A. Greenberg and N. Madras. How fair is fair queuing? Journal of the ACM, 39(3):568--598, 1992.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

....defined as (6) 7) Note that our definitions of the absolute and relative fairness bounds are equivalent to the classic definitions [2] 4] 6] III. RELATIONSHIP BETWEEN AFB AND RFB Lemma 1: Under any work conserving policy and over any interval of time This obvious lemma is also stated in [8]. For the sake of brevity, we denote by . Lemma 2: Over any interval of time and for any pair of flows Proof: Under the GPS scheduler, the service received by each backlogged flow is exactly proportional to its weight, i.e. 8) Thus from (1) we can express the absolute fairness of flow as (9) ....

A. G. Greenberg and N. Madras, "How fair is fair queuing?," J. Ass. Comput. Mach., vol. 39, no. 3, pp. 568--598, July 1992.

....Strict QoS guarantees such as throughput or delays can also be provided by restricting the admission of tra#c. In [15] it is demonstrated that GPS guarantees end to end delay for leaky bucket constrained tra#c. A number of approximations and heuristics of GPS were devised over the years [8, 17, 11, 15, 9, 5, 10]. Implementations of this work, known as Weighted Fair Queuing, can be found in current commercial routers or switches as well as in some servers [6] which provide di#erentiated qualities of service to distinct classes of clients. An increased dependence on network services and the growing demand ....

....load among multiple outgoing links and its impact should be studied. 8. RELATED WORK Our work builds on a number of previous studies of GPSbased scheduling disciplines for single server systems. The concepts of Proportional Sharing and Generalized Processor Sharing are presented in [8] [11] and in [15] Demers et al. introduced a packetized service discipline WFQ in [8] Later on, Parekh and Gallager proved in [15] that WFQ (a.k.a. PGPS) closely approximates the ideal GPS system in terms of packet delay and the cumulative per flow service. Their work also showed end to end packet ....

A. Greenberg and N. Madras. How Fair is Fair Queuing. Journal of the ACM, July 1992.

....of packets in the buffer, so This work is partially supported by the CNET, under a CTI contract. y Author to join for all correspondence there is no isolation between sessions and the QoS requirements can not be guaranteed. The Fair Queuing algorithms are proposed to provide these features [8], 4] The underlying idea of these policies is to serve sessions in proportion to some prespecified service shares, independent of the backlog of sessions. On the other hand, these policies must let to use the idle bandwidth, and at the same time, the QoS requirements must be guaranteed in the ....

....service shares, independent of the backlog of sessions. On the other hand, these policies must let to use the idle bandwidth, and at the same time, the QoS requirements must be guaranteed in the presence of congestion. The first proposed policy is the generalized processor sharing (GPS) [8], 4] It provides the perfect isolation between different classes and allows bandwidth sharing among these classes. However it is a fluid model, which means that the flows of sessions are supposed to be infinitesimally indivisible. Therefore, extensions of this policy for packet by packet ....

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A. Greenberg and N. Madras. "How fair is Fair Queuing?". Journal of ACM, 39(3), July 1992.

....single processor (P = 1) In a uniprocessor, the decision when to serve which job is made by a local scheduling policy. Examples of such policies are FirstCome First Served (FCFS) and Processor Sharing (PS) Local scheduling policies have been the subject of intensive research in the past decades [1, 4, 14, 16, 35, 51, 55, 86, 87] and will be studied in Chapter 3 of this thesis. In practical implementations, the processor cannot serve multiple jobs simultaneously, unlike with policies such as Processor Sharing. However, because the latter policies can be approximated with round robin policies [14] we allow local policies ....

....can be applied to other systems as well, such as network routers and manufacturing systems. For example, if a router in a network routes several tra#c streams, it may be desired to ensure that the router capacity is distributed fairly among the tra#c streams, as pointed out by Greenberg and Madras [35]. A major di#erence between this example and our situation is the time scale of scheduling events. For compute intensive workloads in distributed systems, this is in the order of minutes or hours, whereas for routing packets this is in the order of microseconds. 1.5 Related Literature on Share ....

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A.G. Greenberg and N. Madras. How Fair is Fair Queuing? Journal of the ACM, 39(3):568--598, 1992.

....applications. Furthermore, realtime schedulers are often sensitive to system overload. For example, an overload condition may cause the earliest deadline first algorithm to miss subsequent deadlines. Fair queuing scheduling algorithms first appeared in areas of network packet scheduling [18, 34, 17, 30, 33, 76]. When applied to thread scheduling, a fair queuing algorithm assigns each thread a weight, and allocates CPU bandwidth to each thread in proportion to its weight [82, 83, 63, 78, 32, 14] The relative bandwidth allocation among threads is determined only by their respective weights, hence, is not ....

....several reservations. An application is guaranteed to receive the portion it reserved. Admission control policy is enforced before granting a new reservation to prevent overload. 6.1. 3 Fair queuing Schedulers Fair queuing scheduling algorithms first appeared in areas of network packet scheduling [18, 34, 17, 30, 33, 76]. When applied to thread scheduling, a fair queuing algorithm assigns each thread a weight, and allocates CPU bandwidth to each thread in proportion to its weight [82, 83, 63, 78, 32, 14] The relative bandwidth allocation among threads is determined only by their respective weights, hence, is not ....

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A. Greenberg and N. Madras. How Fair is Fair Queuing. The Journal of ACM, 39(3):568--598, July 1992. 114

....Time to Reach Bound policy bounds the size of the longest queue by a constant 2L, where L is the maximum message size. Note that we cannot adopt similar ideas, since we make no assumptions on the arrival rates, and therefore do not know which buffer would reach the bound of 2L first. References [10, 12] achieve the same bound in the same model with a more complicated policy that could also be applied to other models. Reference [9] showed that the Longest Queue First policy fails to bound the longest queue with a constant factor (even under the above assumptions) They proved a logarithmic upper ....

A. G Greenberg and N. Madras. How Fair is Fair Queuing? In Journal of the Association Computing Machinery (JACM), Vol. 39, No. 3, pp. 568--598, 1992.

....and multiple time scale variation in VBR video bit rate, it may not be possible to accurately estimate C(t) Furthermore, this would make the computation of v(t) even more expensive, thereby making WFQ infeasible for high speed networks. Fair Queuing based on Start time (FQS) proposed in [11], computes start tag and finish tag of a packet exactly as in WFQ. However, instead of scheduling packets in the increasing order of finish tags, it schedules packets in the increasing order of start tags. Though FQS has advantages for processor scheduling, it is not known to have any advantage ....

A. Greenberg and N. Madras. How Fair is Fair Queuing. The Journal of ACM, 39(3):568--598, July 1992.

....is based on serving the link which will be the first to overflow if the switch stops its operation. If all buffers are of size 2P then this policy guarantees that for any sequence of packets, buffer overflow does not occur. Parekh and Gallager [5] analyzed a different policy the PGPS policy [4] which also achieves the optimal bound. The PGPS is a packetized version of the GPS algorithm. Both of these policies require complicated decisions on a per packet basis. Hence, the server has to perform a computation proportional to the number of channels after ending the service of a packet in ....

A.G Greenberg and N. Madras. How Fair is Fair Queuing. In Journal of the ACM , 39(3), pages 568--598, July 1992.

....to hold for low throughput applications, we conclude that SFQ provides lower delay to low throughput applications. Since interactive applications are low throughput in nature, this feature of SFQ is highly desirable for CPU scheduling. 14 Fair Queuing based on Start time (FQS) was proposed in [6], to make WFQ suitable for scheduling threads when quantum length may not be known a priori. It computes start tag and finish tag of a quantum exactly as in WFQ. However, instead of scheduling quantums in the increasing order of finish tags, it schedules them in the increasing order of start tags. ....

....and implementation complexity as SFQ but provides significantly larger delay guarantee than SFQ. Specifically, it increases the maximum delay of quantum q j f by l j f rf [5] Though the relationship between fair packet scheduling algorithms and fair CPU allocation was pointed out in [6], it remained largely unknown to the operating systems community. Consequently, a randomized fair algorithm, termed lottery scheduling, was proposed in [14] Due to its randomized nature, lottery scheduling achieved fairness only over large time intervals. This limitation was later addressed by ....

A. Greenberg and N. Madras. How Fair is Fair Queuing. The Journal of ACM, 39(3):568--598, July 1992.

....schemes can significantly improve the performance of TCP over UBR service in terms of fairness. Similar results are also reported in [5] C. Fair Queuing Techniques The design of fair queuing techniques for conventional networks has been a subject of intensive research in recent years [3] 7] [8], 10] 13] 15] 18] These works focus on the fair allocation of network resources for different packet streams. The difficulty arises from the fact that the packets are of different sizes. Even if each packet stream is buffered at a separate queue (perconnection queuing) a round robin ....

A. G. Greenberg and N. Madras. How fair is fair queuing?. Journal of the Association for Computing Machinery, July 1992, vol.39, (no.3):568-98.

....the server. We define work conserving generalized Virtual Clock, PGPS, and SCFQ scheduling algorithms that can allocate variable rate to the packets of a flow, and show that they belong to GR. To prove that many scheduling algorithms belong to GR, we employ a proof methodology (similar to that in [12, 18]) in which we first show that a preemptive equivalent of the algorithm belongs to GR, and then utilize a relationship (also derived in this paper) between preemptive and non preemptive scheduling algorithms to show that the non preemptive algorithm belongs to GR. This methodology leads to the ....

....of the work conserving as well as non work conserving scheduling algorithms that either allocate only rate or separate rate and delay allocation belong to GR. To show that a scheduling algorithm belongs to GR, we would be required to prove a bound on the departure time of a packet. As observed in [5, 12], it is typically easier to bound the departure time of a packet in preemptive scheduling algorithms. Hence, even though packet scheduling algorithms are inherently nonpreemptive in nature, to show that a scheduling algorithm belongs to GR, we employ a proof methodology, similar to the ....

[Article contains additional citation context not shown here]

A. Greenberg and N. Madras. How Fair is Fair Queuing. The Journal of ACM, 39(3):568--598, July 1992.

....to hold for low throughput applications, we conclude that SFQ provides lower delay to low throughput applications. Since interactive applications are low throughput in nature, this feature of SFQ is highly desirable for CPU scheduling. Fair Queuing based on Start time (FQS) was proposed in [7] to make WFQ suitable for CPU scheduling when quantum length may not be known a priori. It computes the start tag and the finish tag of a quantum exactly as in WFQ. However, instead of scheduling quantums in the increasing order of finish tags, it schedules them in the increasing order of start ....

A. Greenberg and N. Madras. How Fair is Fair Queuing. The Journal of ACM, 39(3):568--598, July 1992.

....servers. As we will outline in Section 3, to be useful for hierarchical link sharing [6, 18] a scheduling algorithm must provide fairness over variable rate servers. Consequently, WFQ is unsuitable for supporting hierarchical link sharing also. Fair Queuing based on Start time (FQS) proposed in [14], computes start tag and finish tag of a packet exactly as in WFQ. However, instead of scheduling packets in the increasing order of finish tags, it schedules packets in the increasing order of start tags. Though FQS has advantages for processor scheduling, it is not known to have any advantage ....

A. Greenberg and N. Madras. How Fair is Fair Queuing. The Journal of ACM, 39(3):568--598, July 1992.

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A. Greenberg and N. Madras. How fair is fair queuing? Journal of the ACM, 39(3):568--598, 1992.

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A. Greenberg and N. Madras. How fair is fair queuing? Journal of the ACM, 39(3):568--598, 1992.

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A. G. Greenberg, N. Madras, "How fair is fair queuing?," Journal of the Association for Computing Machinery, vol. 39, no. 3, pp. 568-598, July 1992.

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A. Greenberg and N. Madras. How fair is fair queuing? Journal of the ACM, 39(3):568--598, 1992.

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A. Greenberg and N. Madras. How fair is fair queuing? Journal of the ACM, 39(3):568--598, July 1992.

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