexity, and possesses tight delay bounds and lenient buffer requirements. The proposed scheduling discipline is appropriate for distributed real-time systems as we show that sessions can be configured based on message traffic models and deadline requirements. Also, a modified version of EDF-RR, called EDF-DRR, can be applied as traffic regulator when jitter requirements exist among active sessions. This work was sponsored in part by the Federal Aviation Administration (FAA) via grant DTFA03-01-C-00042. Findings contained herein are not necessarily those of the FAA.     

Generalized guaranteed rate scheduling algorithms: a framework

In this paper, we define a class of generalized guaranteed rate (GR) scheduling algorithms that includes algorithms which allocate a variable rate to the packets of a flow. We define work-conserving generalized virtual clock, packet-by-packet generalized processor sharing, and self-clocked fair queueing scheduling algorithms that can allocate a variable rate to the packets of a flow. We also define scheduling algorithms suitable for servers where packet fragmentation may occur. We demonstrate that if a class of rate controllers is employed for a flow in conjunction with any scheduling algorithm in GR, then the resulting non-work-conserving algorithm also belongs to GR. This leads to the definition of several non-work-conserving algorithms. We then present a method for deriving the delay guarantee of a network of servers when: (1) different rates are allocated to packets of a flow at different servers along the path and the bottleneck server for each packet may be different, and (2) packet fragmentation and/or reassembly may occur. This delay guarantee enables a network to provide various service guarantees to flows conforming to any specification. We illustrate this by utilizing delay guarantee to derive delay bounds for flows conforming to leaky bucket, exponentially bounded burstiness, and flow specification. Our method for determining these bounds is valid in internetworks and leads to tighter results     

Network delay analysis of a class of fair queueing algorithms

A self-clocked fair queueing (SCFQ) scheme has been proposed by Golestani (see Proc. IEEE INFOCOM, p. 636-636, 1994) as an easily implementable version of fair queueing. In this paper, the worst case network delay performance of a class of fair queueing algorithms, including the SCFQ scheme, is studied. We build upon and generalize the methodology developed by Parekh and Gallager (see ACM/IEEE Trans. Networking, vol.1, no.3, p.344-357, 1993, and vol.2, no.2, p.137-150, 1994) to study this class of algorithms based on the leaky-bucket characterization of traffic. Under modest resource allocation conditions, the end-to-end session delays and backlogs corresponding to this class of algorithms are shown to be bounded. For the SCFQ scheme, these bounds are larger, but practically as good as the corresponding bounds for the PGPS scheme. It is shown that the SCFQ scheme can provide adequate performance guarantees for the delay-sensitive traffic in ATM     

Hardware implementation of fair queuing algorithms for asynchronoustransfer mode networks

Providing quality-of-service guarantees in both cell- and packet-based networks requires the use of a scheduling algorithm in the switches and network interfaces. These algorithms need to be implemented in hardware in a high-speed switch. The authors present a number of approaches to implement scheduling algorithms in hardware. They begin by presenting a general methodology for the design of timestamp-based fair queuing algorithms that provide the same bounds on end-to-end delay and fairness as those of weighted fair queuing, yet have efficient hardware implementations. Based on this general methodology, the authors describe two specific algorithms, frame-based fair queuing and starting potential-based fair queuing, and discuss illustrative implementations in hardware. These algorithms may be used in both cell switches and packet switches with variable-size packets. A methodology for combining a traffic shaper with this class of fair queuing schedulers is also presented for use in network interface devices, such as an ATM segmentation and reassembly device     

Hierarchical packet fair queueing algorithms

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 ²Q+ 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-WF²Q+, H-WFQ, H-SFQ, and H-SCFQ     

An efficient ATM network switch scheduling

The problem of allocating network resources to application sessions backlogged at an individual switch has a great impact on the end-to-end delay and throughput guarantees offered by the network. There exists a class of algorithms based on weighted fair queueing (WFQ) for scheduling packets which are work-conserving and they guarantee fairness to the backlogged sessions. These algorithms also apply to ATM networks with a packet equal to a single cell or an ATM block (of fixed size). Bursts are groups of varying numbers of cells. We generalize WFQ to schedule bursts. Our motivation is to derive an adaptive algorithm which generalizes the (fixed size) packet level to a varying size packet level. The new algorithm enhances the performance of the switch service for many important applications. The proposed scheme maintains the work-conserving property, and also provides throughput and fairness guarantees. The worst-case delay bound is also given. We use simulation to study the performance characteristics of our algorithm. Our results demonstrate the efficiency of the new algorithm.     

Carry-over round robin: a simple cell scheduling mechanism for ATMnetworks

We propose a simple mechanism named carry-over round robin (CORR) for scheduling cells in asynchronous transfer mode networks. We quantify the operational complexity of CORR scheduling and show that it is comparable to that of a simple round-robin scheduler. We then show that, albeit its simplicity, CORR is very competitive with much more sophisticated and significantly more complex scheduling disciplines in terms of performance. We evaluate the performance of CORR using both analysis and simulation, We derive analytical bounds on the worst case end-to-end delay achieved by a CORR scheduler for different traffic arrival patterns. Using traffic traces from MPEG video streams, we compare the delay performance of CORR with that of packet-by-packet generalized processor sharing (PGPS) and stop-and-go (SG). Our results show that, in terms of delay performance, CORR compares favorably with both PGPS and SG. We also analyze the fairness properties of CORR and show that it achieves near perfect fairness     

A cell switching WDM broadcast LAN with bandwidth guarantee andfair access

This paper presents the design of a cell-switching wavelength division multiplexing (WDM) local area network (LAN), which constitutes a key component of a next-generation internet (NGI) consortium project recently funded by DARPA. An important goal of the NGI project is to support bandwidth-on-demand services with quality-of-service (QOS) guarantee over WDM networks. As a first step toward this goal, we have developed several fast scheduling algorithms for flexible bandwidth reservations and fair sharing of unreserved bandwidth in a WDM broadcast network with fast-tunable transceivers. Unlike circuit-based bandwidth reservation schemes that impose a fixed schedule precomputed on setup, our scheme deals with bursty traffic by allocating network resources dynamically using very efficient algorithms. Our algorithms are based on a new concept of computing maximal weighted matchings, which is a generalization of maximal matchings on unweighted graphs. We prove that our algorithms can support total reserved bandwidth of up to 50% of the network capacity, and in that case constant delay bounds are also established. Simulations show that our algorithms can in practice support much higher reserved bandwidth-up to 90% of network capacity, and with much better delay bounds, even for burst traffic. In addition to the bandwidth guarantee, the unreserved bandwidth can be shared fairly among the users using our fair access algorithms with case to 100% network utilization in simulations     

A discrete-time queueing network model of a hub-based OBS architecture

We propose and analyze a novel discrete-time queueing network model of a zero loss hub-based Optical Burst Switched (OBS) architecture, consisting of multiple input edge nodes and one destination edge node. The arrival process of bursts is slotted with bulk arrivals as generated by a Time and Burst-Length based burst aggregation algorithm. The queueing network is analyzed by decomposition. We obtain the average end-to-end delay of a burst in the queueing network as well as queueing delays at individual nodes. Our model provides a tight upper bound as shown by comparing the analytical data to simulation results.     

Self-coordinating localized fair queueing in wireless ad hoc networks

Distributed fair queueing in a multihop, wireless ad hoc network is challenging for several reasons. First, the wireless channel is shared among multiple contending nodes in a spatial locality. Location-dependent channel contention complicates the fairness notion. Second, the sender of a flow does not have explicit information regarding the contending flows originated from other nodes. Fair queueing over ad hoc networks is a distributed scheduling problem by nature. Finally, the wireless channel capacity is a scarce resource. Spatial channel reuse, i.e., simultaneous transmissions of flows that do not interfere with each other, should be encouraged whenever possible. In this paper, we reexamine the fairness notion in an ad hoc network using a graph-theoretic formulation and extract the fairness requirements that an ad hoc fair queueing algorithm should possess. To meet these requirements, we propose maximize-local-minimum fair queueing (MLM-FQ), a novel distributed packet scheduling algorithm where local schedulers self-coordinate their scheduling decisions and collectively achieve fair bandwidth sharing. We then propose enhanced MLM-FQ (EMLM-FQ) to further improve the spatial channel reuse and limit the impact of inaccurate scheduling information resulted from collisions. EMLM-FQ achieves statistical short-term throughput and delay bounds over the shared wireless channel. Analysis and extensive simulations confirm the effectiveness and efficiency of our self-coordinating localized design in providing global fair channel access in wireless ad hoc networks.     

Downlink scheduling in a cellular network for quality-of-service assurance

We consider the problem of scheduling data in the downlink of a cellular network over parallel time-varying channels, while providing quality-of-service (QoS) guarantees to multiple users in the network. We design simple and efficient admission control, resource allocation, and scheduling algorithms for guaranteeing requested QoS. In our design, a joint Knopp and Humblet (K&H)/round robin (RR) scheduler, composed of K&H scheduling and RR scheduling, utilizes both multiuser and frequency diversity to achieve capacity gain when delay constraints are loose or moderate. However, for tight delay constraints, an additional reference channel scheduler is required to obtain additional frequency diversity gain. The key advantage of our formulation is that the desired QoS constraints can be explicitly enforced by utilizing the concept of effective capacity.     

一类基于调度表的公平轮循调度算法

本文研究了一类利用时标在调度表中安排信元发送时隙的公平轮循(Fair Round Robin,FRR)调度算法.对其中三种算法的性能进行了分析比较.FRR能够保证连接的带宽和时延,同时实现复杂性低于一些分组公平排队算法,例如WF²Q+.