M. Vojnovic and J. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. IEEE Transactions on Communications, 51(5), Jan. 1991.  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. ....

....idle time before t by t = maxf t : B( 0g : 30) Our assumption that B(0) 0 guarantees that 0 t t. In this section, we bound the time scale T in terms of a bound on the busy period. Alternatively, one can derive a bound on T from bounds on the backlog, e.g. using those derived in [24]. Lemma 1 For an arrival process A and a workconserving scheduler with a constant rate C , assume that =1 P r fA[t ] Gamma A[t] Cg 1 : 31) For 2 (0; 1) choose T P r fA[t ] Gamma A[t] Cg : 32) Then T is a probabilistic bound on the busy period, ....

M. Vojnovic and J.-Y. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. IEEE Transactions on Communications, October 2002. To appear.

....and are generally small, e.g. # 1 ,# 2 =10 9 . If one is interested in statistical bounds on delay, backlog, or loss to the aggregate as a whole (as opposed to bounds for a single flow) we refer to the rich literature on multiplexed regulated traffic e.g. 3] 8] 12] 13] 15] [18], 19] Generally, these results focus on the analysis of a single node, and do not consider a multi node network. The remaining sections of this paper are structured as follows. In Section II, we review relevant results from the statistical network calculus in terms of effective service curves, ....

M. Vojnovic and J.-Y. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. In Proceedings of IEEE Globecom 2001.

.... 2 are violation probabilities and are generally small, e.g. 1 # 2 =10 ;9 . If one is interested in statistical delay, backlog, or loss bounds to the aggregate as a whole (as opposed to lower bounds for a single flow) we refer to the rich literature on multiplexed regulated traffic e.g. [3, 11, 12, 14, 16, 18, 19]. However, generally, the results focus on the analysis of a single node, and do not consider a multi node network. The remaining sections of this paper are structured as follows. In Section 2, we review needed results from the statistical network calculus in terms of effective service curves, as ....

M. Vojnovic and J.-Y. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. In Proceedings of IEEE Globecom 2001.

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M. Vojnovic and J.-Y. Le Boudec, "Bounds for independent regulated inputs multiplexed in a service curve network element," in Proc. Globecom 2001.

....shaped individually at the network ingress points, but are served as aggregates by the nodes in the network. The definition of EF PHB relies on Packet Scale Rate Guarantee (PSRG) 10] defined later) Some sample path properties of PSRG nodes are established, e.g. in [3, 6, 5] In our prior work [23, 24] we obtained some probabilistic bounds on the performance that apply to PSRG nodes. It is of network engineering interest to have tight bounds on the performance of PSRG nodes, which would enable one to dimension the network such that some notion of quality of service is guaranteed. Our approach ....

....curve #(t) r(t . Similarly also, adaptive service curve is a stronger property than service curve. Probabilistic Bounds. In this paper we focus on probabilistic performance bounds for an isolated PSRG or adaptive service curve node. We review our previous results on service curve nodes [23, 24]; from the discussion above, it follows that all the results obtained for service curve nodes also apply to PSRG nodes. Further, we give an improved loss bound that exploits the adaptive service curve or PSRG definition, and does not seem to be readily available for a service curve element. The ....

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Milan Vojnovic and Jean-Yves Le Boudec, Bounds for independent regulated inputs multiplexed in a service curve network element, to appear in IEEE Trans. on Communications, a preliminary version in Proc. of IEEE Globecom 2001.

....proved bound for a node modeled as a constant rate server is found by Kesidis et al. in [84] Another bound for the same model is found later by C.S. Chang et al. [85] who show that their bound is better than the former, and asymptotically tight. These results are extended by Vojnovi c et al. [86] to the case where the node can be modeled with a service curve, instead of being a constant rate server, which better reflects the EF assumptions. More interestingly, Vojnovi c et al. show that all these bounds are application of more generic bounds 17 found by Hoeffding in 1963 [87] which apply ....

..... Combining with (23) gives exp( Ig k ) with # # # # # # # # # #,b #(s k 1 ) 0,b #s k 1 s k 1 #(s k 1 ) #(s k ) b #(s k 1 ) s k 1 , otherwise which, for ct and s k is the bound in [85] Taking the minimum over a set of partitions s gives a better bound [86]. See [88] for the general case where # i s are not identical. Application to DiffServ(EF) The bounds can be used for statistical guarantees. First, an EF node can be modeled as a rate latency service curve. Second, it is necessary to account for traffic inside the network. Chang et 18 al [85] ....

M. Vojnovic and J.-Y. Le Boudec, "Bounds for independent regulated inputs multiplexed in a service curve network element," in Proc. Globecom 2001.

....regulated (resp. heterogeneously regulated for non identical arrival curve constraints) A4) We suppose d 9 N Y 4Q6 8 ; Y 4eM 8fF La Y(476 ;gM 8 a Yh jik # lQmon X Y 476 8 6qp Indeed, the assumption (A4) is implied for the input flows with stationary and ergodic increments [8] [9], but not vice versa. Thus, A4) is a weaker assumption. Note that we allow for the input flows with non stationary increments as long as (A4) is verified. However, for some of our results we need stationary ergodic increments of the inputs to ensure certain limits exist; we explicitly indicate ....

....long as (A4) is verified. However, for some of our results we need stationary ergodic increments of the inputs to ensure certain limits exist; we explicitly indicate when such an assumption is needed. Our results are obtained by combining some queueing results based on stochastic comparisons (see [9] and references therein) with some concepts of network calculus (see [10] and references therein) We now explain the organization of the paper and highlight our main findings. We discuss the state of the art in Section II. In Section III we give theoretical foundations of our work; the results ....

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Milan Vojnovic and Jean-Yves Le Boudec, "Bounds for independent regulated inputs multiplexed in a service curve network element," in Proc. of Globecom 2001.

....and, in particular, we study the leaky bucket regulated E GF : H JI . A4) We suppose ; M : L NF : J , for any , where : PORQS TSUDV 9H: W Indeed, the assumption (A4) is implied for the input flows with stationary and ergodic increments [8] [9], but not vice versa. Thus, A4) is a weaker assumption. Note that we allow for the input flows with non stationary increments as long as (A4) is verified. However, for some of our results we need stationary ergodic increments of the inputs to ensure certain limits exist; we explicitly indicate ....

....discuss the state of the art in Section II. In Section III we give the theoretical foundations of our work; the results given in this section are of general interest for statistical multiplexing of regulated inputs to a multiplexer that offers a service curve to the aggregate input. Our prior work [9] gives us a catalog of probabilistic bounds to the backlog for the latter system. In Section III A we go a step further and give a bound on the backlog that accommodates heterogeneously regulated inputs (Theorem 1) and which performs better than the bounds of Theorems 4 and 5 in [9] Moreover, in ....

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Milan Vojnovic and Jean-Yves Le Boudec, "Bounds for independent regulated inputs multiplexed in a service curve network element," Tech. Rep. DSC/2001.

....regulated (resp. heterogeneously regulated for non identical arrival curve constraints) A4) We suppose # # # # # # # # # # # # # # # # # # # # # # # # , for any # # # , # # # # # # # Indeed, the assumption (A4) is implied for the input flows with stationary and ergodic increments [8] [9], but not vice versa. Thus, A4) is a weaker assumption. Note that we allow for the input flows with non stationary increments as long as (A4) is verified. However, for some of our results we need stationary ergodic increments of the inputs to ensure certain limits exist; we explicitly indicate ....

....long as (A4) is verified. However, for some of our results we need stationary ergodic increments of the inputs to ensure certain limits exist; we explicitly indicate when such an assumption is needed. Our results are obtained by combining some queueing results based on stochastic comparisons (see [9] and references therein) with some concepts of network calculus (see [10] and references therein) 0 7803 7476 2 02 17.00 (c) 2002 IEEE. We now explain the organization of the paper and highlight our main findings. We discuss the state of the art in Section II. In Section III we give theoretical ....

[Article contains additional citation context not shown here]

Milan Vojnovic and Jean-Yves Le Boudec, "Bounds for independent regulated inputs multiplexed in a service curve network element," in Proc. of Globecom 2001.

....formally proven bound for a node modeled as a constant rate server is found by Kesidis et al. in [81] Another bound for the same model is found later by C.S. Chang et al. [82] who show that their bound is better than the former, and asymptotically tight. These results are extended by Vojnovic et al. [83] to the case where the node can be modeled with a service curve, instead of being a constant rate server, which better reflects the EF assumptions. More interestingly, Vojnovic et al. show that all these bounds are application of more generic bounds found by Hoeffding in 1963 [84] which apply to ....

.... ### # # ## #### ### # ### # # ### # ### ### ### # ## ### # ### ## ### # # # # # ### # ### ### ### # # ## ### ### ##### # ### ### ### #### ### # ######### which, for #### # ## and # # # # is the bound in [82] Taking the minimum over a set of partitions # gives a better bound [83]. See [85] for the general case where # # s are not identical. Application to DiffServ(EF) The bounds can be used for statistical guarantees. First, an EF node can be modeled as a rate latency service curve. Second, it is necessary to account for traffic inside the network. Chang et al. [82] ....

M. Vojnovic and J.-Y. Le Boudec, "Bounds for independent regulated inputs multiplexed in a service curve network element," in Proc. Globecom

No context found.

M. Vojnovic and J. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. IEEE Transactions on Communications, 51(5), Jan. 1991.

No context found.

M. Vojnovic and J.-Y. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. IEEE Transactions on Communications, October 2002. To appear.

No context found.

M. Vojnovic and J.-Y. Le Boudec. Bounds for independent regulated inputs multiplexed in a service curve network element. In Proceedings of IEEE Globecom 2001.

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