A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, pages 1220 -- 1230, March 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a specific source model. Starting with the seminal work in [8] researchers have investigated the statistical multiplexing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g. by a leaky bucket [5] 8] [7], 9] 10] 12] 16] 17] 19] 20] 21] Henceforth, we will refer to traffic which satisfies these assumptions as regulated adversarial traffic. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, ....

.... conditions derived for various packet scheduling algorithms in the context of a deterministic service, e.g. 4] 15] 23] Note that only few results are available on statistical multiplexing of adversarial traffic, which can consider scheduling algorithms other than a simple multiplexer [7], 12] Related work to this paper are all attempts to consolidate the deterministic network calculus [4] with statistical multiplexing (e.g. 2] 6] 10] 11] 12] 14] In addition, of particular relevance to this paper are all previous results on statistical multiplexing gain with ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220-- 1230, New York, March 1999.

....traffic loss at the scheduler is assumed to be split among real time flows in proportion to their input rates. In contrast, we assume a packet based model, an independent buffer space for each real time flow, and permit explicit delay violation probability bounds for each flow. Elwalid and Mitra[7] have proposed a scheme to provide statistical QoS guarantees in the GPS service discipline for two guaranteed traffic classes and one best effort class. Again a fluid traffic model was considered. Schemes for providing probabilistic QoS in networks using Earliest Deadline First (EDF) scheduling ....

....of admitted VoIP flows and link utilization even when tolerance to delay violations is as small as 10 5 . We are interested in using our algorithm as a building block for more realistic scenarios where flows traverse multiple links served by rate based schedulers. It is shown in earlier research [18, 7, 9] that it is desirable to smooth a flow s traffic as much as possible at the ingress and perform bufferless multiplexing in the network s interior. Thus, in a packetized environment, a flow s per link delay budget will be smaller, consisting of only the packetization and non preemption delay ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proc. of IEEE INFOCOM'99, pages 1220--1230, March 1999.

....solving for in Cf( Gamma Bg( f( 14) where f( S i Gamma g( S i Gamma 2 ff = The optimum value for N is given by N = f( for satisfying (14) C. Relation to GPS and Buffer Management We may use the optimal partitioning results to set GPS weights (see [9], 14] for GPS weight computation using the methods of [10] and perform buffer management in an integrated fashion. Given the optimal (B i ; C i ) split, the GPS weight OE i for each class i connection (assuming per connection queueing) can be set as OE i = C i = N i C) If the queueing is ....

A. Elwalid and D. Mitra. Design of Generalized Processor Sharing Schedulers Which Statistically Multiplex Heterogeneous QoS Classes. In Proc. IEEE INFOCOM 1999.

....is assumed to be split among real time flows in proportion 12 to their input rates. In contrast, we assume a packet based model, an independent buffer space for each real time flow (virtual connections) and permit explicit delay violation probability bounds for each flow. Elwalid and Mitra[13] have proposed a scheme to provide statistical QoS guarantees in the GPS service discipline for two guaranteed traffic classes and one best effort class. Again a fluid traffic model was considered. Schemes for providing statistical QoS in networks using Earliest Deadline First (EDF) scheduling ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proc. of IEEE INFOCOM'99, pages 1220--1230, March 1999.

....bandwidths has emerged in the literature (see for example [23] 14] and the references therein) which permits packet delay distributions under FIFO scheduling to be determined. Recently, frameworks involving more sophisticated schedulers like Static Priority [15] and GPS [24] 26] 4] [7] have also been developed. In this paper, we focus on the EDF scheduling scheme, since it is known to provide the optimal delay performance [9] 17] in the deterministic environment, and can hence be expected to perform well in the statistical setting as well. Specifically, we develop a ....

A. I. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proceedings of INFOCOM '99, New York, NY, March 1999.

....[3] in this area derive probabilistic bounds on the delay of flows in a net work, while [44] discusses a conceptual framework for QoS assurances in a network. A scheme which is able to provide end4o end statistical QoS in a network of Generalized Processor Sharing (GPS) schedulers is developed in [14]. End to end statistical QoS guarantees are also provided by the scheme proposed in [25] which employs Traffic Controlled Rate Monotonic Priority Scheduling [24] Our approach was developed independently of [14] 25] and was first presented in [41] 42] In this article we extend our approach ....

.... QoS in a network of Generalized Processor Sharing (GPS) schedulers is developed in [14] End to end statistical QoS guarantees are also provided by the scheme proposed in [25] which employs Traffic Controlled Rate Monotonic Priority Scheduling [24] Our approach was developed independently of [14], 25] and was first presented in [41] 42] In this article we extend our approach and present it in a comprehensive manner. The GPS based scheme [14] is further refined in [22] Schemes for providing end4o end statistical QoS in a network of Earliest Deadline First (EDF) schedulers are ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor shar- ing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE Infocorn '99, pages 1220 1230, New York, NY, March 1999.

....et al. 6] have derived statistical delay bounds for traffic flows in a single link and network settings. They ap1 proximate the loss probability at a link using independent Bernoulli random variables. However they consider a fluid traffic model rather than a packetized model. Elwalid and Mitra[7] have proposed a scheme to provide statistical QoS guarantees in the GPS service discipline for two guaranteed traffic classes and one best effort class. Again a fluid traffic model was considered. Schemes for providing statistical QoS in networks using EDF scheduling were proposed by Andrews[8] ....

....during a new admission and does not account for the future impact of an incoming flow s traffic. We are also interested in using our algorithm as a building block for more realistic case where flows traverse multiple links served by rate based schedulers. It is shown in earlier research [6, 7, 19] that it is desirable to smooth a flow s traffic as much as possible at the ingress and perform bufferless multiplexing in the network s interior. Thus, in a packetized environment, a flow s per link delay budget will be smaller, consisting of only the packetization and nonpreemption delay ....

A. Elwalid and D. Mitra, "Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes," in Proc. of IEEE INFOCOM'99, pp. 1220--1230, March 1999.

....(CAREER) ANI 9903001, DMS 9971493, and ANI 0085955, and by an Alfred P. Sloan research fellowship. Sidi [23] and Starobinski and Sidi [22] Results on statistical end to end delay guarantees in a network have been obtained for speci c scheduling algorithms, such as EDF [20, 21] and GPS [13], and a class of coordinated scheduling algorithms [2, 17] Several researchers have considered 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. ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 122012.

....require per flow traffic processing in core nodes and do not exploit the coordination property. For work conserving service disciplines, a key issue is traffic distortion. Previous approaches include bounding this distortion [7] 11] 23] 35] and exploiting isolation properties of GPS servers [14], 19] 26] 38] While such techniques are important for their generality, we will show that they can be conservative in practice. In contrast, our work develops a general framework for end to end services in CMS networks. Our solution applies to the broad class of (workconserving) CMS servers, ....

A. Elwalid, D. Mitra, and R. Wentworth. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, March 1999.

....protocol is used to determine which packets can proceed and which packets must wait. Recently, there has been a great deal of work on the analysis of networks that are subject to worst case traffic patterns. This work can broadly be divided into two groups. In the sessionoriented model [2, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20], packets are injected into the network in sessions. Each session is associated with a fixed path and an injection rate. This model is appropriate for the study of networks where connections persist for long periods. In this paper we refer to it as the permanent session model. Alternatively, in ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, pages 1220 -- 1230, March 1999.

....arrivals are generated by stochastic processes. Each packet is allowed to miss its delay requirement with a small probability. In this framework of statistical multiplexing, more stringent delay requirements are schedulable. For examples, see Elwalid, Mitra and Wentworth [10] and Elwalid and Mitra [9]. 2 The Distributed Protocol 2.1 Overview Our protocol uses randomization and an earliest deadline first approach. For each session i packet, the protocol assigns deadlines D 1 ; D 2 ; DK i for each link that the packet goes through. In case of contention, a link services the waiting ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. Bell Labs. Technical Memorandum, May 1998.

....then the allocation of s appears to be straightforward. The situation becomes more complicated if we consider that network traffic could be bursty or self similar. Though there has been work on the weight assignment problem (see, e.g. 7] it is still considered quite challenging (see, e.g. [8]) One of the contributions of this work is that our algorithm yields the optimal set of weights which minimizes a cost function representing the queuing delays of mobile users. Before we give a mathematical description of this cost function in Section 2.3, let us cast an eye to how bandwidth is ....

A. Elwalid and D. Mitra, "Design of Generalized Processor Sharing Schedulers Which Statistically Multiplex Heterogeneous QoS Classes," in Proc. of INFOCOM'99, Piscataway, NJ, USA, 1999, pp. 1220--1230.

....then the allocation of # s appears to be straightforward. The situation becomes more complicated if we consider that network traffic could be bursty or self similar. Though there has been work on the weight assignment problem (see, e.g. 15] it is still considered quite challenging (see, e.g. [16]) Apart from the weight assignment problem, another important issue is the implementation of GPS: real world routers operate at the packet or cell level, whereas GPS assumes a fluid model of traffic. Hence, in practice GPS needs to be approximated by a Packet Fair Queueing (PFQ) algorithm [2] ....

....extends the algorithms of [2, 5] by addressing (1) 2) and (3) while maintaining the same complexity as the algorithm of [5] We remark that our scheme provides an exact algorithm for the weight assignment, unlike [15] which provides only a heuristic way of # assignment. Also, different from [16] which looks at the feasible region of weights for only two sessions, our scheme supports an arbitrary number of sessions. An approach different that ours is taken in [28] which proposes the adaptive modification of the session weights: the dynamic programming algorithm of [28] attempts to ....

A. Elwalid and D. Mitra, "Design of Generalized Processor Sharing Schedulers Which Statistically Multiplex Heterogeneous QoS Classes," in Proc. of INFOCOM'99, Piscataway, NJ, USA, 1999, pp. 1220--1230.

....[3] in this area derive probabilistic bounds on the delay of ows in a network, while [44] discusses a conceptual framework for QoS assurances in a network. A scheme which is able to provide end to end statistical QoS in a network of Generalized Processor Sharing (GPS) schedulers is developed in [14]. End to end statistical QoS guarantees are also provided by the scheme proposed in [25] which employs Trac Controlled Rate Monotonic Priority Scheduling [24] Our approach was developed independently of [14] 25] and was rst presented in [41] 42] In this article we extend our approach and ....

.... QoS in a network of Generalized Processor Sharing (GPS) schedulers is developed in [14] End to end statistical QoS guarantees are also provided by the scheme proposed in [25] which employs Trac Controlled Rate Monotonic Priority Scheduling [24] Our approach was developed independently of [14], 25] and was rst presented in [41] 42] In this article we extend our approach and present it in a comprehensive manner. The GPS based scheme [14] is further re ned in [22] Schemes for providing end to end statistical QoS in a network of Earliest Deadline First (EDF) schedulers are developed ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE Infocom '99, pages 1220-1230, New York, NY, March 1999.

....years there have been several studies on the performance of packet switched nodes that multiplex regulated trac, e.g. trac which conforms to known constraints imposed by leaky buckets. These studies suppose that the trac from the sources is adversarial to the extent permitted by the regulators [1, 3, 4, 5, 6, 7, 9, 8, 12, 11, 10, 13, 14, 16, 19, 20, 21, 23, 24, 25, 2, 26, 27]. Some of these studies assume that the multiplexer provides deterministic QoS guarantees (e.g. no packet loss) whereas others assume that multiplexer provides less stringent probabilistic QoS guarantees (e.g. a limit on the packet loss probability) In a recent paper, LoPresti et al. 16] ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneuos QoS classes. In Proceedings of IEEE Infocom '99, New York, NY, March 1999.

....[3] in this area derive probabilistic bounds on the delay of ows in a network, while [40] discusses a conceptual framework for QoS assurances in a network. A scheme which is able to provide end to end statistical QoS in a network of Generalized Processor Sharing (GPS) schedulers is developed in [12]. Our approach was developed independently of [12] and was rst presented in [36] 37] In this article we extend our approach and present it in a comprehensive manner. Schemes for providing end to end statistical QoS in a network of Earliest Deadline First (EDF) schedulers are developed in [1] ....

....the delay of ows in a network, while [40] discusses a conceptual framework for QoS assurances in a network. A scheme which is able to provide end to end statistical QoS in a network of Generalized Processor Sharing (GPS) schedulers is developed in [12] Our approach was developed independently of [12] and was rst presented in [36] 37] In this article we extend our approach and present it in a comprehensive manner. Schemes for providing end to end statistical QoS in a network of Earliest Deadline First (EDF) schedulers are developed in [1] 45] A comparison of the EDF based schemes and ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE Infocom '99, pages 1220-1230, New York, NY, March 1999.

....are exponentially bounded. Different bounds for exponentially bounded arrivals are derived by Yaron and Sidi [23] and Starobinski and Sidi [22] Results on statistical end to end delay guarantees in a network have been obtained for specific scheduling algorithms, such as EDF [20, 21] and GPS [13], and a class of coordinated scheduling algorithms [2, 17] Several researchers have considered 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. ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220--1230, New York, March 1999.

.... control conditions derived for various scheduling algorithms in the context of a deterministic service, e.g. 9] 25] 40] This is encouraging since only few results are available on statistical multiplexing of adversarial traffic which can consider nontrivial scheduling algorithms, e.g. [14], 21] Let us make a few remarks on the scope of this paper. The scheduling algorithms considered here are first come firstserved (FCFS) static priority (SP) and earliest deadline first (EDF) see footnotes 2 and 3 in Section V) The first two scheduling algorithms were selected because of ....

....number . Elwalid, Mitra, and Wentworth [15] consider a multiplexer which sees arrivals from regulated peak rate constrained leaky buckets. The adversarial traffic pattern used in [15] is a periodic on off source, which is known to maximize the overflow probability in a bufferless multiplexer. In [14], the solution approach of [15] is applied to the GPS [29] scheduling algorithm. The work of [15] has been extended by LoPresti, Zhang, Towsley, and Kurose [26] and by Rajagopal, Reisslein, and Ross [31] The question of the adversarial traffic pattern at a buffered multiplexer with regulators ....

A. Elwalid and D. Mitra, "Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes," in Proc. IEEE INFOCOM'99, New York, Mar. 1999, pp. 1220--1230.

....= X i 1 S i r j i p 2 i 2 i ffi i 2 S i Gamma 2 p (S i Gamma ) ff = X i j i T i P i S i : The optimum value for N is given by N = B f( for satisfying (14) C. Relation to GPS and Buffer Management We may use the optimal partitioning results to set GPS weights (see [9], 14] for GPS weight computation using the methods of [10] and perform buffer management in an integrated fashion. Given the optimal (B i ; C i ) split, the GPS weight OE i for each class i connection (assuming per connection queueing) can be set as OE i = C i = N i C) If the queueing is ....

A. Elwalid and D. Mitra. Design of Generalized Processor Sharing Schedulers Which Statistically Multiplex Heterogeneous QoS Classes. In Proc. IEEE INFOCOM 1999, pages 1220--1230, 1999.

....reasonably accurate estimates of the real schedulable 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 ....

....for real time traffic. In the following, we summarize the two frameworks that we are aware of that permit computation of the schedulable regions under GPS in the presence of dual leaky bucket regulated sources with heterogeneous statistical delay requirements: the first by Elwalid and Mitra [5] (and its extension [11] that is based on Chernoff approximations, and the other by Qiu and Knightly [16] that employs gaussian approximations. A.1 Elwalid Mitra (EM GPS) Framework The EM framework [5] considers two heterogeneous QoS classes (the extension to multiple classes is addressed in ....

[Article contains additional citation context not shown here]

A. I. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proceedings of INFOCOM '99, New York, NY, March 1999.

....protocol is used to determine which packets can proceed and which packets must wait. Recently, there has been a great deal of work on the analysis of networks that are subject to worst case traffic patterns. This work can broadly be divided into two groups. In the sessionoriented model [2, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20], packets are injected into the network in sessions. Each session is associated with a fixed path and an injection rate. This model is appropriate for the study of networks where connections persist for long periods. In this paper we refer to it as the permanent session model. Alternatively, in ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, pages 1220 -- 1230, March 1999.

....arrivals are generated by stochastic processes. Each packet is allowed to miss its delay requirement with a small probability. In this framework of statistical multiplexing, more stringent delay requirements are schedulable. For examples, see Elwalid, Mitra and Wentworth [10] and Elwalid and Mitra [9]. 2 The Distributed Protocol 2.1 Overview Our protocol uses randomization and an earliest deadline first approach. For each session i packet, the protocol assigns deadlines D 1 ; D 2 ; DK i for each link that the packet goes through. In case of contention, a link services the waiting ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. Bell Labs. Technical Memorandum, May 1998.

....has focused on worst case delay bounds. However, this approach necessarily leads to conservative bounds since they must allow for the possibility that bursts from all the sources incident to a server arrive at the server simultaneously. In another approach, known as statistical multiplexing [7] [6], 13] all the sources are assumed to be independent which implies that if there are many sessions then such simultaneous bursts are extremely unlikely. This enables us to derive much tighter delay bounds that hold with high probability. Equivalently, for a given set of delay bounds, the ....

....For this network problem we present a method for defining the deadlines at each hop that leads to a tractable analysis of delay bound violations. Towards the end of the paper we give numerical examples that illustrate our techniques and we compare the results with estimates for GPS obtained in [6], 13] We also examine how the choice of deadlines can affect the violation probabilities. In order to describe our results in more detail we must define our model. The Model We consider a network of servers. Each server e has a total processing rate C e . Packets are injected into the network ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, pages 1220 -- 1230, March 1999.

....formulating a statistical framework which employs a scheduling scheme more sophisticated than FIFO to guarantee heterogeneous delays to connections. A framework which provides statistical delays has been developed in [17] for priority scheduling; two frameworks which use GPS have been developed in [28,9], although the one in [28] assumes a rather specific source model, while the one in [9] is limited to two classes of traffic. In our case, we have chosen the EDF scheduling scheme, since it is known to provide the optimal delay performance [11,18] in the deterministic environment (as reviewed in ....

....FIFO to guarantee heterogeneous delays to connections. A framework which provides statistical delays has been developed in [17] for priority scheduling; two frameworks which use GPS have been developed in [28,9] although the one in [28] assumes a rather specific source model, while the one in [9] is limited to two classes of traffic. In our case, we have chosen the EDF scheduling scheme, since it is known to provide the optimal delay performance [11,18] in the deterministic environment (as reviewed in greater detail in Section 2) We therefore consider a switch operating at a constant ....

A. I. Elwalid, D. Mitra, Design of Generalized Processor Sharing Schedulers which Statistically Multiplex Heterogeneous QoS Classes, In Proceedings of INFOCOM '99, New York, NY, March 1999.

....equal to the average resource requirements for a single flow. Recent research on statistical QoS has attempted to exploit statistical multiplexing gain by taking advantage of knowledge about the characteristics of traffic sources, but without assuming knowledge of traffic source characteristics [5, 12, 14, 15, 20, 21, 23, 27, 29, 34, 35, 36]. Under a very general set of traffic assumptions, which are sometimes referred to as regulated adversarial traffic , one merely assumes that (1) traffic arrivals from a flow are constrained by a deterministic regulator, e.g. a leaky bucket, and (2) traffic arrivals from different flows are ....

....the same class have identical deterministic envelopes. At each node, flows from the same class have identical delay bounds. 2 A function f : 7 is subadditive if f(t1 t2 ) f(t1 ) f(t2) for all t1 ; t2 0: 4 These or similar assumptions are used in many recent work on statistical QoS [5, 12, 14, 15, 20, 21, 23, 27, 29, 34, 35, 36]. The assumptions are very general. Specifically, no assumptions are made on the distribution of flow arrivals, other than that each flow satisfies a worst case constraint. Within the constraints of assumptions (A1) A5) we consider arrival scnearios where each flow exhibits its worst possible ....

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220--1230, New York, March 1999.

....model provides a uniform basis for the description of real time traffic, and dualleaky bucket traffic descriptors are generally accepted in practical networks. Recently, statistical frameworks in the setting of regulated source models have been developed for priority scheduling [15] and GPS [9]. In our case, we have chosen the EDF scheduling scheme, since it is known to provide the optimal delay performance [12] 17] in the deterministic environment, and we expect the advantages to carry over to the statistical setting (indeed, a comparison study is performed in [25] to quantify the ....

....in the sense of imposing the maximum stress on network resources, thereby realizing the maximum delay violation probability. Identifying such a traffic pattern, however, is non trivial. In frameworks which employ buffer losses as the performance measure, numerous authors (e.g. 8] 18] [9]) have suggested the use of the extremal on off traffic model. In this model, a (p, #, #) dual leaky bucket regulated source switches on whenever its token bucket is full, and keeps generating traffic at the peak rate p till the bucket empties; at this point, it switches off and waits for the ....

A. I. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proceedings of INFOCOM '99, New York, NY, March 1999.

.... the National Science Foundation through grants NCR 9624106 (CAREER) ANI 9730103, and DMS 9971493, and by the New York State Center for Advanced Technology in Telecommunications (CATT) and that traffic from each flow is constrained by a deterministic regulator, e.g. by a leaky bucket [6] 9] [8], 11] 12] 14] 18] 19] 21] 22] 23] Henceforth, we will refer to traffic which satisfies these assumptions as regulated adversarial traffic. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, ....

.... conditions derived for various packet scheduling algorithms in the context of a deterministic service, e.g. 4] 17] 25] Note that only few results are available on statistical multiplexing of adversarial traffic, which can consider scheduling algorithms other than a simple multiplexer [8], 14] Related work to this paper are all attempts to consolidate the deterministic network calculus [4] with statistical multiplexing (e.g. 5] 2] 7] 12] 13] 14] 16] In addition, of particular relevance to this paper are all previous results on statistical multiplexing gain with ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220--1230, New York, March 1999.

....has focused on worst case delay bounds. However, this approach necessarily leads to conservative bounds since they must allow for the possibility that bursts from all the sources incident to a server arrive at the server simultaneously. In another approach, known as statistical multiplexing [7] [6], 13] all the sources are assumed to be independent which implies that if there are many sessions then such simultaneous bursts are extremely unlikely. This enables us to derive much tighter delay bounds that hold with high probability. Equivalently, for a given set of delay bounds, the ....

....For this network problem we present a method for defining the deadlines at each hop that leads to a tractable analysis of delay bound violations. Towards the end of the paper we give numerical examples that illustrate our techniques and we compare the results with estimates for GPS obtained in [6], 13] We also examine how the choice of deadlines can affect the violation probabilities. In order to describe our results in more detail we must define our model. The Model We consider a network of servers. Each server has a total processing rate . Packets are injected into the network ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, pages 1220 -- 1230, March 1999.

....a specific source model. Starting with the seminal work in [8] researchers have investigated the statistical multiplexing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g. by a leaky bucket [5] 8] [7], 9] 10] 12] 16] 17] 19] 20] 21] Henceforth, we will refer to traffic which satisfies these assumptions as regulated adversarial traffic. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, ....

.... conditions derived for various packet scheduling algorithms in the context of a deterministic service, e.g. 4] 15] 23] Note that only few results are available on statistical multiplexing of adversarial traffic, which can consider scheduling algorithms other than a simple multiplexer [7], 12] Related work to this paper are all attempts to consolidate the deterministic network calculus [4] with statistical multiplexing (e.g. 2] 6] 10] 11] 12] 14] In addition, of particular relevance to this paper are all previous results on statistical multiplexing gain with ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220-- 1230, New York, March 1999.

....a specific source model. Starting with the seminal work in [8] researchers have investigated the statistical multiplexing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g. by a leaky bucket [5] 8] [7], 9] 10] 12] 16] 17] 19] 20] 21] Henceforth, we will refer to traffic which satisfies these assumptions as regulated adversarial traffic. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, ....

.... conditions derived for various packet scheduling algorithms in the context of a deterministic service, e.g. 4] 15] 23] Note that only few results are available on statistical multiplexing of adversarial traffic, which can consider scheduling algorithms other than a simple multiplexer [7], 12] Related work to this paper are all attempts to consolidate the deterministic network calculus [4] with statistical multiplexing (e.g. 2] 6] 10] 11] 12] 14] In addition, of particular relevance to this paper are all previous results on statistical multiplexing gain with ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220-- 1230, New York, March 1999.

....schedulers. GPS promises substantial sharing as well as isolation and QoS guarantees [CRU91] PGA93] PGA94] KES96] KES97] SVA98a] These properties of GPS follow from the proper design of weights assigned to individual connections. Also, GPS with output regulation has been proposed in [EMI99] to accommodate best effort traffic by enforcing a peak rate on guaranteed service connections, which provides no better service to the latter than just what is guaranteed. Weight assignments in GPS are strongly driven by the traffic characteristics and QoS requirements. We restrict ourselves in ....

....no better service to the latter than just what is guaranteed. Weight assignments in GPS are strongly driven by the traffic characteristics and QoS requirements. We restrict ourselves in this paper to the worst case DualLeaky Bucket Regulated connections [EMW95] LZT97] RRR98] RRR99] [EMI99], in which connections are classified by their leaky bucket parameters. QoS is specified by the probability of violating the delay bound, where the probability and delay bound are QoS parameters associated with each connection class. Multiplexing gains are extracted by assuming that the regulated ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of Generalized Processor Sharing Schedulers Which Statistically Multiplex Heterogeneous QoS Classes. In Proc. IEEE INFOCOM'99, pages 1220--1230, 1999.

....schedulers. GPS promises substantial sharing as well as isolation and QoS guarantees [CRU91] PGA93] PGA94] KES96] KES97] SVA98a] These properties of GPS follow from the proper design of weights assigned to individual connections. Also, GPS with output regulation has been proposed in [EMI99] to accommodate best effort traffic by enforcing a peak rate on guaranteed service connections, which provides no better service to the latter than just what is guaranteed. Weight assignments in GPS are strongly driven by the traffic characteristics and QoS requirements. We restrict ourselves in ....

....no better service to the latter than just what is guaranteed. Weight assignments in GPS are strongly driven by the traffic characteristics and QoS requirements. We restrict ourselves in this paper to the worst case DualLeaky Bucket Regulated connections [EMW95] LZT97] RRR98] RRR99] [EMI99], in which connections are classified by their leaky bucket parameters. QoS is specified by the probability of violating the delay bound, where the probability and delay bound are QoS parameters associated with each connection class. Multiplexing gains are extracted by assuming that the regulated ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of Generalized Processor Sharing Schedulers Which Statistically Multiplex Heterogeneous QoS Classes. In Proc. IEEE INFOCOM'99, pages 1220--1230, 1999.

....reflect costs. In the case of perfect competition prices will be dictated by costs, and therefore we think that then prices agree with effective bandwidths: P (T spec ) E(T spec ) If there are multiple QoS levels possible, the region R is bounded by multiple linear constraints as in Figure 1 [4, 5, 6, 22], that depend on the queuing mechanism in the switch or router. In this situation there is no notion of effective bandwidth anymore; the shadow prices given by the bottleneck constraint will determine the prices [15] But again, in the situation of many suppliers, the prices will be determined by ....

....first and second constraints, respectively. Note that e (j) i may be interpreted to be the effective bandwidth for Class i calls when the jth constraint is binding. Approximations to the admissible regions in which the boundaries have linear segments arise in various contexts, see for example [4, 5, 6, 7, 22]. The special case wherein e (1) 2 = 0 is of particular interest, since it arises for the priority system shown in Figure 1(b) see [4, 5] In this system Class 1 traffic has strict priority over Class 2, i.e. the contents of the buffer that is used exclusively for Class 1 traffic has priority ....

[Article contains additional citation context not shown here]

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proc. IEEE INFOCOM'99, pages 1220--1230, 1999.

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A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM '99, pages 1220 -- 1230, March 1999.

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A. Elwalid and D. Mitra, "Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes," in Proceedings of IEEE INFOCOM '99, March 1999, pp. 1220 -- 1230.

No context found.

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proc. of IEEE INFOCOM'99, pages 1220--1230, March 1999.

No context found.

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proc. of IEEE INFOCOM'99, pages 1220--1230, March 1999.

No context found.

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes. In Proceedings of IEEE INFOCOM'99, pages 1220--1230, New York, March 1999.

No context found.

A. Elwalid and D. Mitra, "Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes," in Proc. IEEE INFOCOM, 1999, pp. 1220--1230.

No context found.

A. Elwalid and D. Mitra. Design of generalized processor sharing schedulers which statistically multiplex heterogeneous qos classes. In Proc. of IEEE INFOCOM, pages 1220--1230, March 1999.

No context found.

A. Elwalid and D. Mitra. Design of Generalized Processor Sharing Schedulers which Statistically Multiplex Heterogeneous QoS Classes. Proc. of IEEE INFOCOM'99 , March 1999, pp. 1220-1230.

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