J.-Y. Le Boudec. Application of Network Calculus To Guaranteed Service Networks. IEEE Trans. on Information Theory, 44(3), May 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... process A (with A(t) being the cumulative number of arrivals by time t) is f upper constrained for some function f if A(t) A(s) f(t s) s t: 1) Based on such a trac characterization, a ltering theory is recently developed for deterministic trac regulation and service guarantees (see e.g. [5, 1, 14, 21]) The ltering theory is developed under the (min; algebra, where one replaces the usual addition by the min operator and the usual multiplication by the addition operator. As in the classical linear system theory, the new ltering theory treats an arrival process A (or a departure process B) ....

....in Lemma 3.10 are without segmentation and reassembly delay. The case with segmentation and reassembly delay can be treated by the O d server discussed in the next section. 4 Service guarantees for marked point processes 4. 1 g server In this section, we extend the concept of service curve in [25, 5, 1, 21] to guarantee deterministic quality of service for marked point processes. De nition 4.1 (g server) A server is called a g server (g 2 F inc ) for an input marked point process = if its output marked point process ; satis es L g, i.e. m) g(L(n) L(m) ....

[Article contains additional citation context not shown here]

J.Y. Le Boudec, \ Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, Vol. 44, pp. 1087-1096, 1998.

....available service. Definition 1 Given an arrival process A, an effective service curve is a non negative real valued function that satisfies for all t 0, D(t) A S By letting 0, effective service curves recover the service curves of the deterministic calculus with probability one [2]. We also use a probabilistic measure for the traffic arrivals, called effective envelopes from [28] Definition 2 An effective envelope for an arrival process A is a non negative function G such that for all t and A[t ] Gamma A[t] G 1 Gamma : 3) Simply, an effective ....

....1 Gamma : 5) 2. Backlog Bound: For any time t 0, 3. Delay Bound: If d 0 satisfies max T ( Gamma S (d ) 0, then for any time t, By setting s = b = g = 0, we recover the corresponding statements of the deterministic network calculus as presented in [2, 6, 1]. Proof. First, we prove that G is an effective output traffic envelope. Fix t; 0. D[t ] Gamma D[t] G (8) A[t ] Gamma A[t Gamma x] G ( x) 9) A[t ] Gamma A[t Gamma x 1 ] G ( x 1 ) 10) 11) In Eqn. 8) we have ....

J.-Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, 44(3):1087--1096, October 1998.

....from the i port is bounded above by d(s i;j oe i;j ) r i;j e (assuming FIFO for the traffic A i;j ) where dxe is the smallest integer that is not less than x. We note that our guarantee in Theorem 3 is a very strong one and it implies the usual service curve guarantee in [24] 6] 1] [16]. Such a strong guarantee allows us to provide per flow QoS for flows aggregated within A i;j via the Service Curve based Earliest Deadline (SCED) policy in [24] 10] 100 throughput: Suppose that the traffic A i;j is now a stationary and ergodic stochastic process with the mean rate r i;j , ....

J.Y. Le Boudec, " Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, Vol. 44, pp. 1087-1096, 1998.

....uses this service, the application s packets have guaranteed bounds on delays with no packet loss. The guaranteed QoS service is a natural outgrowth of a body of research in the area of delay bound calculations for queueing networks with regu lated traffic [7] 8] 34] 35] 58] 57] 18] [27], 4] 26] It can be argued, however, that guaranteeing absolutely no packet loss is overly conservative for continuous media applications, which can typically tolerate a small rate of loss. In fact, users may not perceive any quality degradation when there is infrequent packet loss, especially ....

J.Y. LeBoudec. Applications of network calculus to guaranteed service networks. IEEE Transactions on Information Theory, 44(3):1087 1096, May 1998.

.... allocation strategies could be based on the average rate, or on the value of the equivalent bandwidth, that is a scalar quantity, ranging from the average rate rs to the peak rate Ps of the flow, that depends on the traffic characteristics and the requested performance (see, e.g. 9] 10][11]) In conclusion, the value orBres is such that rs Br Ps. Charging the services with pre allocated network resources is a complex task. We can analyze this issue from different viewpoints. First of all, once the traffic and performance descriptors are defined, the amount of reserved resources ....

J.Y. Le Boudec, "Application of Network Calculus to guaranteed service networks," IEEE Transactions on Information Theory, 44(3), pp. 1087-1096, May 1998.

....misses and 2) Whose traffic is bursty. The statistical multiplexing gain is known to be substantial, especially in Variable Bit Rate (VBR) applications such as MPEG coded video. While much work has been done to realize determi nistic real time communication over multihop networks [9] 11] [12], much less has been done to provide statistical real time guarantees over multihop networks. Ferrari and Verma [4] introduced the concept of statistical performance guarantees and proposed a method for statistical real time communication in WANs using the Earliest Due Date (EDD) packet scheduling ....

J. LeBoudec, "Applications of Network Calculus to Guaranteed Service Networks," IEEE Trans. Information Theory, vol. 44, no. 3, pp. 1087-1096, May 1998.

....presented above encompasses the case of an IP source declared with a TSPEC and the case of a VBRATM source. An ATM VBR source is constrained by a pair of GCRA algorithms with parameters (T , #) and (T # , # # #) Let # be the cell size in bits. A minimal arrival curve # for a VBR source is (see [15]) #(t) min(p t b p , R t b M ) where p = is the peak rate of the source in bit s, R = T # is the sustainable rate in bit s, b p = p # # corresponds to the bits v(a,b) a,b) h b Fig. 3. Upper bounds on backlogs and delays cell jitter (in bits) and b M = # # R ....

J.-Y. Le Boudec, "An application of Network Calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, no. 3, May 1998.

....S has thus one QoS constraint, which is its maximum end to end delay requirement (the traffic management scheme ensures a zero loss rate) 3.2 Deterministic Effective Bandwidth Central to our proposal is the concept of deterministic effective bandwidth. It has been first introduced by Le Boudec [11] in the context of the Network Calculus [12] The Tokens rate R Token bucket depth M peak rate p Source Fig. 1. Leaky bucket controller time interval t (t) Q b a Fig. 2. Upper bound on backlog and virtual delay Network Calculus provides deterministic bounds on end to end delays and ....

....bounds on end to end delays and backlogs. A source is modeled through an arrival curve that represents an upper bound on the volume of traffic it can send during any time interval # . In the case of a leaky bucket constrained source S with parameters (p, R, M) an arrival curve # is (see [11]) #(#) min p#, R# M , # 0 (4) Servers are modeled through a service curve representing a lower bound on the service they are able to provide during some time intervals. For instance, a service curve # for a FIFO server (and, more generally, for any server implementing a ....

[Article contains additional citation context not shown here]

Le Boudec, J.Y: An application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory 44 (1998)

....powerful tools for reasoning about delay and backlog in a network with service guarantees to individual traf c ows. Using the notion of arrival envelopes and service curves [11] several recent works have shown that delay and backlog bounds can be concisely expressed in a min plus algebra [1, 5, 8]. However, the deterministic view of traf c only provides worst case bounds and does not take advantage of statistical multiplexing gain. The problem of trying to exploit the resource savings of statistical multiplexing while preserving the elegant formalism of the network calculus has been the ....

....A S(t) 5) A maximum service curve for a ow is a function S which speci es an upper bound on the service given to a ow such that, for all t 0, D(t) A S(t) 6) The following theorem summarizes some key results of the deterministic network calculus. These results have been derived in [1, 5, 8]. We follow the notation used in [1] A proof of the theorem is included in Appendix A. Theorem 1 Deterministic Network Calculus. Given a ow with arrival envelope A and with minimum and maximum service curves S and S, the following hold: 1. Output Envelope: The function D S is an ....

J. Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, 44(3):10871097, May 1998.

....are often referred to as (#, #) regulators and a very powerful formalism to study worst case delay bounds called network calculus has been developed for such inputs. The systematic approach goes back to the seminal work of Cruz [2] 3] but has been greatly extended in the works of Le Boudec [4] and Chang [5] The recent monograph of Chang [6] gives an excellent account of the approach. Network calculus is essentially a deterministic worst case approach. An advantage of the approach is that it readily leads to a calculus valid for obtaining an end to end worst case delay bound knowing ....

J-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Trans. Inform. Theory, vol. 44, no. 3, pp. 1087--1096, 1998.

....per flow basis. While the lack of reshaping implies a progressive alteration of the statistical properties of each micro flow along the path, some QoS guarantees are still provided to each micro flow while operating only on behavior aggregates in core routers. Using the so called network calculus [3, 4, 5, 6, 7, 8] bounds on delay and loss are derived within each network node. Depending on the processing and signaling load that we are willing to tolerate in core routers, we define three alternate approaches. The first one is based on traffic measurements at core routers and CAC at edge routers, where ....

....with statistical traffic sources. They allow us to compute in a straightforward way the buffer and bandwidth resources required by an aggregated flow. To compute the equivalent parameters, a variety of models have been proposed in the literature (see [22] for a survey) Many of these [23, 3] produce similar results (albeit via different approaches) If we select a particular pair (b 0 ; c 0 ) satisfying pre defined criteria (i.e. maximum queueing delay) this pair represents the equivalent buffer and the equivalent capacity of the regulated stream. The selection of this pair starts ....

[Article contains additional citation context not shown here]

J-Y Le Boudec, Application of Network Calculus to Guaranteed Service Networks, IEEE Transactions on Information Theory, Vol. 44, no.3, May 1998.

....be generalized to a multiple leaky bucket [9] A i (t) min 1# k# K # i,k # i,k t . Multiple leaky buckets capture the notion of multiple transmission rates (over different periods of time) and provide a parsimonious way of describing real world traffic sources (see, e.g. 9] and [10] for an algorithm to determine the parameters of the leaky buckets) From a practical point of view, leaky buckets are attractive as traffic policing mechanisms because they can implemented by just a few lines of C or assembly code, and have been incorporated in the ATM standard (in the GCRA ....

....efficient bandwidth utilization, because it allows time varying service guarantees, which have the potential to meet the needs of multirate users and applications. From a theoretical point of view, SCs possess two important properties: i) rate based schedulers can be cast into the SC framework [10], and (ii) the Earliest Deadline First (EDF) algorithm can be modeled using service curves (recall that the importance of property (ii) stems from the proven optimality of EDF Deterministic Time Varying Packet Fair Queueing 77 in admitting the maximum number of sessions given delay bounds and ....

[Article contains additional citation context not shown here]

J.Y. LeBoudec, "Application of Network Calculus to Guaranteed Service Networks," IEEE Trans. on Information Theory, vol. 44, no. 3, 1998, pp. 1087--1096.

....turns out to be non trivial (Section 4) The analysis shows that in some cases the delays may be considered as additive. In the case where this property does not hold, a bound is derived which could allow some kind of decomposition between stages. 2. NETWORK CALCULUS TOOLS Network Calculus [2 5] provides an easy way to describe sources upper bounded with deterministic constraints and network elements (multiplexers, switches, and to derive end to end bounds on delay and queues backlog. We present hereafter the basic ideas of this method on which the paper relies. 2.1. Sources and ....

J.-Y. Le Boudec. An application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, May 1998.

No context found.

J.-Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory, 44:1087--1096, May 1998.

No context found.

J.-Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory, 44:1087--1096, May 1998.

No context found.

J. Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Trans. Inform. Theory, vol. 44, pp. 1087--1096, May 1998.

No context found.

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....destined to a particular output from one or more inputs. PSRG can be viewed as a characterization of how far a node differs from an ideal node that would implement Generalized Processor Sharing (GPS) 3] Previous abstractions such as Guaranteed Rate Clock (GRC) 4] or service curves [5] 6] [7] capture how much a node can be late with respect to GPS. PSRG goes one step further and captures how much a node is either late or early with respect to GPS, thus providing a better way of defining a node as being approximately GPS . For a discussion of PSRG versus GRC, see [1] and comment 2 ....

....BOUND FOR ARRIVAL CURVE CONSTRAINTS In this section we give a bound on delay which does not depend on the queue size, but on an arrival curve constraint. It is well known that such a constraint can be used to derive delay bounds, assuming that the node offers a service curve guarantee [9] 6] [7]. If a node offering a packet scale rate guarantee is FIFO, it follows from [11] Theorem 7.3.1, that it also offers a rate latency service curve, from which a delay bound can be derived. In this section, we show that the same delay bound holds in the absence of FIFO assumption. Contrary to the ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....results focus on work conserving queuing systems that offer a constant service rate. However, in practice, the network nodes are often not work conserving and do not offer the constant service rate at each instant of time. It turns out that many network nodes satisfy a service curve property [13] [14], 15] 16] 17] In a deterministic context, a service curve property, with service curve , means that at any time , the total output traffic observed in at least equal to for some total input traffic in . Thus, it is of a practical importance to derive ....

....independent. A2) For all has as an arrival curve, i.e. for all ) KJ ( L K1L M NO is a non negative, wide sense increasing function P BQR . We assume, without loss of generality, that is sub additive, i.e. S J ( T ( for all GI [14], 15] 16] 17] A3) For each ) 8 KJ V (LW L (1) A ,X 51200 6 5 [fe [ gY8hji [ k l b c [me [ The last equality is by sub additivity of [20] A4) There exists a sequence of random points ( the construction points ) jQRnAopF QRnCoq HQPnrlsJt ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service network," IEEE Trans. on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....delay is due to queuing in, for example, guaranteed rate schedulers. The relationship between R # and R # cannot be known exactly by the sending side, because it depends to some extend on tra#c conditions; however, the guarantee provided by the network can be formalized by a condition of the form [6, 7] #t # #s # t, such that R # (t) R # (s) #(t s) 1.1) In the condition, # is a function, called the network service curve, which is negotiated during the reservation setup phase. For example, the Internet guaranteed service assumes the form #(t) #(t L) where L is called the ....

....gives the smallest value of the playback delay that can be obtained by any smoothing strategy satisfying the arrival curve constraint #, given that the network service curve guaranteed to the flow is #. The minimum delay D can be better interpreted using the concept of horizontal deviation [7], which we now recall. Figure 2 gives an intuitive definition. Definition 2.1. For two functions # and #, define the horizontal deviation h(#, #) by h(#, #) sup s#0 (inf T : T 0 and #(s) #(s T ) 2.8) It is shown in [12] that the value of the minimum playback delay D in the ....

[Article contains additional citation context not shown here]

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, , no. 44, pp. 1087--1096, May 1998.

....results focus on work conserving queuing systems that offer a constant service rate. However, in practice, the network nodes are often not work conserving and do not offer the constant service rate at each instant of time. It turns out that many network nodes satisfy a service curve property [13] [14], 15] 16] 17] A service curve property, with service curve , means that at any time , the total output traffic observed in is at least equal to for some , where is the total input traffic . Thus, it is of a practical importance to derive ....

....For all has as an arrival curve, i.e. for all : DZ = C 7 ]7 where = is a non negative, wide sense increasing function 1 such that N . We assume, without loss of generality, that is sub additive, i.e. V DZ = a P = G [14], 15] 16] 17] A3) For each : c Ded = 1) gf 50 lhcm n i o#p = The last equality is by sub additivity of [21] A4) There exists a sequence ( the construction points ) 78787 q)r W qIr T sq p t q T q W s78787 such thatfch ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service network," IEEE Trans. on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....by J unchanging leaky buckets, but whose initial conditions (initial bucket levels and initial buffer content) are not zero. We call this model a leaky bucket shaper with non zero initial conditions. We find the input output characterisation of this model# for this we use min plus algebra ( 12] [13], 6] 11] Then we apply this iteratively to derivetheinput characterisation of a time varying leaky bucket shaper (Section 2) The RVBR Service and its application to RSVP We derivetheinput output characterisation of the RVBR service as a special case of the time varying leaky bucket shaper. ....

.... Guaranteed Service [19] is matter of further study) Previous results and work breakdown Recent researchhasintroduced an output characterisation of shaper systems in terms of the network calculus theory [20]and[11] This was used in several papers to characterise the VBR service [13] and [6] The optimisation problem for the VBR service was studied in [5] 6] Renegotiation was first specified in ATM networks for CBR class service [21] and only very recently to VBR class service [14] In the reservation protocol for Integrated Services Internet networks, namely RSVP, a ....

[Article contains additional citation context not shown here]

J.-Y. Le Boudec, "Application of Network Calculus To Guaranteed Service," Technical Report 97/251, DI-EPFL, CH-1015 Lausanne, Switzerland, November 1997.

....of variable length packets. While the original work by Cruz in [1] defines a leaky bucket regulator as a system handling variable length packets, the theory of regulators (which we now call greedy shapers ) that was later developed by Agrawal, Chang, Cruz, Le Boudec, Okino and Rajan [2] 3] [4], 5] either focused explicitly on flows of constant size packets (namely ATM) or applies only to fluid systems. We say that we have bit by bit greedy shapers. The theory of bit by bit greedy shapers is extremely powerful (in its context) it allows to establish a number of invariance or ....

....if a regulated flow is passed through a second regulator, then the final output keeps the arrival curve constraint imposed by the first regulator. In the discrete time setting, the regulator is exactly a buffered leaky bucket controller. The concept was further generalized independently in [3] [4], 5] under various names. In the context of this paper, we call them bit by bit greedy shapers. Given some wide sense increasing function #, a greedy shaper takes some flow as input and forces its output to be # smooth; it delays the input data in a buffer, whenever sending data would violate ....

[Article contains additional citation context not shown here]

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....which we explain in this section. In short, network calculus can be viewed as the application of min and max algebra to flow problems. It was pioneered by Chang [14] and Cruz [15] 16] and found its final form in subsequent work by the same authors and by Agrawal, Le Boudec and Rajan [17] [18], 19] A comprehensive treatment can be found in two textbooks [5] 6] We first introduce network calculus on an example, then we review applications to integrated services, differentiated services, and the computation of minimum playback delay for video sequences. A. Introductory Example: The ....

....is that routers may implement very different scheduling strategies. This is solved with the concept of service curve.It was introduced by Parekh and Gallager [7] and Cruz [23] in a restricted sense, then independently in its final form by Agrawal, Chang, Cruz, Le Boudec, Okino and Rajan [19] [18], 17] It is defined as follows. Consider a system and a flow through with input and output function R and R # . Let #(t) be a non negative wide sense increasing function We say that offers to the flow a service curve # if and only if # (4) In practical terms, it means that for any ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....by J unchanging leaky buckets, but whose initial conditions (initial bucket levels and initial buffer content) are not zero. We call this model a leaky bucket shaper with non zero initial conditions. We find the input output characterisation of this model# for this we use min plus algebra ( 4] [14], 8] 13] Then we apply this iteratively to derive the input characterisation of a time varying leaky bucket shaper (Section 2) The RVBR Service and its application to RSVP Wederive the input output characterisation of the RVBR service as a special case of the time varying leaky bucket ....

....and used to compute the optimal p, r and b to generate the new Tspec. Previous results and work breakdown Recent researchhasintroduced an output characterisation of shaper systems in terms of the network calculus theory [5] and [13] This was used in several papers to characterise the VBR service [14]and [8] The optimisation problem for the VBR service was studied in [7] 8] Renegotiation was first specified in ATM networks for CBR class service [21] and only very recently to VBR class service [15] In the reservation protocol for Integrated Services Internet networks, namely RSVP, a source ....

[Article contains additional citation context not shown here]

J.-Y. Le Boudec, "Application of Network Calculus To Guaranteed Service," Technical Report 97/251, DI-EPFL, CH-1015 Lausanne, Switzerland, November 1997.

....destined to a particular output from one or more inputs. PSRG can be viewed as a characterization of how far a node differs from an ideal node that would implement Generalized Processor Sharing (GPS) 3] Previous abstractions such as Guaranteed Rate Clock (GRC) 4] or service curves [5] 6] [7] capture how much a node can be late with respect to GPS. PSRG goes one step further and captures how much a node is either late or early with respect to GPS. Note that PSRG does not imply that the node is workconserving; indeed, it is intended to model complex nodes, such as Internet routers, ....

....BOUND FOR ARRIVAL CURVE CONSTRAINTS In this section we give a bound on delay which does not depend on the queue size, but on an arrival curve constraint. It is well known that such a constraint can be used to derive delay bounds, assuming that the node offers a service curve guarantee [8] 6] [7]. If a node offering a packet scale rate guarantee is FIFO, it follows from [10] Theorem 7.3.1, that it also offers a rate latency service curve, from which a delay bound can be derived. In this section, we show that the same delay bound holds in the absence of FIFO assumption. Contrary to the ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....approach to the end to end analysis of packet flows in connection oriented networks, IEEE ACM Trans. Networking, vol. 6, no. 4, pp. 422 431, Aug. 1998. II. IMPROVING THE BOUNDS IN [2] Our starting point is a number of results, which we collectively refer to as network calculus [3] [1], 2] 6] These results give deterministic bounds on buffer and delay, assuming input processes are limited by some arrival curves, and the service element offers some form of service guarantee. We say that a flow admits a function ff(t) as arrival curve if the number of cells that can be ....

....number of cells of flow r, which have entered node e and did not depart yet. The strict service curve property was defined for example in [5] and is an abstraction of the generalized processor sharing concepts introduced in [5] The following theorem is a new variant of classical results in [3] [1], 2] and [6] Theorem 2.1: Consider a node that receives an input connection, with a buffer large enough to avoid discarding data. Assume that the node offers a strict service curve fi and that the input connection has an arrival curve ff: Assume that ff(u0 ) fi(u0 ) for some u0 0: Then the ....

[Article contains additional citation context not shown here]

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Trans. Inform. Theory, vol. 44, pp. 1087--1096, May 1998.

.... a node offers to the aggregate of all EF traffic a service curve , i.e. for all there exists 4Q6 8 N 4RM 8 35476= SM 8 (1) 4Q6 is the output data from the node on 9 T 6UF 476 is the data which is accepted for service (i.e. not lost) at the input of the node during [4] 5] [6]. Second, in Section IV, we use another property of PSRG, namely, the fact that delay can be bounded from backlog. In addition, we do the following assumptions. A2) We suppose EF traffic inputs (micro flows) at the network ingress points are mutually independent. This assumption is also made in ....

....0 0.2 0.4 0.6 0.8 1 HET1 HET(a) a=0.6 0 0.2 0.4 0.6 0.8 1 HET1 HET(a) a=0.7 0 0.2 0.4 0.6 0.8 1 HET1 HET(a) a=0.8 0 0.2 0.4 0.6 0.8 1 HET1 HET(a) a=0.9 Fig. 3. A comparison of backlog bounds HET(a) x line) 3) solid light line) and HOM (Theorem 3 in [6]) solid bold line) All individual flows have identical leaky bucket regulators; homogeneous case. respectively as HET(a) HET(b) and HET(c) We suppose two traffic classes each consisting of 50 flows; thus r 1 . Class1 4 a (c 8 leaky bucket regulated; respectively, class 2 ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087-- 1096, May 1998.

....destined to a particular output from one or more inputs. PSRG can be viewed as a characterization of how far a node differs from an ideal node that would implement Generalized Processor Sharing (GPS) 3] Previous abstractions such as Guaranteed Rate Clock (GRC) 4] or service curves [5] 6] [7] capture how much a node can be late with respect to GPS. PSRG goes one step further and captures how much a node is either late or early with respect to GPS. PSRG is related to the concept of adaptive service curve, another abstract node model introduced in [8] 9] It is shown in [10] ....

....BOUND FOR ARRIVAL CURVE CONSTRAINTS In this section we give a bound on delay which does not depends on the queue size, but on an arrival curve constraint. It is well known that such a constraint can be used to derive delay bounds, assuming that the node offers a service curve guarantee [8] 6] [7]. If a node offering a packet scale rate guarantee is FIFO, it follows from [10] Theorem 7.3.1, that it also offers a rate latency service curve, from which a delay bound can be derived. In this section, we show that the same delay bound holds in the absence of FIFO assumption. Contrary to the ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

.... to the aggregate of all EF traffic a service curve , that is 758 # (1) where ( is the output data from the node on ( and ( is the data which is accepted for service (i.e. not lost) at the input of the node during ( 3] 4] [5]. The most recent definition of EF PHB (Def. IV.1 in [6] or DEF 1 in [1] referred to as Packet Scale Rate Guarantee (PSRG) implies the service curve property, where has the form ( 0 1 32 54 (this is called a rate latency service curve, with rate and latency 2 ) A special case of ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

No context found.

J.-Y. Le Boudec, `Application of Network Calculus To Guaranteed Service Networks,'IEEE Trans. Information Theory, vol 44(3), May 1998.

....some of the problems caused by traffic regulation for flows of variable length packets. While the original work by Cruz in [1] defines a leaky bucket regulator as a system handling variable length packets, the theory of regulators (which we now call greedy shapers ) that was later developed [2, 3, 4, 5] either focused explicitly on flows of constant size packets (namely ATM) or applies only to fluid systems. The theory of greedy shapers is extremely powerful (in its context) it allows to establish a number of invariance or optimality properties; for example, re shaping keeps original arrival ....

....if a regulated flow is passed through a second regulator, then the final output keeps the arrival curve constraint imposed by the first regulator. In the discrete time setting, the regulator is exactly a buffered leaky bucket controller. The concept was further generalized independently in [3, 4, 5] under the name of greedy shaper. Given some wide sense increasing function #, a greedy shaper takes some flow as input and forces its output to be # smooth; it delays the input data in a buffer, whenever sending data would violate the constraint #, but outputs them as soon as possible. This ....

[Article contains additional citation context not shown here]

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

....destined to a particular output from one or more inputs. PSRG can be viewed as a characterization of how far a node differs from an ideal node that would implement Generalized Processor Sharing (GPS) 3] Previous abstractions such as Guaranteed Rate Clock (GRC) 4] or service curves [5] 6] [7] capture how much a node can be late with respect to GPS. PSRG goes one step further and captures how much a node is either late or early with respect to GPS. Note that PSRG does not imply that the node is workconserving; indeed, it is intended to model complex nodes, such as Internet routers, ....

....BOUND FOR ARRIVAL CURVE CONSTRAINTS In this section we give a bound on delay which does not depend on the queue size, but on an arrival curve constraint. It is well known that such a constraint can be used to derive delay bounds, assuming that the node offers a service curve guarantee [8] 6] [7]. If a node offering a packet scale rate guarantee is FIFO, it follows from [10] Theorem 7.3.1, that it also offers a rate latency service curve, from which a delay bound can be derived. In this section, we show that the same delay bound holds in the absence of FIFO assumption. Contrary to the ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087--1096, May 1998.

.... to the aggregate of all EF traffic a service curve # , i.e. for all # there exists # # # such that # # # # # # # # # # # # # # # # (1) is the output data from the node on # # # is the data which is accepted for service (i.e. not lost) at the input of the node during # # # # # [4] 5] [6]. Second, in Section IV, we use another property of PSRG, namely, the fact that delay can be bounded from backlog. In addition, we do the following assumptions. A2) We suppose EF traffic inputs (micro flows) at the network ingress points are mutually independent. This assumption is also made in ....

....0 0.2 0.4 0.6 0.8 1 HET1 HET(a) #=0.6 0 0.2 0.4 0.6 0.8 1 HET1 HET(a) #=0.7 0 0.2 0.4 0.6 0.8 1 HET1 HET(a) #=0.8 0 0.2 0.4 0.6 0.8 1 HET1 HET(a) #=0.9 Fig. 3. A comparison of backlog bounds HET(a) x line) 3) solid light line) and HOM (Theorem 3 in [6]) solid bold line) All individual flows have identical leaky bucket regulators; homogeneous case. of light and heavy loaded node, respectively. The bounds are computed as the infimum over uniform partition of # # # # # ( # # # # # # # , for # # # # # # # # # ) In Fig. 2 (two upper graphs) we ....

J.-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Transactions on Information Theory, vol. 44, pp. 1087-- 1096, May 1998.

No context found.

J.-Y. Le Boudec. Application of Network Calculus To Guaranteed Service Networks. IEEE Trans. on Information Theory, 44(3), May 1998.

No context found.

J.-Y. Le Boudec, Application of Network Calculus to Guaranteed Service Networks, IEEE Transactions on Information Theory, Vol. 44, No. 3: 1087--1096, May 1998.

No context found.

J.-Y. Le Boudec. An application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory, May 1998.

No context found.

J.-Y. Le Boudec. An application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, May 1998.

No context found.

J.-Y. Le Boudec, An application of network calculus to guaranteed service networks, IEEE Transactions on Information Theory , (May 1998).

No context found.

J.-Y. Le Boudec. An application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, May 1998.

No context found.

J. Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, 44(3):1087--1097, May 1998.

No context found.

J. Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE/ACM Transactions on Information Theory, 44(3):1087--1097, May 1998.

No context found.

J-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Trans. Inform. Theory, vol. 44, no. 3, pp. 1087--1096, 1998.

No context found.

J-Y. Le Boudec, "Application of network calculus to guaranteed service networks," IEEE Trans. Inform. Theory, vol. 44, no. 3, pp. 1087--1096, 1998.

No context found.

Jean-Yves Le Boudec. Application of Network Calculus To Guaranteed Service Networks. IEEE/ACM Transactions on Information Theory, 44(3):1087--1096, May 1998.

No context found.

J.-Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory, 44(3):1087--1096, May 1998.

No context found.

J.-Y. Le Boudec, Application of Network Calculus to Guaranteed Service Networks, IEEE Transactions on Information Theory, Vol. 44, No. 3: 1087--1096, May 1998.

No context found.

J-Y. Le Boudec. Application of network calculus to guaranteed service networks. IEEE Trans. Inform. Theory, 44(3):1087--1096, 1998.

No context found.

J. Le Boudec. Application of network calculus to guaranteed service networks. IEEE Transactions on Information Theory, 44(3):1087--96, May 1998.

No context found.

J.Y. Le Boudec and G. Hebuterne. Application of network calculus to guaranteed service networks. IEEE/ACM Trans. on Networking, 8(3), 1998.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC