C.-S. Chang. Stability, Queue Length, and Delay of Deterministic and Stochastic Queueing Networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.  Home/Search   Document Not in Database   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. ....

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....This report is an abbreviated version of [1] I. INTRODUCTION Performance guarantees in QoS networks are either deterministic or statistical. A deterministic service guarantees that all packets from a flow satisfy given worst case end to end delay bounds and no packets are dropped in the network [2], 4] 8] 15] A deterministic service provides the highest level of QoS guarantees, however, it leaves a significant portion of network resources on the average unused [22] A statistical service makes probabilistic service guaran This work is supported in part by the National Science ....

....a statistical service can be done in a similar 1 (t) flow1 N (t) flowN A 1 (t, t t) A N (t, t t) Regulators Buffer with Scheduler . unregulated) arrivals (regulated) Fig. 1. Regulators and Scheduler at a Link. fashion as with deterministic envelopes for a deterministic service [2], 4] In fact, we show that one can reuse admission control 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 ....

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C. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....by a deterministic subadditive envelope A j as A j (t; t ) A j ( for all t 0 and for all 0. The selection of subadditive bounds is motivated by the result that a bound for a traffic flow, which is not subadditive, can be improved by replacing it with a tighter subadditive bound [3]. Given the traffic arrivals of a video flow, a deterministic envelope for that video flow can be constructed by E j ( sup t0 A j [t; t ] 8 0 : 1) In [13] this function is referred to as empirical envelope , and shown to be the smallest subadditive envelope for a traffic flow. To ....

C. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....could achieve very high network utilization both in a well known network and randomly generated networks. Our methodology presented in this paper can be easily extended to deal with statistical delay guarantees. Much progress has been made in derivation of statistical delay bounds [11] [2], 12] 20] However, all these previous results require information on flow population to obtain the statistical delay bounds. For example, in [11] statistical delay bounds are obtained by using approximated normal distribution, of which the parameters, in turn, depend on the flow population. ....

C. Chang, Stability, Queue Length, and Delay of Deterministic and Stochastic Queueing Networks, IEEE Transactions on Automatic Control, 39(5):913-931, May 1994.

....that operates at 155 Mbps, and we assume that all traffic is packetized in 53 byte ATM cells with a payload of 48 bytes each. We use the so called empirical envelope of a video sequence to characterize its traffic, where the empirical envelope E of a sequence with traffic A is given by [4, 25]: E (t) sup A[ t] 8t 0 (13) The empirical envelope is the tightest traffic characterization available for a video sequence and, when used with admission control, will result in the admission of a maximal number of connections. By using empirical envelopes for traffic ....

C.-S. Chang. Stability, Queue Length, and Delay of Deterministic and Stochastic Queueing Networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....of effective envelopes from [3] Effective envelopes are functions that express probabilistic upper bounds for the traffic from an aggregate of flows. A desirable feature of effective envelopes as compared with other methods that express statistical multiplexing gain, e.g. effective bandwidth [7], 14] is that effective envelopes are easily related to the envelope functions used in the deterministic network calculus. A. Effective Envelopes for a Flow Aggregate Let us now consider a set of flows at a node, and let A j and D j , respectively, denote the arrival and departure processes ....

....#. 13) With this choice, t) is always satisfied. Since the derivative of the right hand side of Eqn. 13) is increasing in , there is at most one minimum, which can be found by searching for the zero of the derivative. Note the similarity of Eqn. 13) to the effective bandwidth in [7], 14] Given an effective envelope C,we can construct a strong effective envelope . Lemma 1: Given an effective envelope for a set of heterogeneous flows satisfying (A1) A3) There exists a strong effective envelope for the arrivals in satisfying #,# # , ....

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....reported in [2] 6] 7] This paper reports some recent developments pertaining to probabilistic quality of service guarantees, which may be useful in noisy environments where ARQ protocols are employed. Other related approaches to calculation of probabilistic guarantees have been reported in [4] [1] [8] 3] 5] 2 Tra#c and Service Constraints A proto typical tra#c stream flowing on a link is described by a discrete time sequence R, where R[n] denotes the number of packets traversing the link in slot n. We assume that R[n] 0 for 0 and that R[n] takes on non negative integer values. ....

....with the smallest possible deadline. We assume that the tra#c impairment process is stochastically upper bounded in the following sense. There exist functions #(#) and #(#)such that for all m E[e #I[m 1,n] e #(#(#) #(#) n m) 33) This type of constraint was introduced by Chang [1]. Let # be such that #(#) # 1 for all # in some neighborhood of zero. Proposition 3: Service Curve Delivery over Stochastic Links) Suppose that i=1 S i (x) #x for all x 0. Then in the system described above, the i tra#c stream is delivered service curve S i with deficit and ....

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Trans. on Automatic Control, vol.39, no. 5, ,May 1994, pp. 913-31.

....of effective envelopes from [3] Effective envelopes are functions that express probabilistic upper bounds for the traffic from an aggregate of flows. A desirable feature of effective envelopes as compared with other methods that express statistical multiplexing gain, e.g. effective bandwidth [7, 13], is that effective envelopes are easily related to the envelope functions used in the deterministic network calculus. Let us now consider a set of flows at a node, and let A j and D j , respectively, denote the arrival and departure processes for each flow j 2 C. We will refer to the set ....

....: 12) With this choice, t) is always satisfied. Since the derivative of the right hand side of Eqn. 12) is increasing in s, there is at most one minimum, which can be found by searching for the zero of the derivative. Note the similarity of Eqn. 12) to the effective bandwidth in [7, 13]. Given an effective envelope C, we can construct a strong effective envelope . Lemma 1 Given an effective envelope of heterogeneous flows satisfying (A1) A3) An upper bound for a strong effective envelope for the arrivals in is given by # # 0 # ....

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....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 ....

....under the intserv 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 ....

[Article contains additional citation context not shown here]

C. Chang, Stability, queue length, and delay of deterministic and stochastic queueing networks, IEEE Transactions on Automatic Control, 39(5):913-931, May 1994.

....could achieve very high network utilization both in a well known network and randomly generated networks. Our methodology presented in this paper can be easily extended to deal with statistical delay guarantees. Much progress has been made in derivation of statistical delay bounds [10] [3], 11] 19] However, all these previous results require information on flow population to obtain the statistical delay bounds. For example, in [10] statistical delay bounds are obtained by using approximated normal distribution, of which the parameters, in turn, depend on the flow population. ....

C. Chang, Stability, queue length, and delay of deterministic and stochastic queueing networks, IEEE Transactions on Automatic Control, 39(5):913931, May 1994.

....of service absolute di erentiated services. For absolute di erentiated services, performance guarantees are either deterministic or statistical. Deterministic services support applications that have stringent performance requirements for a service with zero packet drops or delay bound violations [1, 2, 6, 14]. While they provide a very simple service model to the application, deterministic services, by their very nature, tend to heavily overcommit resources because they reserve resources according to a worst case scenario. In real networks, most of time, this often results signi cant portions of ....

....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 ....

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C. Chang, Stability, queue length, and delay of deterministic and stochastic queueing networks, IEEE Transactions on Automatic Control, 39(5):913-931, May 1994.

....multiplexing while preserving the elegant formalism of the network calculus has been the subject of several studies. Kurose [16] uses the concept of stochastic ordering and obtains bounds on the distribution of delay and buffer occupancy of a ow in a network with FIFO scheduling. Chang [7] presents probabilistic bounds on output burstiness, backlog and delays in a network where the moment generating functions of arrivals are exponentially bounded. Different bounds for exponentially bounded arrivals are derived by Yaron and This work is supported in part by the National Science ....

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913931, May 1994.

....[36] 37] While such schemes can have good performance properties, they 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 ....

C. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913-- 931, May 1994.

....multiplexing while preserving the elegant formalism of the network calculus has been the subject of several studies. Kurose [16] uses the concept of stochastic ordering and obtains bounds on the distribution of delay and buffer occupancy of a flow in a network with FIFO scheduling. Chang [7] presents probabilistic bounds on output burstiness, backlog and delays in a network where the moment generating functions of arrivals This work is supported in part by the National Science Foundation through grants ANI 9730103, ECS 9875688 (CAREER) ANI 9903001, DMS 9971493, and ANI 0085955, ....

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

....rate j, so is the loss ratio with the same asymptotic decay rate j. This proposition is important because there is a fairly large class of input processes for which OE 0 (x) converges to a positive constant, e.g. Markov modulated fluid processes, short range dependent Gaussian processes, etc [5, 11]. Now, we focus on the development of the main liminf result of the paper. As one can see in Lemma 1, the liminf part is related to EfZjQ xg. Since it is difficult to know the distribution of Z, we use a stochastic process Xn defined as Xn : n X k=1 k Gamma cn Q 0 ; n 0: 17) Here we ....

Chang, C.-S. (1994). Stability, Queue Length, and Delay of Deterministic and Stochastic Queueing Networks. IEEE Transactions on Automatic Control 39, 913--931.

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C.-S. Chang. Stability, Queue Length, and Delay of Deterministic and Stochastic Queueing Networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

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C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Trans. on Automatic Control, vol.39, no. 5, May 1994, pp. 913-931.

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C.-S. Chang. Stability, queue length, and delay in deterministic and stochastic queueing networks. IEEE Trans. on Automatic Control, 39:913931, 1994.

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C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

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C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

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C.-S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

No context found.

C. S. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

No context found.

C. Chang. Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Transactions on Automatic Control, 39(5):913--931, May 1994.

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C. S. Chang, Stability queue length, and delay of deterministic and stochastic queueing net- works, IEEE Trans. Automat. Contr., vol. 39, no.5, pp. 913-931, May 1994.

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Chang, C.-S. (1994). Stability, queue length, and delay of deterministic and stochastic queueing networks. IEEE Trans. Automatic Control, 39,913-931.

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