F.P. Kelly. Effective bandwidths at multi-type queues. Queueing Systems 9:5--16, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[49] applies to sources modeled by time reversible Markov chains. Many other schemes (most of which are based on different methods for calculating an effective bandwidth associated with the source and its QoS requirements) can also be used to determine the number of calls that can be carried [73, 74, 75, 76, 77, 78, 79], for a specified loss rate and delay. 22 Note that the loss probability calculated is the aggregate loss probability. In some circumstances [59] phase effects caused by the periodic nature of video frames may result in individual sources seeing losses that are an order of magnitude or more ....

F. P. Kelly, "Effective bandwidths at multi-type queues", Queueing Syst. 9, pp. 5-15, 1991.

....and the desired QoS guarantees can together be represented by a single number called the effective bandwidth of the connection. Techniques for computing the effective bandwidth for different traffic characteristics and QoS requirements have been discussed elsewhere in literature [5] 6] [9], 3] and is not the focus of this paper. For example, given a traffic envelope (i.e. a bound on the number of bytes generated by the user in any given time interval) and a desired delay bound, Le Boudec discusses an approach for computing the effective bandwidth which completely characterizes ....

.... the envelope and the delay requirement [3] Similarly, given stochastic characteristics of the traffic, the buffer size at a network element, and a desired bound on probability of packet loss, many different techniques have been proposed to compute the equivalent effective bandwidth [5] 6] [9]. Given the effective bandwidths of all the active connections in a cell and the effective bandwidth of a new connection request, the QoS requirements of all connections can be guaranteed if the sum of the effective bandwidths including the new request is less than or equal to the capacity of the ....

F. P. Kelly. Effective bandwidths at multi-type queues. Queueing systems, 9:5--15, 1991.

....rate is estimated [29, 30] We describe details of these three methods above. Among the CAC methods that use effective bandwidth, use RSM, and are traffic descriptorbased, Kelly analyzed the asymptotic relationship between the buffer size and the CLR and derived the effective bandwidth [31]. Guerin et al. investigated the Anick Mitra Sondhi (AMS) model [32] and derived an explicit formula for determining the link capacity, i.e, the effective bandwidth needed to maintain the target CLR [33] Elwalid and Mitra formulated the effective bandwidth as an inverse eigenvalue ....

F. P. Kelly, Effective bandwidths at multi-type queues, Queuing Syst, vol. 9, pp. 5--15, 1991.

....the buffer is full. A lost cell is considered as a cell with infinite queueing delay. Therefore, this QOS criterion takes into account not only bounds on the delay jitter but also on the cell loss rate. Recently, a number of call admission schemes have been proposed for high speed networks (e.g. [23, 24, 18, 25]) We use the admission control scheme proposed by Gu erin et al. 18] which is based on the fluid flow approximation model of [17] In this model, a number of homogeneous sources described by (r; ae; b) with a QOS requirement Q(D; ffl) are multiplexed 3 Although our traffic model does not have ....

F. P. Kelly, "Effective Bandwidths at Multi-type queues," Queueing Systems, vol. 9, pp. 5--15, 1991.

.... with Synchronous Transfer Mode (STM) a unit of bandwidth is equivalent to a time slot (or channel) Second, when it is used to describe a future B ISDN with Asynchronous Transfer Mode (ATM) the bandwidth requirement of each class of calls is equivalent to the effective bandwidth of the call [34, 38, 43, 54]. For ease in explanation, we will refer to the unit of bandwidth as a circuit , as in traditional circuit switched networks, throughout this chapter. When a call arrives to the network, it will either be carried on a path or lost, depending on the routing policy being used. We assume that each ....

....the buffer is full. A lost cell is considered as a cell with infinite queueing delay. Therefore, this QOS criterion takes into account not only bounds on the delay jitter but also on the cell loss rate. Recently, a number of call admission schemes have been proposed for high speed networks (e.g. [34, 38, 43, 54]) We use the admission control scheme proposed by Gu erin et al. 43] which is based on the fluid flow approximation model of [5] Specifically, consider a number of homogeneous sources described by (r; ae; b) with a QOS requirement Q(D; ffl) which are multiplexed onto a link of capacity C bps. ....

Kelly, F. P. Effective Bandwidths at Multi-type queues. Queueing Systems, 9:5--15, 1991.

....networks, a new connection is accepted if and only if, for each link on the route, adding the new connection will not violate the QOS requirements of all existing connections sharing the same link. Many algorithms have been proposed for determining the resources required, e.g. effective bandwidth [15, 12, 13, 21], for adding a connection. The purpose of this paper is to develop adaptive routing algorithms for multirate networks based on the MDP approach. Implementing MDP based adaptive routing schemes in multirate networks is extremely difficult because of the complexity of the network. In [8] Dziong and ....

....distributed with mean 1= k where 1= 1 = 1. Such a network, as described above, is referred to as a multirate network [6] In the context of a B ISDN with Asynchronous Transfer Mode (ATM) the bandwidth requirement of each class of calls is equivalent to the effective bandwidth of the call [12, 13, 15, 21]. For ease in explanation, we will refer to the unit of bandwidth as a circuit , as in traditional circuit switched networks, throughout this paper. When a call arrives to the network, it will either be carried on a path or lost, depending on the routing policy being used. We assume that each ....

F. P. Kelly, "Effective Bandwidths at Multi-type queues," Queueing Systems, vol. 9, pp. 5--15, 1991.

.... an acceptable level of bandwidth utilization, integrated networks often employ the concept of effective bandwidth in call admission control (CAC) and service scheduling [8] 9] Significant research has been done on the notion of effective bandwidth over wireline networks [10] 8] 11] 9] [12]. Gu erin et al. proposed an approximate expression for the effective bandwidth of both individual and multiplexed connections, arguing that this approximation is necessary for real time network traffic control [9] Elwalid and Mitra studied the effective bandwidth for general Markovian traffic ....

F. P. Kelly, "Effective bandwidths at multi-type queues," Queueing Syst., vol. 5, pp. 5--15, 1991.

....papers, namely the transient cumulant generating function of the arrival process. This approach has been implemented in [35] vi) Finally, in Section 6 we consider the problem of characterizing the effective bandwidth of a single connection from a number of samples. Here, the effective bandwidth [25, 29] is that appearing in the large buffer asymptotic (see e.g. 4, 15, 20, 22, 31, 46] rather than the many sources asymptotic considered hitherto. The central object in this description is the (limiting) cumulant generating function. CAC based on measuring this directly has been proposed in [13] ....

F.P. Kelly. Effective bandwidths at multi-type queues. Queueing Systems Theory Appl. 9:5--16, 1991.

.... the requested QoS while maintaining an acceptable level of bandwidth utilization, ATM employs the concept of effective bandwidth in connection admission control (CAC) and service scheduling [8, 12] Significant research has been done on the notion of effective bandwidth over wireline networks [7, 8, 11, 12, 15]. Gu erin et al. proposed an approximate expression for the effective bandwidth of both individual and multiplexed connections, arguing that this approximation is necessary for real time network traffic control [12] Elwalid and Mitra studied the effective bandwidth for general Markovian traffic ....

F. P. Kelly, "Effective bandwidths at multi-type queues," Queueing Syst., vol. 9, pp. 5--15, 1991.

.... the transition matrix of the arrivals process (see e.g. 1, 8, 11] and more generally for arrivals process satisfying a large deviation principle (see [7, 9] Characterizing the queue length distribution by its asymptotic slope Gammaffi produces the effective bandwidth approximation (see e.g. [11, 12, 13, 19]) with is accurate asymptotically in b for a given L: P[Q L b] e Gammaffib : 2) As can be seen from Figure 1, this is increasingly inaccurate for larger L when b is fixed. Indeed, on the basis of numerical studies of models Choudhury, Lucantoni and Whitt [5] have proposed the ....

F.P. Kelly (1991). Effective bandwidths at multi-type queues. Queueing Systems 9:5--16

.... e Gammaffib : 7) In fact, this formula is invariant under L fold superpositions of identical sources, provided we scale the service rate proportionately. The idea generalizes to heterogeneous superpositions. It has been widely examined as a basis for admission control in ATM networks. See [5, 11, 13, 14, 24] for more details) However, there is already theoretical and numerical work indicating that (7) can be inaccurate when applied to streams which have a high degree of auto correlation. Numerical studies by Choudhury et al. [6] have found in examples that P [Q b] je Gamma L e Gammaffib ....

F.P. Kelly (1991). Effective bandwidths at multi-type queues. Queueing Systems 9:5--16

....of the arrivals process and the service rate of the queue. This result has been proved in various degrees of generality in [6, 18, 23] The consequent effective bandwidth approximation P[Q b] e Gammaffib (1. 2) has been proposed as an estimate of the loss ratio in a buffer of size b (See [26, 34] and references therein) However, there is recent work, both numerical [7] and theoretical [5, 9, 31] which shows that this estimate can be inaccurate when the arrivals are composed of superposition of L streams each with a high degree of autocorrelation, increasingly so as L becomes large. See ....

F.P. Kelly, Effective bandwidths at multi-type queues, Queueing Systems, 9 (1991) 5--16

....cannot meet the requirements, it provides a description of what it can achieve, and the application decides whether to take that. The mathematical basis upon which admission control decisions are made has produced two equivalent definitions. Equivalent bandwidth comes from the work of Kelly [79] and Guerin et al. [80] Sources are modeled as either on and off at their peak rate, and are characterised by the peak rate, the mean rate and the duration of an on period. Under certain assumptions (exponential distribution of burst periods) an equivalent capacity can be calculated for the flow ....

Frank Kelly, "Effective Bandwidth at multi-type queues," Queueing Systems 9 (1991), 5--15.

....; 1) for some positive constant ffi that depends on the service rate at the queue and the statistical properties of the arrivals process. This formula has application in congestion and connection admittance control through the notion of effective bandwidth of a source. See, for example, [4, 11, 13, 14, 22]) These furnish a linear inequality in the numbers of sources of various types which must be satisfied in order to maintain a given quality of service. The asymptotic (1) holds in great generality, and in particular for any Markovian model. The proposal that lrd traffic models be used instead ....

....side of (17) reduces to Gammaffi . Thus the queuetail asymptotics (1) are invariant under L fold superposition, provided the service rate is scaled proportionately. This property remains true for heterogeneous superpositions, and is the basis of the effective bandwidth approximation. See [4, 11, 13, 14, 22] for development and applications to connection admission control) Briefly, consider superpositions of numbers L i of srd arrivals of type i each with scaled cumulant generating function i . From (1) and (7) it follows that a criterion for a loss ratio no worse than e Gamma b to be achieved ....

F.P. Kelly (1991). Effective bandwidths at multi-type queues. Queueing Systems 9 5--16

....[EMI94] the approximation is used for the analysis and admission control of a multi service multiplexing system in which the services are prioritized. The approximation refines the pure exponential form e zB used in effective bandwidth analyses [GAN91, GHU91, EMI93, KWC93, WHI93] Prior studies [HUI90, KEL91, ROB92] have noted that the loss in bufferless multiplexing is very well approximated by the Chernoff large deviations approximation. Note that in typical ATM applications where cell loss probabilities are in the range 10 Gamma6 Gamma 10 Gamma9 , a substantial contribution is derived from the ....

F. P. Kelly, "Effective bandwidths at multi-type queues", Queueing Syst. 9, pp. 5-- 15, 1991.

....effective bandwidth approximation P [Q n nb] e Gammanffib for such flows. Thus by use of (3) we aim to develop connection admission control (CAC) algorithms which can make better use of system resources than those based on the effective bandwidth approximation; e.g. see Kelly [12], and Gibbens and Hunt [10] The relation (3) expresses the asymptotic behavior of Q n as n increases. In view of (2) it is not surprising then that the asymptotic properties of Q n for large n can be expressed in terms of those of A n . Define the moment generating function of an ....

F.P. Kelly. Effective bandwidths at multi-type queues. Queueing Systems 9:5--16, 1991.

....we refine the pure exponential form e zx used in effective bandwidth analyses [GAN91, GHU91, EMI93, WHI93, VCW94] by L 0 e zx , where the prefactor L 0 is simply the loss in bufferless multiplexing. The latter quantity is very well approximated by the Chernoff large deviations approximation [HUI90, KEL91, ROB92] and, moreover, it is easy to calculate for even high dimensional sources. Note that L 0 is our approximation for the probability that the buffer is not empty and, as stated earlier, it is quite small in typical ATM applications. Hence the prefactor L 0 adds significantly to the accuracy of the ....

....in the paper, for estimating L, the stationary probability that the sum of the instantaneous rates of fluid generation by all sources exceeds the channel rate. Thus L is the loss probability in a multiplexing system without a buffer. The basic procedure given here is due to Hui [HUI90] and Kelly [KEL91], and is based on the Chernoff bound. Suppose there are J source classes, and K j sources of class j, all of which are characterized by (M (j) j) let w (j) denote the stationary probability vector. The stationary rate of fluid generation R ji (t) from source i of class j has the ....

F. P. Kelly, "Effective bandwidths at multi-type queues", Queueing Syst. 9, pp. 5--15, 1991.

....QoS given the traffic parameters of a connection and the buffer size at the multiplexer. ATM can provide a required level of QoS by guaranteeing the effective bandwidth associated with that connection. Significant research has been done on the notion of effective bandwidth over wireline networks [7, 8, 11, 12, 15]. Anick et al. provided a framework for analyzing buffer statistics under multiplexed on off fluid sources [4] Gu erin et al. proposed an approximate expression for the effective bandwidth of both individual and multiplexed connections, arguing that this approximation is necessary in real time ....

F. P. Kelly, "Effective bandwidths at multi-type queues," Queueing Syst., vol. 9, pp. 5--15, 1991.

....Buffer Figure 2.1: Functional diagram of GPS scheduling at a node. 2.3. Chernoff Approximation The Chernoff large deviations approximation [BIL86, CSE93, PET65] is an effective technique for estimating loss in bufferless multiplexing systems. The procedure given here is due to Hui and Kelly [HUI90, KEL91]. Consider P loss = Pr (U C) 2.5) where the total instantaneous demand U = P J j=1 PK j k=1 u jk , and fu jk g are independent random variables and fu jk g k are nonnegative identically distributed for each j. Here there are J source classes and K j sources of class j. When C is the nodal ....

F. P. Kelly, "Effective bandwidths at multi-type queues", Queueing Systems 9, 1991, pp. 5--15.

....networks. The analysis is based throughout on fluid models. 3 (ii) The approach taken in this paper, where one of the two key network resources is the buffer, is novel in its use of established techniques for analyzing unbuffered resources, such as the Chernoff large deviations approximation [9, 10, 11, 14]. The important bridge to the case where bandwidth is the other network resource is based on a technique that allows the two resources to be exchangeable. The first phase of the analysis concludes with a reduction from a two resource to a one resource problem, and in the second phase the ....

....This paper pays considerable attention to molding the analytic and qualitative results for the purposes of real time administration of admission control. A key concept here is effective bandwidth, which has recently received considerable attention for both buffered [7, 8, 6, 21] and unbuffered [10, 11, 14] network resources. Underlying the concept is linearity of AL , the boundary of the admissible set al.. , which is the set of combinations of sources of various classes for which the quality of service requirement specified by L is satisfied. The linearity of AL is sometimes exact in an ....

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F. P. Kelly, "Effective bandwidths at multi-type queues", Queueing Systems, 9, pp. 5--15, 1991.

....per class m call on a link l comprising C l circuits, we obtain a multi service loss network representation. The conceptual and computational advantages of that framework for ATM network design have been recognized and are well established. See, for instance, Farag o et al. 6] Hui [8] Kelly [9], Mitra et al. 13] and Ross [15] For cases where some of the constraints may be concave, i.e. d l (x) C l ; l = 1; L; 2) with d l ( Delta) denoting some concave function, Hui [8] and Kelly [9] propose the procedure of bounding the admissible region by a tangent hyperplane passing ....

....recognized and are well established. See, for instance, Farag o et al. 6] Hui [8] Kelly [9] Mitra et al. 13] and Ross [15] For cases where some of the constraints may be concave, i.e. d l (x) C l ; l = 1; L; 2) with d l ( Delta) denoting some concave function, Hui [8] and Kelly [9] propose the procedure of bounding the admissible region by a tangent hyperplane passing through an operating point on the boundary. There are important cases, however, where the boundary may be highly non linear, so that it is not immediately clear if linearizing the boundary is not overly ....

Kelly, F.P. (1991). Effective bandwidths at multi-type queues. Queueing Systems 9, 5-15.

....Brownian motion: this has been proposed as a model for the workload by Leland et al. [25] based on observations of Ethernet traffic. The relation (1.3) is the basis of the effective bandwidth approximation to the queue length distribution: P[Q b] e Gammaffib : 1. 8) See for example, [5, 18, 19, 15, 21, 34] for development, applications and further references) The motivation here is that for ATM multiplexers one wants to estimate exponentially small loss probabilities, which in practice are to be as small as 10 Gamma9 . However, there is already theoretical and numerical work indicating that ....

....c j;t (ffi) Gamma s (1) j ffi j ; 4.85) and s (1) j = c j (ffi) ffi. Note s (1) j s (0) j due to the convexity of c j , since c j (0) 0. s (0) j and s (1) j are the usual effective bandwidths of sources of type j for zero and infinite buffers respectively. See, for example, [21] for further details) 4.2 Superpositions of Gaussian Arrival Processes. In this section we take W L t = A L t Gamma sLt where for each L, A L t is an L fold superposition of independent copies of A t : a zero mean Gaussian process with stationary increments and variance oe 2 t . We make ....

F.P. Kelly (1991). Effective bandwidths at multi-type queues. Queueing Systems 9:5--16

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F.P. Kelly. Effective bandwidths at multi-type queues. Queueing Systems 9:5--16, 1991.

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F. P. Kelly, "Effective bandwidths at multi-type queues," Queueing Syst., vol. 9, pp. 5--15, 1991.

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F. P. Kelly, "Effective bandwidths at multi-type queues," Queueing systems, vol. 9, pp. 5--15, 1991.

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