J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999. 27  Home/Search   Document Details and Download   Summary   Related Articles   Check

....approach to describe arrivals and services in a network. This approach is motivated by the deterministic network calculus [8] which provides an elegant framework for worst case analysis in a network. Several researchers have extended the network calculus to a probabilistic setting, including [5, 17, 20, 22, 24, 26, 28, 27, 29]. An advantage of an envelope approach is that it can provide finite bounds on delay and backlog in a network, as opposed to asymptotic approximations. We present a network calculus in a fully probabilistic setting, where both arrivals and service are expressed in terms of probabilistic bounds. ....

....effective bandwidth (in the sense of [4, 15] has been determined. Specifically, we consider traffic characterizations that relate to regulated, On Off, and Fractional Brownian Motion traffic. The effective service curves in this paper, which are inspired by the statistical service envelopes in [20], can express the service for a wide range of scheduling algorithms. In this way, the effective bandwidth theory can be easily related to scheduling algorithms used in practice. Thus, a contribution of this paper is to link two principal tools for the analysis of network traffic, i.e. effective ....

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J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....there have been several efforts to extend the deterministic net work calculus [7] 8] 9] 4] 26] which relies to a large extend on arrival envelopes and service curves, to probabilistic network services. Different definitions of probabilis tic service curves have been studied in [10] [36]. A prob abilistic network calculus for a class of so called dynamic F servers is developed in [4] A calculus for providing end to end statistical QoS is developed and evaluated in [2] 30] This calculus employs effective service curves and applies in rather general settings. This article ....

J. Qiu and E. Knightly. Inter class resource sharing using sta- tistical service envelopes. In Proceedings of IEEE Infocorn '99, New York, NY, March 1999.

....the Department of Computer Science, Texas A M University, College Station, TX 77843. E mail: fswang, dxuan, bettati, zhaog cs.tamu.edu . # # # # # # # # # # # # ############## ####### ### #### # ##### # # # # # # # # # ################## ## ## # ## ### [10, 22] 11, 13, 15, 36] [6, 8, 19, 28] [21, 34, 35] 29, 30] 31] This study Fig. 1. Problem Space and Related Work While deterministic services provide a simple model to the applications, they tend to heavily over commit resources because they account for the worst case scenario. In practical systems, this likely results in ....

....model in singlenode networks, various solutions have been reported early on [10] and [22] The case of deterministic services within the intserv model in multi node networks, represented by Vertex B in Fig. 1, has been covered in [11] 13] 15] 36] A number of projects ( 6] 8] 19] [28]) address In the following, we will use the term flow to indicate a stream of data between a source and a destination, and the term connection to indicate the virtual circuit that needs to be established to carry the flow. In this paper we use aggregated flow and class interchangeably. the ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly, Inter-class resource sharing using statistical service envelopes, Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....in [11] depends on the information of ow population. To extend it to be in DiffServ fashion, we will develop a method that allows us to analyze the delays without depending on the dynamic status of ow population. Progress has been made to provide statistical performance guarantees in IntServ [1, 8, 9, 11, 12, 17, 20, 25, 26], but no such results are available for absolute statistical performance guarantees in DiffServ. Our approach is based on a simple and general trac characterization which is called rate variance envelope [10, 11] this envelope describes the variances of the ows rates as a function of interval ....

.... has been studied via envelopes of bounding moment generating functions [1] exponentially bounded envelopes [20, 25] and envelopes consisting of families of bounding distributions [12, 26] Statistical envelopes have also been applied to resource allocation for inter class resource sharing [17] and video on demand services [8] Much work has been done to generalize schedulabilty conditions for a deterministic service to a probabilistic framework. Several researchers made probabilistic extensions to deterministic service models. In [9, 11] a rate variance envelope is introduced, which ....

J. Qiu and E. Knightly, Inter-class resource sharing using statistical service envelopes, Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....probabilistic formulations of service curves. Cruz de nes a probabilistic service curve which violates a given deterministic service curve according to a certain distribution [12] Chang (see [9] Chp. 7) presents a statistical network calculus for dynamic F servers . Finally, Knightly and Qiu [19] derive statistical service envelopes as time invariant lower bounds on the service received by an aggregate of ows. This paper proposes a network calculus for statistically multiplexed traf c, expressed in the min plus algebra, where network capacities are allocated to aggregates of ows. ....

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE Infocom '99, pages 3642, March 1999.

....0 or, 1 N log Pr(W m) 1 N log Pr( f W m) Letting N 1, I W (m) I e W (m) 5) From Theorem 2.1 and (5) it follows that I V (m) I W (m) for all m 0. In multi class queues, often the distribution of the virtual delay is easier to characterize than that of the actual delay, see [21, 14, 18] for such examples under various service disciplines. For arrival processes satisfying Assumption 2.1, the above theorem shows that the virtual and actual delay asymptotes are the same if the number of sources is very large. 10 Next, we show an application of this result to priority queueing ....

....LPQ is upper bounded by I V (m) inf T 0 inf (T m 1) x e C(T m 1) fI A 1 ;T m (x) I A 2 ;T (C(T m 1) x)g # Proof: The proof of this result follows similar techniques as in [6] Hence, we have shown that under Assumption 4.2, the upper and lower bounds are the same. We note that [21] has studied virtual delay in priority queues. They bound the delay tail 15 for a single source. The event that they use is the same as (6) We have shown that this is asymptotically (in the many sources regime) tight and is in fact, the actual delay asymptote. We note that the above analysis ....

J. Qiu, C. Cetinkaya, C. Li and E. Knightly, \Inter-Class Resource Sharing using Statistical Service Envelopes," preprint. An earlier version appeared in the Proceedings of IEEE Infocom, New York, NY, 1999. 23

....probabilistic formulations of service curves. Cruz defines a probabilistic service curve which violates a given deterministic service curve according to a certain distribution [12] Chang (see [9] Chp. 7) presents a statistical network calculus for dynamic F servers . Finally, Knightly and Qiu [19] derive statistical service envelopes as time invariant lower bounds on the service received by an aggregate of flows. This paper proposes a network calculus for statistically multiplexed traffic, expressed in the min plus algebra, where network capacities are allocated to aggregates of flows. ....

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE Infocom '99, pages 36--42, March 1999.

....bounded burstiness. The work was recently extended in [36] to more general bounding functions. Cruz [12] computes probabilistic bounds on the delay and backlog at a scheduler, assuming that probabilistic bounds on traffic arrivals and service curves [11] are available. Qiu and Knightly [30] extend this approach and develop a framework for statistical service envelopes. Andrews [2] provides probabilistic bounds for delay violations at an EDF scheduler, assuming that the arrival distribution of traffic is known. Specific results are derived for on off traffic as assumed in [15] ....

J. Qiu and E. Knightly, "Inter-class resource sharing using statistical service envelopes," in Proc. IEEE Infocom '99, Mar. 1999, pp. 36--42.

....In particular, we exploit the notion of effective envelopes, which are functions that provide bounds on traffic arrivals with high certainty. In addition, previous work on rate based scheduling algorithms with statistical service guarantees in single node networks is very relevant to our work [16, 30, 43, 44]. The remainder of this paper is structured as follows. In Section 2 we state our assumptions on traffic arrivals and we introduce the notion of effective envelopes. In Sections 3 and 4, respectively, we present our two designs for end to end statistical QoS and analyze their ability to exploit ....

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proc. IEEE Infocom '99, pages 36--42, March 1999.

....regions. Analytical frameworks have already been developed in the literature for estimating the losses (throughout this work losses refers to delay bound violations) at GPS and EDF schedulers. For GPS, we use the analytical frameworks of [5] 11] based on the Chernoff approximation) and [16] (based on the central limit approximation) while for EDF we employ [19] based on the Bene s approach) and [16] based on the central limit approximation) In contrast to GPS, where the losses are computed on a per flow basis, the statistical frameworks for EDF estimate the loss probabilities ....

....this work losses refers to delay bound violations) at GPS and EDF schedulers. For GPS, we use the analytical frameworks of [5] 11] based on the Chernoff approximation) and [16] based on the central limit approximation) while for EDF we employ [19] based on the Bene s approach) and [16] (based on the central limit approximation) In contrast to GPS, where the losses are computed on a per flow basis, the statistical frameworks for EDF estimate the loss probabilities over the aggregate (i.e. over the entire set of flows multiplexed at the scheduler) To make the comparison ....

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J. Qiu and E. D. Knightly. Inter-class resource sharing using statistical service envelopes. Technical report, Rice University, January 1999. An earlier version appeared in INFOCOM '99.

....classes. In general, the extent to which an increased load in one class affects the performance of another class is a complex function of the total system load, the particular resource scheduling algorithm, and the low level interactions among the server s resources. Building on the results of [19], we use the envelopes as a way to characterize the high level isolation sharing relationships among classes and design a general multiclass algorithm to exploit these effects. Finally, by decoupling access control and resource allocation from the internals of the server, we obtain a general ....

....these limitations in a realistic scenario. 4 ENVELOPES: A GENERAL SERVICE AND DEMAND ABSTRACTION In this section, we describe envelopes as a tool for developing an admission control algorithm which can overcome the limitations of the baseline scheme. Deterministic [13] and statistical [5] 9] [19] traffic envelopes have been developed to manage network QoS. Moreover, deterministic [13] and statistical [19] service envelopes have provided a foundation for multiclass network QoS, in [19] also incorporating interclass resource sharing. Below, we extend these techniques to the scenario of ....

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J. Qiu and E. Knightly, "interclass Resource Sharing Using Statistical Service Envelopes," Proc. IEEE INFOCOM '99, Mar. 1999.

....and analyzing non work conserving elements such as rate limiters. In contrast, long time scale measurements best reveal link sharing rules and weights. Thus, a key aspect of our contribution is that we develop all such measurement tools using a unifying abstraction of envelopes [5] 9] [16], hypothesis testing, and maximum likelihood estimations. In this way, we treat phenomena occurring at different time scales in a uniform and methodical way. In addition to network services, our techniques also have applications to other multi class systems such as quality of service web servers ....

....Arrival Model Here we describe a general arrival characterization which can be applied to the multi class inference problem. The technique is based on traffic envelopes which provide a unifying abstraction for both arrivals and services and incorporate the system s behavior across time scales [16]. Measurement at multiple time scales is important in this context as different system components are most accurately detected at different time scales. Focusing on a single class for illustration, Figure 4 depicts an example arrival departure sequence, with the packet having , arrival ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....article, please send e mail to: tpds computer.org, and reference IEEECS Log Number 115671. 1045 9219 03 17.00 # 2003 IEEE Published by the IEEE Computer Society key aspect of our contribution is that we develop all such measurement tools using a unifying abstraction of envelopes [19] 20] [21], hypothesis testing, and maximum likelihood estimations. In this way, we treat phenomena occurring at different time scales in a uniform and methodical way. We, therefore, consider a general system model that encompasses a broad class of multiservice elements ranging from routers to Web servers, ....

....class is statistical arrival envelope as B t, which is a sequence of random variables that characterizes arrivals from class i over time intervals of duration t. It is assumed that each class arrival process is stationary and that B and B are statistically independent when i j. In [21], statistical admission control tests are developed for several multiclass schedulers. The key technique for exploiting interclass resource sharing is to characterize a class available service beyond its worst case allocation. For example, in a WFQ server, a class with weight # i receives service ....

J. Qiu and E. Knightly, "Inter-Class Resource Sharing Using Statistical Service Envelopes," Proc. IEEE INFOCOM '99, Mar. 1999.

....the difficulties of achieving precise control of class QoS measures, but do indicate that the algorithm can control admissions so that empirical QoS has a strong correspondence to the targeted values. V. RELATED WORK Aggregate statistical traffic envelopes for QoS have been studied in [1] [25]. The focus of [1] is statistical multiplexing of adversarial flows while the focus of [25] is interclass resource sharing. Both studies address statistical multiplexing in a number of multiclass schedulers such as strict priority and earliest deadline first. In contrast, our MBAC algorithm ....

....that the algorithm can control admissions so that empirical QoS has a strong correspondence to the targeted values. V. RELATED WORK Aggregate statistical traffic envelopes for QoS have been studied in [1] 25] The focus of [1] is statistical multiplexing of adversarial flows while the focus of [25] is interclass resource sharing. Both studies address statistical multiplexing in a number of multiclass schedulers such as strict priority and earliest deadline first. In contrast, our MBAC algorithm utilizes measurements to characterize and control the aggregate traffic envelope. Several ....

J. Qiu and E. W. Knightly, "Interclass resource sharing using statistical service envelopes," in Proc. IEEE INFOCOM, New York, Mar. 1999, pp. 1404--1411.

....control not only the service across a particular ingress egress pair, but also implicitly control other paths, thereby ensuring that all classes on all paths maintain their required service levels. For admission control, our key technique is to develop a measurement based theory of envelopes [22] to accurately characterize and control both arrivals and services in a general way. In particular, we introduce a measurement based service envelope as a new way to adaptively describe the end to end service available to a traffic class. By developing our approach using a black box system ....

....discipline remains important in quality of service provisioning, as a poorly chosen scheduler will result in lower network utilization. Below, we develop a framework for assessing and controlling a class service using measurement based service envelopes. We build on the general abstraction of [22], which uses statistical service envelopes to study inter class resource sharing. 1) Service Definition: To devise a multiclass admission control algorithm with controlled statistical sharing across classes, a theory is needed which can characterize the extent to which classes can be ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly, "Inter-class resource sharing using statistical service envelopes," in Proc. IEEE INFOCOM '99, New York City, Mar. 1999.

....path is modeled as a black box with an unknown service discipline and cross traffic that cannot be directly measured. An important part of egress admission control is assessing the available service along this path. We will show how the abstraction of a statistical service envelope [11] provides a general framework for characterizing service, including fluctuating available resources due to varying demands of cross traffic. Arrivals Services [ n Figure 1: Egress Admission Control System Model This paper describes our design, implementation, and measurement study of Egress ....

....traffic such as NFS (Network File System) traffic. Second, the empirical service envelope is actually an approximation to the true available service. For example, while an infinite rate input flow would indeed measure a service envelope of 9t, a minimally backlogged flow, such as described in [11] would measure a lower service envelope due to its own rate variations. In the experiments, the maximum number of admitted flows is 19, corresponding to an average link utilization of 84 , quite similar to utilizations obtained in theory for similar types of flows (see [7] for example) 5 In this ....

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

.... limit congestion levels so that (for example) targeted latencies and throughputs are ensured, thereby providing services with predictable and controlled performance levels [22] For example, statistical class based admission control tests have been derived for Earliest Deadline First (EDF) 4] [27], 31] Weighted Fair Queueing (WFQ) 12] 27] 38] Strict Priority [27] and Virtual Clock [20] Moreover, techniques for providing multi node or end to end statistical services have been developed for several classes of non work conserving schedulers [5] 28] 31] 37] and for Weighted ....

.... targeted latencies and throughputs are ensured, thereby providing services with predictable and controlled performance levels [22] For example, statistical class based admission control tests have been derived for Earliest Deadline First (EDF) 4] 27] 31] Weighted Fair Queueing (WFQ) 12] [27], 38] Strict Priority [27] and Virtual Clock [20] Moreover, techniques for providing multi node or end to end statistical services have been developed for several classes of non work conserving schedulers [5] 28] 31] 37] and for Weighted Fair Queueing networks with isolation among flows ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service 13 envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....in the core and edge routers, like insertion of packet state in the headers, a special scheduler to be implemented in each router and rate monitoring. To prevent the use of a signaling protocol and special packet processing in core nodes, a call admission control mechanism based on probing [8] was proposed, where a test flow is inserted into the network to measure its congestion level. This paper is organized as follows. In section II we describe several call admission control mechanisms. In section III we discuss in more detail the probing mechanism. In section IV we present a set of ....

....incorporate the cross traffic effects without explicitly measuring it or controlling it. Cross traffic is the traffic that is merged in some links with the traffic that is being measured in the egress, but has a different egress router. For this purpose the measurement based theory of envelopes [8] is used to characterize and control both arrivals and services in a general way. Arrival envelopes are based on the maximum rate of the arrivals. Service envelopes are based on the minimum service available. By measuring the aggregate rate envelope, the short time scale burstiness of the traffic ....

J. Qiu and E. Knightly "Inter-class Resource Sharing using Statistical Service Envelopes", In Proceedings of IEEE INFOCOM'99, New York, NY, March 1999.

....and analyzing non work conserving elements such as rate limiters. In contrast, long time scale measurements best reveal link sharing rules and weights. Thus, a key aspect of our contribution is that we develop all such measurement tools using a unifying abstraction of envelopes [5] 9] [16], hypothesis testing, and maximum likelihood estimations. In this way, we treat phenomena occurring at different time scales in a uniform and methodical way. In addition to network services, our techniques also have applications to other multi class systems such as quality of service web servers ....

....Arrival Model Here we describe a general arrival characterization which can be applied to the multi class inference problem. The technique is based on traffic envelopes which provide a unifying abstraction for both arrivals and services and incorporate the system s behavior across time scales [16]. Measurement at multiple time scales is important in this context as different system components are most accurately detected at different time scales. Focusing on a single class for illustration, Figure 4 depicts an example arrival departure sequence, with the packet having size ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....can control not only the service across a particular ingress egress pair, but also implicitly control other paths, thereby ensuring that all classes on all paths maintain their required service levels. For admission control, our key technique is to develop a measurement based theory of envelopes [22] to accurately characterize and control both arrivals and services in a general way. In particular, we introduce a measurement based service envelope as a new way to adaptively describe the end to end service available to a traffic class. By developing our approach using a black box system ....

....discipline remains important in quality of service provisioning, as a poorly chosen scheduler will result in lower network utilization. Below, we develop a framework for assessing and controlling a class service using measurement based service envelopes. We build on the general abstraction of [22], which uses statistical service envelopes to study interclass resource sharing. B.1 Service Definition To devise a multi class admission control algorithm with controlled statistical sharing across classes, a theory is needed which can characterize the extent to which classes can be ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....path is modeled as a black box with an unknown service discipline and cross trac that cannot be directly measured. An important part of egress admission control is assessing the available service along this path. We will show how the abstraction of a statistical service envelope [8] provides a general framework for characterizing service, including uctuating available resources due to varying demands of cross trac. Core Nodes Unknown Service Arrivals Services Interfering Cross traffic Edge Nodes Fig. 1. Egress Admission Control System Model This paper describes our ....

....need to be incorporated: otherwise egress routers may over estimate the available service along a path, as not all arriving trac is incorporated into the measurement. Computing a Path s Available Service To assess the available service on a path, we measure a path s statistical service envelope [8], a general characterization of the end to end service received by a trac class. This service abstraction can incorporate the e ects of interfering cross trac without explicitly measuring or controlling it. Moreover, the service envelope exploits features of the backbone nodes schedulers and the ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

....and analyzing non work conserving elements such as rate limiters. In contrast, long time scale measurements best reveal link sharing rules and weights. Thus, a key aspect of our contribution is that we develop all such measurement tools using a unifying abstraction of envelopes [5] 9] [16], hypothesis testing, and maximum likelihood estimations. In this way, we treat phenomena occurring at different time scales in a uniform and methodical way. In addition to network services, our techniques also have applications to other multi class systems such as quality of service web servers ....

....Arrival Model Here we describe a general arrival characterization which can be applied to the multi class inference problem. The technique is based on traffic envelopes which provide a unifying abstraction for both arrivals and services and incorporate the system s behavior across time scales [16]. Measurement at multiple time scales is important in this context as different system components are most accurately detected at different time scales. Focusing on a single class for illustration, Figure 4 depicts an example arrival departure sequence, with the j th packet having size p j , ....

[Article contains additional citation context not shown here]

J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

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J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999. 27

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J. Qiu and E. Knightly. Inter-class resource sharing using statistical service envelopes. In Proceedings of IEEE Infocom '99, pages 36--42, March 1999.

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J.-y. Qiu, E. Knightly,Inter-class resource sharing using statistical service envelopes, in: Proceedings of the Conference on Computer Communications #IEEE Infocom#, New York, U.S.A., 1999.

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