F. P.Kelly, `Effective Bandwidths at Multi-Class Queues', Queueing Systems Theory and Applications, Vol. 9, No. 1-2, pp 5-15, Oct. 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a j;k (t) given the tail distribution of queue j is exponentially decayed with rate j . This concept of effective bandwidth, evidently suitable for bandwidth allocation, has recently generated a tremendous amount of interest in the field, e.g. Gu erin, Ahmadi and Naghshineh [18] Kelly [22], Gibbens and Hunt [15] Chang [6] Kesidis, Walrand and Chang [24] Chang, Heidelberger, Juneja and Shahabuddin [8] Elwalid and Mitra [12] Whitt [35] Glynn and Whitt [16] Chang [7] Kesidis and Walrand [23] Nagarajan, Kurose and Towsley [28] Veciana and Walrand [36] and Veciana, ....

F.P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, Vol. 9, pp. 5-16, 1991. 25

....have higher priority when OE 1 = 1 and lower priority when OE 1 = 0. We can therefore obtain the performance of these twoprioritypolicies as a by product of our analysis. Note that the result for the policy that assigns higher prioritytoclass 1 customers, matches the FCFS single class result (see[21,19,4]) since under this policy,class 1 customers are oblivious of class 2 customers. We summarize the performance of priority policies in the next corollary, the proof of whichcan be found in [3] Corollary 7.1. Prioritypolicies) Under strict prioritypolicy for class 1 customers (P 1 assuming that ....

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

....terminology, the problem of local GOS guarantees is then equivalent to nding or bounding the tail distributions of queue lengths and delays at the local nodes. One of the most interesting approaches in dealing with this problem is the recently developed theory of e ective bandwidth (see e.g. [21, 23, 18, 5, 25, 8, 16, 33, 19, 6, 24, 30, 34, 35, 14], and references therein) Research partially supported by the National Science Council, Taiwan, R.O.C. under Contracts NSC 83 0208 M007 091 and NSC 83 0404 E007 052. This theory, strongly connected to the large deviation principle, provides the asymptotic decay rate of the tail distribution ....

F.P. Kelly, \Effective bandwidths at multi-class queues," Queueing Systems, Vol. 9, pp. 5-16, 1991.

....multiplexing. 1 Introduction To exploit statistical multiplexing gain of traffic sources in a network, service provisioning requires a framework for the stochastic analysis of network traffic and commonly used scheduling algorithms. The most influential such framework is the effective bandwidth [11, 12, 13, 14] which, from a qualitative point of view, describes the minimum bandwidth required to provide an expected service for a given amount of traffic. The effective bandwidth concept was related to the theory of large deviations in [4, 25] However, applications of the effective bandwidth approach have ....

F. Kelly. Effective bandwidths at multi-class queues. Queueing Systems, Theory and Applications, 9(1-2):5--16, 1991.

.... P[Q x] e holds# this approximation is commonly referred to as [9] the effective bandwidth (EB) approximation (sometimes it is also called the dominantrootapproximation) Following this result admission control policies based on the concept of effective bandwidth have been developed# see [7,16,18,17,27]. However, as discussed in [9] the EB approximation may often be very inaccurate. This is usually the case when many sources (N ) are multiplexed# under this assumption it was shown in [9] that ff e ;flN forsomeconstant fl. A more formal analysis of the multiplexing of a large number of ....

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

....in many models for telecommunications systems, notably truncated multiclass M G # queues. They model traditional circuit switched networks with fixed routing, cellular networks with frequency reuse constraints [1 3] packet networks with fixed routing using effective bandwidth admission control [4,5] or with marking based admission control [6] or intelligent networks in which connections require a particular set of services for the duration of the call [7] Many other applications are listed in [8] The importance of product form networks has led to many techniques for analysing them [9] ....

Frank P. Kelly. Effective bandwidths at multi-class queues. Queue. Syst., 9, 1991, 5--16.

....related work and conclude the paper, respectively. trunk. It indicates the amount of bandwidth that must be reserved for a trunk in order to satisfy its QoS requirements. A tnmk s effective bandwidth may be deftned in terms of link operating points as well as the trunk s traffic characteristics [8, 9]. Therefore, we use o: t to refer to the effective bandwidth of trunk t at link e. Let represent a traffic trunk that is requesting an LSP. Denoting s descriptors using in place of t, we assume that an LSP request provides the network admission control and routing decision maker with s ....

F. P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, vol. 9, no. 1, pp. 5-16, 1991.

....allocation in time domain. In a cellular network, let cell i be the current location of the mobile user x as shown in figure [1] Let C be the set of cells where mobile user x requests to reserve resources D(x) as shown by shaded region in figure [1] D(x) refers to the effective bandwidth [14] [15], 16] requirement of the user computed based on users individual requirement regarding channel quality, delay requirements etc. The set of cells C correspond to the spatial component of the resources that maybe reserved on behalf of the user. Minimizing the number of cells in C will therefore ....

F. P. Kelly, "Effective bandwidth of multi-class queues," Queuing Systems, Vol 9, pp 5-16, 1991

....this paper, we will assume that the interconnection time and size of the network are constant and focus on the costs related to bandwidth and quality of service. Before we develop the cost functions of the QoS network, let s briefly review the model of effective bandwidth developed by Kelly et al. [10]. Kelly developed a quite general model expressing the association between effective bandwidth with a source traffic load and network resource characteristics, such that, if the sum of the effective bandwidth of the source using the network resource is less than a certain level, then the resource ....

KELLY, F. P. Effective bandwidth at multi-class queues. Queueing Systems (1991), 5--16.

....buffer overflow for traffic characterization, and relates the time parameter of the many sources asymptotic with the results from frequency domain approaches to traffic characterization. The analysis in [RE96, MdV96] used the many source asymptotic. The effective bandwidth, first introduced in [Kel91, GH91] Hui88, GAN91] also contained related notions) is a scalar which gives the amount of resources that must be reserved for a source in order to satisfy its QoS requirements; such a scalar enables problems (e.g. admission control, routing) in broadband networks carrying bursty traffic to ....

.... multiplexed is either fully on or fully off over the typical period during which the buffer fills; this gives the simplification that the overflow probability depends on the source characteristics only through the peak and mean rates, hence the bufferless on off fluid model can be used [Hui88, Kel91] In ATM networks, when the buffer size is small, overflow can occur due to cell scale congestion; the latter is related to the transfer of information in small, fixed size cells. The fluid model fails to capture such congestion. Prior work [RSKJ91, NRSV91, FLVO94] has modeled the burst and the ....

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

....CB2 1RX, U.K. ideas from circuit switched networks, such as the well developed theory of trunk reservation and dynamic routing) can be applied to ATM networks. This paper builds on the work of Courcoubetis and Walrand [6] De Veciana, Olivier and Walrand [7] Gibbens and Hunt [10] and Kelly [11]. Kelly obtained effective bandwidths for a problem of controlling the average work seen by a customer arriving to a D=GI=1 queue. Courcoubetis and Walrand obtained effective bandwidths for a model in which the number of cells that a source delivers to the buffer at discrete time points is a ....

....can be approximated in a manner that makes sense for large buffers and which is a function of just two parameters: the source mean rate and index of dispersion. Thus the index of dispersion is identified as an appropriate measure of burstiness. Our effective bandwidths agree with those of Kelly [11] and they agree with the formula obtained in [7] and [10] for a two level Markov modulated fluid when the size of the buffer is large. 2 White noise stationary sources Consider a switch that carries traffic comprised of N i independent sources of class i, i = 1; M . Suppose time is ....

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

.... assume that each source is fully on or fully off over the typical period during which the buffer fills; this gives the simplification that the cell loss probability (CLP) depends on the source statistics only through the peak and mean rates, and the bufferless on off fluid model can be used [Hui88, Kel91, Kel96]. If the time for buffer overflow t is in the order of magnitude of 1=h, which occurs when the buffer per source b is very small, cell scale effects can not be disregarded; in this case, use of the bufferless fluid model may underestimate the CLP by several orders of magnitude. As an ....

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

....sources will be producing cells above their average rate and other sources will be producing cells below their average rate, there is potential for statistical multiplexing. Thus a source s effective bandwidth need not be as great as its peak rate. Of course, as other authors have noted, e.g. [9], the motivation for seeking to assign effective bandwidths to bursty ATM sources is that, if this can be done, then problems of admission control and routing in ATM networks resemble those in circuit switched networks. Subsequent research can focus on how ideas from circuit switched networks, ....

....from circuit switched networks, such as the welldeveloped theory of trunk reservation and dynamic routing) can be applied to ATM networks. This paper builds on the work of Courcoubetis and Walrand [4] Veciana, Olivier and Walrand [5] Kesidis and Walrand [10] Gibbens and Hunt [6] and Kelly [9]. Kelly obtained effective bandwidths for a problem of controlling the average work seen by a customer arriving to a GI=D=1 queue. Courcoubetis and Walrand obtained effective bandwidths for a model in which the number of cells that a source delivers to the buffer at discrete time points is a ....

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

....statistical characterization of its behavior. Typically this is achieved by constructing and analyzing a parametric model of the source, based on precise or statistical descriptions of its behavior. Parameters of the model may be fitted from actual measurements of the traffic, made in isolation[10], 11] The second approach argues that it is unreasonable to expect traffic sources to provide these parameters. Instead, its supporters argue that the network is capable of deriving the traffic characteristics in a concise and efficient way. This approach, based on on line measurements of ....

F.P. Kelly, Effective Bandwidths at Multi-Class Queues, Queueing Systems, 9:5-16, 1991.

....networks congestion manifests itself as buffer overflows; the Quality of Service (QoS) faced by various connec tions can be quantified by the buffer overflow probability. To provide QoS guarantees the so called effec tive bandwidth admission control mechanism has been proposed [1] 2] [3], 4] 5] 6] Briefly, effective bandwidth is a number between the peak ad average rate of a connection such that when connections are allocated their effective bandwidth in an appropri Research partially supported by the NSF under a Career award ANI 9983221 and grants NCR 9706148 and ....

F.P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, vol. 9, pp. 5-16, 1991.

....of cell capacity. The concept of EB has been discussed for CDMA networks. Tse and Hanly [9] obtain EB asymptotically for different receiver structures. Evans and Everitt [10] show EB is also applicable to CDMA. Due to the ufferless nature of a CDMA cell, we follow the approximation used in [14] for the derivation of effective bandwidth for a bufferless server. To guarantee user QoS, we require user outage probability to be confined. Therefore, we start from the evaluation of outage probability in (3) for the study of capacity. Assume there are J types of user traffic, each having nj ....

F. P. Kelly, "Effective bandwidths at multi-class queues," Queue- ing Sys, vol. 9, pp. 5-15, 1991.

.... purposes, impossible to compute analytically (based on inexact data and imperfect models) much research has been devoted to deriving successful approximations of such a region (see [1, 9, 13] One possible approximation for the acceptance region is based on the concept of an effective bandwidth [2, 7, 11, 13]. The effective bandwidth of a given call is the amount of bandwidth that this call must be allocated so as to statistically guarantee an acceptable level of QoS for the new call and all other calls currently being served. The traffic load on a link is therefore defined in terms of the number of ....

F.P. Kelly, "Effective Bandwidths at Multi-class Queues," Statistical Laboratory, University of Cambridge, preprint, 1991.

....effective bandwidth, e, of the source can be shown to be equal to: e = log( 1 2 P 11 exp(ffiR)P 22 q (P 11 exp(ffiR)P 22 ) 2 4exp(ffiR) 1 Gamma P 11 Gamma P 22 ) ffi (2) where P 11 = R Gamma r)b Gamma r) R Gamma r)b and P 22 = 1 Gamma 1=b. Other related work is Kelly [9] and Whitt [13] 3 Effective Bandwidth of an Arbitrary on off Source Consider a traffic source which alternates between on and off periods where the lengths of the on and off periods have an arbitrary probability distribution. The distributions of the off and the on periods are given by: f ....

F. P. Kelly. Effective Bandwidth at Multi-Class Queues. Queueing Systems, 9:5--16, 1991. 19

....correct as the buffer size gets large and the tail probabilities get small, and because it provides a basis for assigning actual effective bandwidth values to different sources (voice, data, video, etc. e.g. see Hui [31] Gibbens and Hunt [26] Guerin, Ahmadi and Naghshineh [28] Kelly [32], Sohraby [41] 42] Chang [10] Whitt [45] Elwalid and Mitra [23] Kesidis, Walrand and Chang [33] Glynn and Whitt [27] Courcoubetis, Kesidis, Ridder, Walrand and Weber [20] and Chang, Heidelberger, Juneja and Shahabuddin [11] The additive nature of effective bandwidths is clearly ....

....Lucantoni. A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance. IEEE J. Sel. Areas Commun. SAC4 (1986) 856 868. 31] J. Y. Hui. Resource allocation for broadband networks. IEEE J. Select. Areas Commun. SAC 6 (1988) 1598 1608. [32] F. P. Kelly. Effective bandwidths at multi class queues. Queueing Systems 9 (1991) 5 16. 33] G. Kesidis, J. Walrand and C. S. Chang. Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEE ACM Trans. Networking 1 (1993) 424 428. 34] A. Kuczura. The interrupted Poisson ....

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

....the behaviour of connections already admitted. For example, traffic models based on fluid flow approximations have been used in analysing network bandwidth and buffer utilisation. Based on the aboveknowledge, CACschemes have been developed in whicheach source is assigned an effective bandwidth [8] in order to meet its QOS while still permitting a statistical multiplexing gain. 5.1.1 Effective Bandwidths Effective bandwidths are a way of summarising the statistical information of a source in a single parameter. The complex problem of resource allocation of a multi service network can be ....

....effective bandwidths it is possible to get a linear equation similar to the circuit switched networks and see if there is 12 sufficient bandwidth left to admit another connection. The original idea of effective bandwidths can be attributed to Hui [10] and a summary of the uses can be found in [8]. Using that notation, here is an overview of the mathematical formulation. The simplest model is that there are J sources that are sharing the same link whichhas a capacityofC. Let X j be the load produced bysourcej and assume that all the X j s are independent random variables with possibly ....

F. P.Kelly, `Effective Bandwidths at Multi--Class Queues', Queueing Systems Theory and Applications, Vol. 9, No. 1--2, pp 5--15, Oct. 1991.

....the behavior of calls already admitted. For example, traffic models 3 based on fluid flow approximations have been used in analyzing network bandwidth and buffer utilization [9] Based on the aboveknowledge, CACschemes havebeendeveloped in which each source is assigned an effective bandwidth [10] in order to meet its QOS while still permitting a statistical multiplexing gain. There are many problems with these approaches. Users maynotknow enough about the statistics of their calls to provide accurate traffic descriptors to the network. This is particularly true for certain data transfers ....

F. P. Kelly, `Effective Bandwidths at Multi-Class Queues', Queueing Systems Theory and Applications, Vol. 9, No. 1-2, pp 5-15, Oct. 1991.

....system (WCS) with transmission bandwidth and infinite finite buffer capacity, one can get the following steady state queue distribution as a function of (2) where the random variable denotes the queue length. We call this function a PBC of an input process. Many approaches [8] 10] 12] [13] have been developed to upper bound the tail distribution of queue. Particularly in [8] Chang considered an arrival process whose moment generating function is upper bounded by a linear envelope process, which is viewed as a stochastic version of (1) and derived an exponential bound of the tail ....

....arrival process whose moment generating function is upper bounded by a linear envelope process, which is viewed as a stochastic version of (1) and derived an exponential bound of the tail distribution of queue. In addition, 8] proved the equivalence between well known effective bandwidth [12] [13] and the minimum envelope rate of feasible linear envelope processes. Given the theory of effective bandwidth [12] 13] also gives an upper bound of the tail distribution of a queue in a regime where is very large and the tail probability is very small. In summary, the PBC is not those asymptotic ....

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F. P. Kelly, "Effective bandwidths at multi-class queues," Queueing Syst., vol. 9, pp. 5--16, 1991.

....approach, each flow is allotted an effective bandwidth that is larger than its average rate but less than its peak rate, thus increasing the network utilization. In most cases the a priori characterization of flows is based on a statistical model [13] 14] or on a fluid flow approximation [15] [16]. But it is definitely not possible to provide accurate and tight statistical models for each individual flow. Therefore, a priori traffic characterizations in service admission control will have fairly loose upper bounds. We advocate that measurement based admission control schemes will play a ....

F. P. Kelly, "Effective Bandwidths at Multi-Class Queues", Queuing Systems, 9:5-16, 1991.

....computation. In this chapter we will resort to a popular (conservative) approximation based on the Chernoff s bound in the context of bufferless multiplexing. Most of the ideas herein follow from the qualitative characteristics of the admissible region which are captured by this bound, see e.g. [32, 25]. Suppose N i.i.d. traffic streams are carried on a bufferless link, and each stream has a stationary cell arrival rate A i ; i 2 f1; Ng. Assume that the link capacity is c and we require that the aggregate arrival rate to the link exceeds the capacity only rarely with a probability no ....

....(3.3) for a given n. 2 Note that the q is an implicit function of n. Hence the bandwidth requirement (per connection) for each traffic type is affected by the traffic mix. It has been shown in [26] that the complement of the admissible set in R J is a convex region. It was suggested in [32, 25] that a linear approximation could thus be used to conservatively represent the boundary of the admissible region. However, a linear approximation of the admissible region boundary is not always accurate, and may affect performance. The nonlinearity in the admissible region is called the ....

F.P. Kelly. Effective bandwidths of multi-class queues. Queueing Systems, Vol. 9, No. 1:5--16, 1991.

....or routing. On line evaluation of effective bandwidth have been proposed by De Veciana, Kesidis and Walrand [20] Duffield et al. 21] proposed maximum entropy as a method for characterizing traffic sources and their effective bandwidth. Further relevant references are Gibbens and Hunt [22] Kelly [23], Kesidis, Walrand and Chang [24] Gu erin and Gun [25] and Dziong, Juda, and Mason [26] 11 3.2 Heavy traffic approximation Sohraby [27] proposed an approximation for bandwidth allocation based on the asymptotic behavior of the tail of the queue length distribution It is known that the ....

F. P. Kelly, Effective bandwidths at Multi-Class Queues, Queueing Systems, 9:5--16, 1991.

....formula given in Section 4 to the queue. In such a queue, it is hard to obtain the asymptotic decay constant in general. For this reason, the asymptotic decay constant has been assumed to be one in most studies of call admission control (CAC) based on the effective bandwidths technique (see, e.g. [4, 7, 20, 21, 34, 35] and references therein) It is known, however, that the asymptotic decay constant can vary by several orders of magnitude depending on source models [5] Contrary to the previous works, we discuss an approximate formula of the loss probability taking the asymptotic decay constant into account. In ....

....buffer size N . In the past, several researchers have discussed CAC based on the tail distribution, rather than the loss probability. In most studies, the tail distribution hasbeenapproximated as T k (1=z ) k , which is the basis of the effective bandwidths technique (see, e.g. [4, 7, 20, 21, 34, 35] and references therein) Further, by identifying the loss probability with the tail distribution, the loss probability has been approximated as P loss (1=z ) N # (30) where N denotes the buffer size. Note here that the asymptotic decay constant is assumed to be equal to one in this ....

F. P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, Vol.9, pp.5--16, 1991.

....the efficiency stems from a separation of independent sources (see Theorem 3 in Section 2) the rest stems from the heavy traffic expansion. For additional related work on admission control, see Chang [9] Elwalid and Mitra [14] Gibbens and Hunt [17] Guerin, Ahmadi and Naghshineh [19] Kelly [23], Sohraby [37,38] Whitt [43] and references therein. In this context Sohraby [37,38] also considers (one term) heavy traffic approximations for the decay rates. It turns out that the first term of the heavy traffic expansion for the asymptotic decay rates coincides with the rate of the ....

....the number of required terms increases as r decreases; see the numerical examples in Section 6. The asymptotic expansions only yield approximations for the asymptotic decay rates. This applies directly to admission control based solely on asymptotic decay rates, e.g. on effective bandwidths [9,14,17,19,23,37,38,43], but for approximations of the tail probabilities themselves we also need the asymptotic constant. In [1] we suggested a simple approximation for the asymptotic constant, in particular, the product of the asymptotic decay rate and the mean (which becomes a relatively simple approximation upon ....

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

....by numerically inverting equation (2) to find the largest number of connections maintaining a cell loss probability still below the CLR objective. The effective bandwidth is then given by . Various approaches have been proposed that give an approximation of the effective bandwidth (Gurin, 1991; Kelly, 1991; Lindberger, 1991; Lindberger 1994, Sykas et al. 1992) Among them the solution presented by Lindberger (1994) which is also described in (Roberts et al. 1996) is promising as it yields a simple formula for computing the effective bandwidth based on the source parameters and , the service rate ....

Kelly, F.P. (1991) "Effective bandwidths at multi-class queues", Queueing Systems, Vol. 9, pp. 5-15.

....The total traffic stream offered to the buffer is a mix of the N traffic streams, each stream generated by a class of j sources; this mixed stream is characterised by the vector (n 1 ; nN ) A performance measure P of the buffer is obviously a function of this vector. In his study Kelly [1] shows that for many, relevant p.m. s P the components n j of the mix (n 1 ; nN ) satisfy in first approximation a linear relation for given value of P i.e. N X j=1 c j n j = 1; 1.1) with of course c j depending on the type of chosen p.m. P . In (1.1) the coefficient c j of n j is ....

Kelly, F. (1991). Effective bandwidth at multi-class queues, Queueing Systems 9, p. 5-16.

....would be willing to provide this sensitive information. Our ultimate goal is to integrate the Resource Agent into the switch. Since the connection admission control scheme of the switch is not available at this point, we use one of the equivalent bandwidth evaluation methods described in [4] [5], 6] 7] 8] The equivalent bandwidth computation scheme does not have to be accurate or complicated because the Resource Agent is only responsible for performing a preliminary admission control. If the preliminary admission control is too optimistic, excessive bandwidth may be used by one CNRMS ....

F. Kelly, "Effective bandwidths at multi-class queues," Queuing Sys., vol. 9, pp. 5-15, 1991.

....the GOS of this request and other traffic that are currently being served are satisfied. Otherwise, the service request is rejected. As noted in [42, 40, 34] an open and challenging problem is how to design a network controller to make such a decision. Recent research in this area can be found in [5, 14, 15, 19, 21, 22, 20, 23, 25, 26, 30] and many others. Motivated by the problem in communication networks, in this paper we study two types of stability problems: i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length ....

....then the queue length cannot be bounded exponentially with respect to . In particular, when the arrival process is a 18 superposition of independent two state Markov modulated processes, we show that the notion of MER is equivalent to the recently developed notion of effective bandwidth in [26, 20, 23] and is also related to the Perron Frobenius eigenvalue in [37] In order to extend these results to networks, in Section 3.3 we consider marked point processes, in which there are a sequence of arrival points and a sequence of marks associated with the arrival points. The marks can be viewed ....

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F.P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, Vol. 9, pp. 5-16, 1991.

....tail distribution of quantities such as buffer occupancy and response times can be used in the design of high speed networks. In addition, bounds can also be used to develop policies for controlling the admission of new applications or sessions to the network. The interested reader is referred to [2, 3, 4, 6, 7, 9, 10, 13, 14, 16] where these issues have been addressed. 2 Exponential Bounds In what follows, for any probability measure q on IR we will substitute the notation q c (s) for q( s; 1) for all s 2 IR. 3 Let ffl(s; Delta ) s 0g be a collection of measures on IE such that Z IE Q(x; A) Z s Gamma1 fl(s ....

F. P. Kelly, "Effective Bandwidths at Multi-Class Queues", Queueing Systems, 9, pp. 5-16, 1991.

....with (k; j) entry given by E[exp( A i n ) Y i n 1 = j) j Y i n = k) Therefore, we deduce from Proposition 2.4 that P (X x) C( e Gamma x ; 8x 0 if N X i=1 log( i ( c: 4. 2) The quantity c i ( log( i ( is called the effective bandwidth of the process (A i n ) n [14, 24, 29, 32, 39, 29]. A similar result was presented by Chang and Cheng in [11, Example 3.4] but with a different coefficient C( The coefficient in [11] denoted as Gamma( is given by Gamma( max i;j r i ( r j ( where (r 1 ( r K ( T is the (positive) right eigenvector of the matrix ....

F. P. Kelly, "Effective Bandwidths at Multi-Class Queues", Queueing Systems, 9, pp. 5--16, 1991.

....enables us to determine that call acceptance regions based on deterministic delay constraints are convex. This is in contrast to call acceptance regions based on statistical multiplexing with large deviation asymptotics, in which case it is the complement in the positive orthant which is convex [15]. This also shows that, in general, the limit of the call acceptance region based on statistical multiplexing when the loss probability target tends to may be strictly larger than the call acceptance region based on lossless multiplexing. We also define similarly the deterministic equivalent ....

....with large deviation asymptotics. In such cases, a set of values is acceptable if a given upper bound on loss probability is less than , where is a small, fixed value. In a broad family of cases, and especially for bufferless models, it is the complement in the positive orthant which is convex [15]. Call the acceptance region for a given value of . becomes smaller as decreases to , and the limit is Under the assumptions in [15] the complement of in the positive orthant is also convex, since the union of an increasing set of convex sets is convex. Of course, we have for all and thus . ....

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F. Kelly, "Effective bandwidths of multiclass queues," Queueing Syst., vol. 9, no. 1, pp. 5--15, 1991.

.... for the worst case scenario, instead it guarantees a bound on the probability of lost late packets based on statistical characterization of traffic [VPV88] In most cases the a priori characterization of flows is based on a statistical model [Hui88, SS91] or on a fluid flow approximation [GHN91, Kel91] 1 In this kind of approach, each flow is allotted an effective bandwidth that is larger than its average rate but less than its peak rate. If one can precisely characterize traffic a priori, this approach will increase network utilization. However, we think it will be quite difficult, if not ....

F.P. Kelly. "Effective Bandwidths at Multi-Class Queues". Queueing Systems, 9:5--16, 1991.

....traffic, an input may be connected to multiple outputs requiring a list of outputs to configure an input. Because an output can still receive a cell from at most one input, it is still sufficient to indicate to each output which input is connected to. 1 N log CHAPTER 1 Introduction 8 [29], 30] 31] 44] 45] This is not generally possible with input queued switches due to variations in delay caused by contention for the switching fabric and queueing at the input.The main disadvantage of output queueing is that for a N port switch, the internal interconnect and output queues ....

Kelly, F.P.. "Effective bandwidths at multiclass queues," Queueing Systems Theory and Applications, Oct. 1991, vol.9, (no.1-2):5-15.

....cells. All cells are the same size and a network connection s traffic contracts for a certain CLR to be provided by the network. To address this problem at least two methods have been developed. One involves computing an equivalent bandwidth (EBW) that the requesting call s traffic will use [2, 4, 6, 5, 7, 10, 9]. More recently, another approach based on modeling the volatility of call traffic using Reflected Brownian Motion (RBM) 8] has been proposed. In our study, we compare two CAC schemes in terms of network cost. Our results indicate that the selection of one from the many different schemes for CAC ....

F.P. Kelly. Effective bandwidth at multi-class queues. Queuing Systems, 9:5--15, 1991.

....have shown that the constant ff is usually of the order one. This led many authors to believe that the following simple approximation is true IP[Q x] e Gamma x : 2. 3) Based on this result, admission control policies derived on the concept of effective bandwidth have been developed; see [20, 45, 51, 50, 72, 103, 102]. For this reason equation (2.3) is usually called [25] the effective bandwidth (EB) approximation. However, as discussed in [25] the EB approximation may often be highly inaccurate. This is usually the situation when many sources (N) are multiplexed; in this case it was shown that ff e ....

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

.... may be justified on the basis of the fact that the small packet delays in future high speed networks and projected network operation under conditions of low loss will result in near preservation of connection traffic characteristics as it proceeds through the network [O 91] see also Kelly [Kel91, pp. 12] Consider first an arbitrary allocation policy, that assigns q i of the end to end QOS, Q, to node i. The maximum number of connections supportable under this policy is then N = Min 1ih F i (q i ; R i ) 19) We are now interested in the maximum relative improvement (over policy ) ....

F. P. Kelly. Effective bandwidths at multi-class queues. QUESTA, 9:5--16, 1991.

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

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

....classes, and is the best possible linearly constrained region for the expected mix. For many realistic examples of source classes the region A(n ) is not that sensitive to the precise choice of n the boundary of A is approximately a hyperplane see for example [10] Next we show, following [17], that the notion of an effective bandwidth, additive over sources of different classes, generalizes to certain models of a buffered resource. Our first model of a buffered resource is as follows. Suppose that bursts from a source of class j arrive in a Poisson stream of rate j and have lengths ....

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

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F. P.Kelly, `Effective Bandwidths at Multi-Class Queues', Queueing Systems Theory and Applications, Vol. 9, No. 1-2, pp 5-15, Oct. 1991.

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F. P. Kelly. Effective Bandwidth at Multi-Class Queues. Queueing Systems, 9:5--16, 1991. 19

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F. P. Kelly (1991). Effective bandwidths at multi-class queues. Queueing Systems, no. 9:5--16.

No context found.

F. Kelly. Effective bandwidths at multi-class queues. Queueing Systems, Theory and Applications, 9(1-2):5--16, 1991.

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F.P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, 9(1991).

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F.P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, Vol. 9, pp. 5-16, 1991.

No context found.

F.P. Kelly, "Effective bandwidths at multi-class queues," Queueing Systems, Vol. 9, pp. 5-16, 1991.

No context found.

Kelly, F.P., "Effective Bandwidths at Multi-class Queues," QUESTA 29 pp. 1474--1481, 1981.

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