An adaptive algorithm for measurement-based admission control in integrated services packet networks

Computer Communications 23 (2000) 1363–1376 www.elsevier.com/locate/comcom

An adaptive algorithm for measurement-based admission control in integrated services packet networks C. Casetti a,*, J. Kurose b, D. Towsley b a

Dipartimento di Ingegneria Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy b Computer Science Department, University of Massachusetts, Amherst, MA 01003, USA

Abstract Call admission control is typically devised so as to employ the declared worst-case traffic descriptors for incoming calls, a solution resulting in poor bandwidth utilization. A measurement-based admission scheme is an appealing alternative, offering adaptivity to the changing traffic conditions, while allowing statistical multiplexing gains to be exploited. In this paper, we examine the problem of determining which traffic characterization a measurement-based admission control algorithm should require of sources requesting access. We also propose an adaptive measurement-based admission control algorithm that simplifies the estimation process. We test the new algorithm under different traffic scenarios and show that a high utilization level is achieved without violating delay-based QoS guarantees. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Call admission control; QoS guarantee mechanisms; Integrated services packet networks

1. Introduction The increasing bandwidths offered by today’s high-speed switching and transmission technologies have enabled a new generation of real-time applications that require Quality of Service (QoS) guarantees from the network. As a result, numerous researchers [1,2,6,9,15,19,22] have advocated extending the Internet service model to accommodate the varying bandwidth, delay bound, and loss tolerance requirements of these applications. One widely discussed network service model is one which provides “hard” guarantees to an application. In this case, an application is guaranteed a specified bandwidth, maximum end-to-end delay and no packet loss. While such a guaranteed service is appropriate for the CBR-like applications with strict loss and delay requirements, it may not be appropriate for variable bit rate, adaptive, real-time applications [2] that can both tolerate and adapt to certain amounts of loss and/or end-to-end delay. Thus, additional service models that provide “softer” or statistical (rather than hard) guarantees have been proposed [1,2,26]. These alternate service models seek to provide such guarantees while still exploiting the advantage * Corresponding author. Tel.: 1 39-011-5644126; fax: 1 39-0115644099. E-mail addresses: [email protected] (C. Casetti), [email protected] (J. Kurose), [email protected] (D. Towsley).

of statistical multiplexing at routers. Several recent IETF RFCs [23,26] lay the foundation for an Integrated Services Internet architecture based on such service models. Of particular interest to us in this paper is the proposed Internet service class known as controlled-load service [1,26]. With this kind of service, measurements of ongoing admitted calls are used together with the declared traffic parameters of a call seeking admission to the network in making the call acceptance/rejection decision. The goal of this admission control process is to admit a call only if there are sufficient resources to satisfy the QoS requirements of the new call, while at the same time not violating QoS guarantees made to existing, already-admitted calls. In this paper, we propose and evaluate a new measurement-based admission control algorithm. Our work extends existing work on measurement-based admission control [2,17] in three important directions: • We examine the question of how best (from an admission control standpoint) to characterize a source among several “equivalent” leaky bucket source characterizations. We find that among equivalent characterizations, an admission control algorithm that uses a characterization with a smaller token bucket size and a higher token rate can often achieve an overall higher utilization than with other equivalent characterizations, without significantly increasing the percentage of bits experiencing a delay violation.

0140-3664/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S0140-366 4(00)00182-1

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Fig. 1. Network Scenario.

• We investigate which performance metrics should be measured. We show that measuring rate rather than delay provides us with more stable estimates and results in a simpler admission scheme. • We consider how to adaptively adjust the length of the window of time over which measurements are made. This obviates the need to choose, a priori, a length for a fixed measurement window. We show that our algorithm achieves a high utilization while being able to keep its delay commitments. Our study is chiefly conducted through simulation. The remainder of this paper is organized as follows. In Section 2, we provide a brief overview of the past work in the area of measurement-based admission control, and summarize the specific algorithm proposed in Ref. [17], tailoring the description to the simple network setting we have considered. Section 3 addresses the issues of source characterization and suggests that measuring sources’ rates, rather than their packet delays, may be a better choice for a measurement-based admission control process. Our adaptive, window-based measurement and admission control algorithm is detailed in Section 4. Section 5 presents the simulation results of this algorithm under different traffic scenarios, including the empirical traffic patterns such as video traces. Section 7 concludes the paper. 2. Previous work on measurement-based admission control While the problem of admission control to a shared resource has been addressed by many researchers in recent years, the idea of using on-line measurements in the admission control process has been studied in only a few selected works. In Ref. [24], Tedijanto and Gu¨n propose an admission control mechanism based on the on-line estimation of the equivalent bandwidth of an ATM connection using a dynamically adjusted token bucket. Also in an ATM frame-work, but considering the superposition of sources rather than a single connection, the work by Dziong et al. [4] employs a Kalman filter to estimate the aggregate effective bandwidth for admission control purposes. Vin et al. [25] present an observation-based mechanism to estimate the retrieval time of a media block from a multimedia server, using such

information to grant access to clients who requested predictive service. Measurement-based admission control for predictive service in Integrated Services Packet Networks was first introduced in Ref. [2] and then further developed in Refs. [17,18], where a delay and rate measurement scheme for the predictive service was proposed. Jamin et al. [16] examine and compare four admission control algorithms (a “simple sum” and a “measured sum” of requested resources, an “acceptance region” following the scheme detailed in Ref. [11], and an Hoeffding bound-based equivalent bandwidth approach) and three measurement mechanisms (timewindow, point samples and exponential averaging). In a recent paper [13], Grossglauser and Tse offer a quantitative description of the impact of several key aspects of measurement-based admission schemes, such as flow arrival dynamics, parameter estimation and memory requirements; their insights confirm some of the results shown in this paper, particularly the need for a large amount of memory in the traffic estimator for reliable admission. Grossglauser and Tse [14] also point out that large link capacity as well as separation of time-scales of call arrivals and bandwidth requirements fluctuations make it very unlikely that a string of wrong estimates may lead to resource overallocation. Our work has also benefited from ideas in Ref. [8], particularly where it is advocated that the admission control algorithms should not rely on over-detailed sources characterization and that traffic models for multimedia sources (especially audio) should exhibit long-range dependence. As our work builds on Ref. [17], we next describe the admission scheme proposed in that paper. The interested reader is referred to Ref. [17] for further details. As our extensions will be considered in the context of a simpler network model than the one considered in Ref. [17], we first describe our network model. 2.1. Network model We consider the network scenario shown in Fig. 1: a link of capacity m connects two switches; each switch is assumed to have an infinite buffer, so that packet loss probability is not a factor in our study. This allows us to focus on other QoS metrics related to delay and throughput. Sources connect to the first switch through infinite bandwidth links. The first switch concentrates (multiplexes) packets destined to the downstream switch. All traffic from the source belongs to a single traffic class. While there is no guaranteed-service traffic in our model, we note that other traffic classes can be handled using such techniques as Weighted Fair Queuing [2,3,12,20] or classbased queuing [9]. 2.2. Source model New calls arrive to R1 in Fig. 1 according to a Poisson process with rate rs calls per second. Call holding times are independent and identically distributed exponential random variables with mean Th. The traffic generated by an accepted

C. Casetti et al. / Computer Communications 23 (2000) 1363–1376

call is modeled by an On/Off Markov-modulated fluid process. While in the On state, a source generates traffic at the peak rate r; during the Off period no traffic is generated. In our simulations, unless otherwise noted, we use m ˆ 10 Mb=s; rs ˆ 10 calls=s; and Th ˆ 135 s: In our simulations, On and Off periods are either exponentially distributed or Pareto distributed with a Pareto shape parameter equal to 1.5. In either case, On and Off periods have the mean 1=a ˆ 0:3125 s and 1=b ˆ 0:3125 s; respectively. It should be noticed that Pareto On periods alter the actual lifespan of sources as we chose not to end sessions in the middle of a Pareto On period, so as not to miss the effect of long activity periods. The resulting average source holding time was therefore slightly higher than the exponential mean (i.e. approx. 142 s). Depending on the scenario we are considering, the peak rates of admitted sources are either fixed (we refer to these as homogeneous sources) or exponentially distributed with mean r ˆ 64 kb=s (heterogeneous sources). Our motivation for choosing fluid sources, rather than a discrete, packetized source model will be explained in Section 3. We note that with the choice of the parameters above, the resulting network load is so high that, without any admission control mechanism, the network would achieve close to 100% utilization. 2.3. The admission algorithm We now describe the measurement-based admission algorithm proposed in Ref. [17], in the context of the simple network scenario described above. The key to the admission process is that the new call (or “flow” of data) should be accepted only if: • The current traffic conditions at the switch can ‘guarantee’ that the call receives the QoS it requests. In the following we will precisely define what we mean by ‘guarantee’. • The acceptance of the new call does not cause QoS guarantees previously made to admitted flows to be violated. To achieve these goals, a call seeking admission is required to provide a traffic characterization, known as a TSpec [23,26]. Specifically, the call characterizes its traffic with two token bucket parameters: r (a token generation rate) and s (a bucket depth) such that over a period of time T, the traffic generated by the call will not exceed rT 1 s: We will address the problem of choosing appropriate values of r and s in Section 3. The measured system quantities are: • D, the delay experienced by the traffic in the switch queue; • n , the aggregate traffic rate at the switch. As a result of the measurement process, the call admission algorithm will have an estimate of these two quantities, D^ and n^ at any given time. Given these estimates, an arriving

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call is granted admission if the following two conditions hold [17]: ^ a new estimate of 1. Given a current delay estimate, D; delay provided the call is admitted, D^ 0 ; is formed such that D^ 0 ˆ D^ 1 s=m: Note that s=m is the amount of time required to transmit a full token bucket’s worth of data from the new call. This new delay estimate must satisfy:

s D bound . D^ 0 ˆ D^ 1 m

…1†

2. If the upper-bound rate declared by the new call, r , is added to the current estimate of the aggregate traffic rate, n^ ; the estimate of the rate provided the call is admitted is n^ 0 and it satisfies:

m T . n^ 0 ˆ n^ 1 r

…2†

the utilization bound, mT, is referred to as the utilization target and is meant to be ‰0; m† in range. If the new call is admitted, the new estimates for delay and rate are then taken to be D^ 0 and n^ 0 : We now discuss how these values are subsequently updated. 2.4. The estimation process In the following, we will find it useful to distinguish between the “estimates” and “measurements” of delay or the rate. “Measurements” are the observed delay values made over time, and “estimates” are constructed using these measurements, as well as the declared traffic parameters of arriving calls. Delay measurements are collected for a fixed period of time known as the “measurement window”. In the simplest case, at the end of a measurement window, an estimate is set to the highest observed value of that measure during the measurement window. In certain cases, however, the measurement window will be terminated prematurely and the estimates updated in a different manner. Specifically [17]: • When a new call is admitted, the delay and rate estimates are updated using Eqs. (1) and (2). It is worth noting that these estimates are not updated when a call terminates. • When a single measurement exceeds the current estimate, the estimate is updated to be l times the sampled value. The factor l allows us to be more conservative by overestimating the quantity, resulting in more conservative admission control when the measure is close to the bound. In Ref. [17] it is suggested that l ˆ 2 be used for delay and l ˆ 1 for rate estimates. We will use these values. In our fluid-flow simulation model, a single, ‘instantaneous’ delay measurement is computed by dividing the switch queue length at that time by the queue’s service rate m . Since there is no such thing as an ‘instantaneous’ rate

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Table 1 Equivalent token buckets with measurement window ˆ 10 s

s

r

% Utilization

% Late bits

Max. obs. Delay

% Delay rej.

% Rate rej.

1 4 10 20

64 62.8 61.1 58.8

74.53 74.46 55.35 32.24

0.0 0.0 0.0 0.0

0.334 0.0 0.0 0.0

0.0 0.73 98.28 100.00

100.00 99.27 1.72 0.00

measure, a small interval S is specified and a rate measurement is taken as the number of bits transmitted on the link during this interval. In our model, we assume S ˆ 0:5 s; i.e. comparable to the average duration of On/Off periods. It should be pointed out that the quality of the call admission scheme [17] is highly dependent on the values of the so-called ‘performance tuning knobs’ (target utilization, l , length of the measurement window). Selection of these values is an open problem that goes beyond the simple task of fine-tuning the behavior of the admission scheme. Arguably, a very challenging issue is finding the ‘right’ length of the measurement window, since the performance of the admission scheme heavily relies on it. As noted in Ref. [17], too short a window lowers the admission threshold as soon as the traffic thins out, leaving the network dangerously exposed to bursts. On the other hand, too long a measurement window leads to an excessively conservative scheme by delaying the time when flows’ TSpecs (that give a worst case traffic characterization) are replaced with on-line measurements (that reflect that call’s actually generated traffic). It is our experience that it is difficult to determine an appropriate length of the measurement window without a priori knowledge of the traffic. For these reasons, a measurement window that adapts to the network traffic is desirable. We present such an adaptive algorithm in Section 4. First we consider the problem of source characterization.

3. Source characterization and measured parameters 3.1. How should we characterize sources? The admission control process discussed above uses the token bucket parameters as a source traffic characterization. In our simulations, we will model sources as Markovmodulated fluid sources whose smallest unit is the bit. By virtue of this choice, we are not committed to any packet

size. However, tokens are representative of whole data units like cells and packets. We assume that a token is equivalent to a 1-kb data unit (as in Ref. [17]). Following Ref. [5], we consider bufferless leaky-bucketconstrained Markov-modulated On/Off fluid sources with parameters (s , r ). This introduces the problem of how to choose values for s and r . In Ref. [17], it is suggested that (s , r ) pairs be chosen empirically as the smallest s and r that result in the desired loss rate at the token bucket. Of course, such strategy cannot be employed if the traffic characteristics of the ON/OFF sources have not been evaluated in advance. Using Eqs. (2.18), (2.21) and (8.8) in Ref. [5], we can derive the following expression relating the bucket depth, s , the token rate, r , the source peak rate, r, and the source’s fluid loss probability, p at the leaky bucket:

s ˆ 2…r 2 r†

 ln 1 2

ar a…r 2 r† 1 …a 1b†rbp br  ar … a 1 b† 1 2 … a 1 b† r

 …3†

For a given bucket size, Eq. (3) can be used to obtain the value of the token rate which results in a target loss probability of p at a bufferless token bucket. We chose p ˆ 10 25 : We will refer to (s ,r ) pairs with the same target loss probability as equivalent. Given the set of equivalent source characterizations satisfying Eq. (3), we would like to choose a characterization that, when coupled with the admission control process described in Section 2, results in high link utilization at the switch without excessive QoS violation. In order to explore the impact of using different “equivalent” source characterizations, we ran simulations using the call admission algorithm and the homogeneous source model described in Section 2. Delay and rate estimates were computed using the procedure outlined above, with a delay bound of 16 ms and a utilization target of 95% (which yields a rate bound of 9.5 Mb/s).

Table 2 Equivalent token buckets with measurement window ˆ 1 s

s

r

% Utilization

% Late bits

Max. obs. Delay

% Delay rej.

% Rate rej.

1 4 10 20

64 62.8 61.1 58.8

91.30 91.25 91.25 90.70

0.37 0.35 0.29 0.18

65.32 41.55 39.40 43.15

3.74 4.12 6.53 23.60

99.76 99.67 98.54 86.07

C. Casetti et al. / Computer Communications 23 (2000) 1363–1376 Table 3 Average and variance of delay and rate measure Window length (s)

Avg. delay

Avg. rate

Delay variance

Rate variance

1 3 5 10

9.51 0.48 0.056 0.0371

9.24 8.49 8.01 6.99

543.8 7.994 0.705 0.493

1.55 1.33 1.22 1.12

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and the token rate is computed on-line for each newly generated call with random peak rate, using Eq. (3). We omit those results for reasons of space. Given these observations regarding the equivalent token bucket characterizations, for the remainder of this paper we will use s ˆ 1; which results in a value of r equal to a source’s peak rate.

3.2. Which performance measures should be observed? Tables 1 and 2 summarize the results we obtained for measurement window lengths of 1 and 10 s, respectively. Simulations were run for a total of 10 000 s of simulated time each, which is at least 3 orders of magnitude longer than the measurement window. The computed utilization values were such that the width of the 99.8% confidence interval was within 1% of the point estimate; the percentage of late bits showed significantly more variability. Each row in a table shows for an equivalent (s ,r ) pair, • the resulting utilization of the switch output link; • the percentage of bits that violated the delay bound; • the maximum delay in ms observed during the simulation (i.e. the maximum queue length divided by the service rate); • the percentage of flows, among those rejected, that were rejected because of delay constraint violations (see Eq. (1)); • the percentage of flows, among those rejected, that were rejected due to target utilization constraint violations (see Eq. (2)). Thus, for example, the first row of Table 2 indicates that among those flows rejected, 3.74% violated the delay constraint and 99.76% violated the target rate constraint. Note that the percentages do not add up to 100%, since a portion of the flows violated both bounds. Several observations are in order. Comparing Tables 1 and 2 indicates that a longer measurement window results in more conservative admission control: with a 10 s window, no late bits were observed, while with a smaller window (1 s), there was a small amount of delay violation. However, the achieved link utilization is much higher in the case of the small window. Interesting observations can also be made regarding the different bucket sizes used in the source characterization. The larger the bucket declared by the source, the more likely it is that a flow requesting admission is denied access on the grounds that it might violate the delay bound. This is because a larger s in Eq. (1) provides a higher delay estimate. However, with a large s , a number of these flows would appear to have been unnecessarily rejected, since none of the admitted flows ever experienced a delay violation for any of the values of s shown. We observed a similar behavior for other window lengths, as well as with bucket sizes larger than 20. We also observed similar behavior with heterogeneous sources, where only the bucket size is fixed

The admission scheme described above makes use of both delay and rate measures. An adaptive window algorithm would be noticeably simpler if it could rely on one parameter only. Tables 1 and 2 show that, especially for small values of s , the large majority of rejected calls are rejected on the basis that they violate the rate criteria Eq. (2). An argument for using rate measurements rather than delay measurements is provided by a simulation experiment in which we evaluated the mean and the variance of both delay and rate measures (not estimates) using the window length as a parameter. Our purpose in doing so is to determine which is a more “stable” estimate. The simulation scenario is essentially the same as in the previous Section. However, rather than running fixedlength simulations, we used the batch means approach [7] as a stopping criteria. The simulations were run until the width of the 90% confidence interval was within 10% of the point estimate of the aggregate source rate. Table 3 shows the mean and variance of delay and rate measurements for different measurement window sizes, for the case that the admission control algorithm had a utilization target of 100%. The average delay is in ms, its variance is in ms 2, while the average rate is in Mb/s and its variance is in (Mb/s) 2. These results discourage the use of delay measurements to obtain estimates. Not only is the delay variance extremely high for small windows, but it is also very sensitive to the window length. Also, note the impact that varying the measurement window length has on delay and rate averages. While the rate merely shows a 25% decrease over the range of window sizes considered, the average delay values differ by 2–3 orders of magnitude. Jamin et al. [17] suggest using a utilization target equal to 0.9, which drastically reduces the delay variance stabilizing the measures. However, since our algorithm seeks to control admission using the fewest possible number of parameters, we chose not to rely on any utilization target. The adaptive measurement-based admission control algorithm we present in the following section thus only uses rate measurements. We note that this also fits well with the IETF specification of the Controlled Load Service [26], in that it does not make use of target values for such direct performance measures (e.g. delay or loss) but rather ensures that adequate bandwidth is available to handle the declared traffic rate.

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Fig. 2. First-level algorithm.

4. A new measurement-based admission algorithm In the previous sections we have discussed several aspects of measurement-based call admission control. We enumerate these and other considerations by pointing out that a measurement-based admission algorithm should: • in order to adapt to changing traffic conditions, enlarge or shrink its measurement window so as to realize a more or less conservative admission process; • not require sources to supply more than their peak rate; • rely upon rate, rather than delay measurements. We note, however, that delay measurements could be used in conjunction with rate measurements. We present a two-level adaptive measurement-based call admission algorithm. The first-level algorithm, which in essence forms the core of the algorithm, uses rate measurements and the declared traffic parameters of accepted calls to adaptively adjust the length of the measurement window. The second-level algorithm adjusts the values of parameters used by the first-level algorithm. The idea behind the first-level algorithm is quite simple. The algorithm continually shrinks the length of the measurement window (resulting in admission control decisions that

Fig. 3. Second-level algorithm.

work towards increasing link utilizations; see Tables 1 and 2, and the discussion in Ref. [17] until the utilization reaches a threshold, which we will identify through a trigger rate. This trigger rate is smaller than the output link capacity and provides an early warning that the system is about to reach a load where a greater degree of control is required (this does not necessarily mean that we are approaching overload, see Ref. [26]). The first-level algorithm then reacts by enlarging the measurement window until the measured rate drops below the trigger, at which point the window can be shrunk again. In a sense, the admission control algorithm operates like the TCP congestion control-it tries to be more and more aggressive in admitting calls until something “bad” happens. At that point it backs off (i.e. it shrinks the window, resulting in a strict call admission process) but after backing off again begins to decrease the measurement window. Fig. 2 illustrates the first-level algorithm. The variables used are: • W, length of the measurement window. In our simulations, we do not allow the measurement window to become smaller than 1 s. • fu, window enlargement factor. • fd, window shrinking factor. We will refer to fd and fu as window shaping factors. Although the algorithm does away with the “performance tuning knobs” and fixed length window in the original algorithm ([17], Section 2), it appears that we have traded these for equally uncertain parameters: the trigger value and the shaping factors. The second-level algorithm addresses the issue of how to use long-term measures to fine-tune these parameters. Fig. 3 illustrates the second-level algorithm. It lowers and raises the trigger rate in search of a good operating point, in response to traffic fluctuations. The algorithm reacts to delay bound violations while cushioning the negative effects of the delay variance. Two delay-related measures are used. The first delay measure is the instantaneous delay violation percentage; it provides a warning that a percentage of bits in the switch’s queue are violating the delay bounds (and thus is easily implementable). The second delay measure is the long term delay violation percentage; it is the percentage of late bits observed since time 0. We stress that this is only one of the possible solutions: an alternative scheme might choose to address the instantaneous delay alone rather than also including the long-term percentage. The algorithm operates as follows: at time 0 we set a target value for the long-term delay violation percentage, which we strive to guarantee over a period of time which we will refer to as the target commitment period. On resetting the measurement window, whenever the first-level algorithm attempts to change the window length, it checks a flag indicating whether the instantaneous delay percentage has been detected to be higher than the target delay percentage at any time during the past window. If so, the admission

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Table 4 Adaptive-window algorithm-homogeneous exponential sources

Table 6 Adaptive-window algorithm-heterogeneous Pareto sources

Target (%)

Avg. window size

Percentage of adm. flows

Percentage of late bits

Utilization (%)

Target (%)

Avg. window size

Percentage of adm. flows

Percentage of late bits

Rel. util. (%)

0.01 0.05 0.10 0.20 1.00 2.00

5.1 4.5 3.9 3.4 2.3 1.8

19.7 20.0 20.2 20.5 20.8 21.3

0.019 0.054 0.108 0.202 1.000 1.996

84.97 85.91 87.23 87.93 90.40 91.67

0.01 0.05 0.10 0.20 1.00 2.00

10.1 10.1 8.4 7.3 5.1 4.0

0.2 0.2 0.2 0.2 0.2 0.2

0.0599 0.0530 0.1064 0.2081 1.0347 1.9939

75.16 75.43 77.40 78.85 82.25 84.44

algorithm has been too aggressive and the trigger rate value is lowered, resulting in more conservative admission control. If the instantaneous delay percentage never exceeded the target, the algorithm checks whether the long term delay violation percentage is currently under the target value. If it is, the window trigger value is raised. If it is not, no action is performed. This last choice is motivated by the fact that if the instantaneous target delay is not violated, the trigger is sufficiently low and the overall delay only needs more time to settle under the target. In order to lessen the scheme’s sensitivity to delay variations, we suggest additive rather than multiplicative trigger increments. Of course, the trigger cannot be higher than the rate bound, i.e., the output link capacity. We will indicate trigger increments by tu and td . It is worth pointing out that, although the algorithm does not explicitly use the loss rate as a driving parameter, a finite buffer at the switch would account for an upper bound on the delay accumulated by the travelling packets. Conceivably, this upper bound exceeds the delay target. Therefore, if we assume that packets reaching the destination after the delay target are useless as far as the end applications are concerned, their loss has no negative impact on the overall performance. If anything, a finite buffer results in reduced delay fluctuations. As a final remark, a possible drawback of our algorithm is its lack of fairness regarding two or more flows exhibiting the same peak rate but different average rate; the flows are treated equally by our admission algorithm, and may be rejected based of their peak rate. Still, the one with the lowest average rate, if admitted, may have had a lesser impact on the CAC performance than the others, thanks to a better chance of exploiting statistical multiplexing. IndisTable 5 Adaptive-window algorithm-heterogeneous exponential sources Target (%)

Avg. window size

Percentage of adm. flows

Percentage of late bits

Utilization (%)

0.01 0.05 0.10 0.20 1.00 2.00

5.2 3.9 3.9 3.2 2.0 1.6

21.8 23.5 23.4 24.4 27.0 28.4

0.017 0.055 0.102 0.207 1.009 1.999

76.75 79.94 79.96 81.88 86.40 88.30

criminate rejection may thus appear unfair, unless a classdependent admission scheme is deployed. Multiple-class extensions of our CAC algorithm are left for future studies. 5. Simulation results We now evaluate the proposed algorithm under different traffic scenarios. Basically, we will consider scenarios with ON/OFF sources only, as well as a mix of video traces and ON/OFF sources. 5.1. ON/OFF sources The first scenario uses the source model described in Section 2.2. The algorithm’s parameters are: • • • •

f u ˆ 1:2; fd ˆ 0:9; tu ˆ 0:01 Mb=s; td ˆ 0:05 Mb=s:

In our first set of results, the target commitment period was 12 h, and a delay bound of 16 ms was chosen. Ideally, a 12-h period would allow network administrators to alternate between more and less stringent commitments depending on the portion of the day when the network is likely to be more congested. The trigger was initially set at 9.0 Mb/s. Tables 4–6 show the performance of the two-level algorithm using different target values for the long term delay violation percentage, ranging from 0.01 to 2%, for both homogeneous and heterogeneous exponential sources as well as for heterogeneous Pareto sources (see Section 2.2). As expected, as the target (allowable) percentage of delay violations (column 1 in the tables) increases, so does the achieved utilization (column 5) and the percentage of flows that were admitted to the network (column 3). Note that both types of sources adhere to the guaranteed target, i.e., the percentage of late bits observed (column 4) closely matches the long term delay violation target values. We also observe that homogeneous sources achieve a higher utilization than heterogeneous exponential sources, which, in turn, appear to utilize the network better than Pareto sources. Intuitively, this is because fixed rate sources (and exponential sources in general) yield a more ‘predictable’ behavior, and increased predictability results in more reliable estimates of both

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Fig. 4. Percentage of overall late bits, as a function of time, for different delay targets-heterogeneous sources.

Fig. 5. Trigger values as a function of time, for different delay targetsheterogeneous sources.

delay and bandwidth utilization at the time of admission. This, in turn, yields fewer violations and provides the opportunity of better exploiting the available bandwidth, thus increasing utilization. The effects of the ‘unpredictability’ of Pareto sources can also be observed for very low delay violation target values (i.e. 0.01): the algorithm did not have time to recover from an unexpectedly large spurt of delay violations early on. We will gain a better insight into similar transient behaviors looking at Figs. 4 and 5. Fig. 4 plots the percentage of late bits since time 0 for three different values of the target long term delay violation percentage (1, 0.1 and 0.01%) as a function of time for heterogeneous exponential sources (in the plot, a generic point at time t is averaged over a [0,t] time window). For each curve, we can identify two critical regions in Fig. 4: a transient region where the curve reaches a peak and then converges to the target value, and a steady state region capturing the algorithm’s effort to preserve the target percentage. The transient peak is generated by the lack of information available to the network at the beginning of each 12-h target commitment period, resulting in the algorithm being unable to find a stable operating point. When the targets are 1% and 0.1% the system reaches the steady state long before the commitment period has expired. However, this is not the case when the target is 0.01%. Actions that might reduce the transient length include setting a lower starting value of the trigger or initializing

the measurement window length, W, to several hundred seconds. In Section 6, we suggest a strategy to reduce the transient, observing how the use of a sliding window restricts the unwanted transient to the algorithm’s startup phase only. The trigger rate dynamics for the three experiments from Fig. 4 are shown in Fig. 5. We observe that the trigger rates increase at times when the percentage of late bits is below the delay target (this is particularly evident for the 0.1% case at approximately times 13 000, 23 000, 32 000 and 41 000 s). Indeed, the algorithm raises the trigger rate each time the target value is reached. So far, we have studied the behavior of the algorithm when the network operates in overload. In the next set of experiments, we investigate the algorithm’s response to traffic fluctuations. Specifically, the call arrival process was modified so that every 100 s on average (values were determined as i.i.d. exponential random variables with mean 100), the call arrival rate was switched between 10 sources per second with a probability 2/3, and 0.01 sources per second with a probability of 1/3. The workload consists of heterogeneous sources. Although the ensuing traffic pattern is not meant to model the actual network traffic, it is nevertheless interesting to test how the algorithm handles extreme situations where prolonged underload periods are followed by sharp traffic increases. The trigger was initialized at 7 Mb/s so as to reduce the length of the transient period. Using the same algorithm parameters listed above, we obtained the results in Table 7. Note that the algorithm fails to meet the target value of the long-term delay violation percentage when the target is smaller than 0.1%. Also, the utilization percentage has to be related to the utilization which could be achieved, under the same traffic conditions, if no admission control were enforced, i.e. approx. 77%. Fig. 6 compares the performance of our algorithm to that of the fixed-window admission scheme described in Section 2. The comparison focuses on each scheme’s ability to provide a bounded percentage of late bits (0.5% in our case) over a period of 12 h (however, a width of the 95%

Table 7 Adaptive-window algorithm-sensitivity to traffic fluctuations Target (%)

Avg. window size

Percentage of adm. flows

Percentage of late bits

Utilization (%)

0.01 0.05 0.10 0.20 1.00 2.00

1.83 1.80 1.77 1.45 1.38 1.16

25.2 25.5 26.1 30.2 31.7 35.3

0.0954 0.0904 0.1326 0.2345 0.9988 1.9999

44.66 44.83 45.83 46.02 60.47 53.35

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Fig. 8. Utilization as function of trigger increments and decrements-heterogeneous sources. Fig. 6. Comparison of fixed-window and adaptive-window admission schemes-heterogeneous sources.

confidence interval within 5% of the point estimate of the delay was reached well before the end of the simulation of the fixed-window algorithm). Each point on the ‘fixedwindow curve’ identifies the delay violation percentage and utilization for a given fixed-window length (whose value in seconds is plotted next to each point). It can be seen that, when the target delay violation is 0.5%, the adaptive window scheme achieves a percentage of delay violations of 0.497%, while providing a utilization of 83.7%. If we want to achieve better performance in terms of both delay violations and utilization with the fixed-window scheme, we are forced to try different values of the fixedwindow size. Fig. 6, however, shows that only a 1 s range of window lengths (delimited by the dotted lines) around W ˆ 2:5 s fits our needs. A smaller window would lead to a much higher percentage of late bits, whereas larger values entail lower utilization. Also note that, the fixed-window scheme can provide a higher link utilization than the adaptive one for the same percentage of late bits (88.2 vs. 83.7%); this can be explained by the more conservative approach employed by the adaptive window to achieve the intended target. The above considerations illustrate the tradeoff we are confronted with: we can achieve better performance

using a fixed-window scheme, provided we can find the proper range of window sizes. However, it is difficult for a network manager to choose the appropriate fixed-window size to handle the current traffic pattern (besides, in our fixed-window simulations we have assumed W identical for both delay and rate measurements, and chosen l ˆ 2; although we had no reason to believe these choices to be either good or bad). So far, we have taken for granted that our values for the window shaping factors and the target increments are good. Figs. 7 and 8 give an indication of how sensitive our algorithm is to the choice of these parameters. The figures show the percentage of late bits and the utilization with a target value of 0.05% for the long-term delay violation percentage, heterogeneous sources and constant overload (i.e. no traffic fluctuations). The increments are expressed in Mb/s and range from 0.001 to 1 and the results are shown for three different choices of first-level algorithm parameters. In each figure, we can identify two regions: a flat portion of the surface, corresponding to “desirable” performance, and an incline (upper right corner in Fig. 7, defined by tu . 0:1 and td , 0:05; and near end of Fig. 8, defined by td . 0:1†: These inclines correspond, respectively, to missed targets (too aggressive) and poor utilization (too conservative). We make two observations. First of all, we observe that extra care must be taken in choosing the values of td : very low decrements appear to have little effect on keeping the percentage of late bits close to the target, unless paired with equally low increments, while large decrements result in poor utilization. Second, these results underscore the role of the second-level algorithm in driving the operations of Table 8 Video sequences statistics

Fig. 7. Percentage of overall late bits as a function of trigger increments and decrements-heterogeneous sources.

Trace

Mean rate (Mb/s)

Peak rate (Mb/s)

H

Lambs Simpsons Asterix Mr. Bean Race

0.18 0.46 0.59 0.44 0.77

0.85 1.49 1.85 1.76 3.24

0.89 0.89 0.81 0.85 0.99

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Table 9 Adaptive-window algorithm-heterogeneous sources 1 video traces Target (%)

Avg. window size

Percentage of adm. Flows

Percentage of late bits

Utilization (%)

0.01 0.10 0.50 1.00 2.00

8.19 7.34 5.36 4.60 3.48

27.2 29.9 31.2 32.5 35.3

0.0928 0.2286 0.5506 1.0327 2.0484

88.20 88.88 89.92 90.29 91.00

the first-level algorithm: flat regions are almost overlapping regardless of the values of the first-level parameters. We have observed a similar behavior for other scenarios as well, confirming a simple “rule of thumb”—that increments should be additive, while decrements should be multiplicative. Also, these curves justify the choice of the algorithm parameters used in our simulations, although a robust procedure for choosing these values remains a topic for future research. 5.2. Video traces In order to test algorithm’s response to traffic exhibiting long-range dependence (LRD), we also ran simulations using video traces in combination with a background of ON/OFF sources. One issue which a measurement-based admission control for video traffic must deal with is the non-stationarity of flows: while it is possible to “safely” grant access to a call on the grounds that its peak rate is lower than the (measured) available link bandwidth, it is also true that this source’s peak rate (its TSpec) is forgotten as soon as a new measurement is carried out. As in our algorithm the network is not aware of when the peak will occur, it has no means of preventing any queue build-up it may cause, other than by enlarging the window and slowing down the admission process from then on. Also, these results allow us to investigate the behavior of the algorithm under a mix of longer-lasting, fixed-length flows (video traces) and shorter, random-length flows (ON/OFF sources). In our simulations, video traffic was generated using about 30 min worth of data from five randomly phased MPEG-I video traces. Specifically, we used excerpts from: “The Silence of the Lambs” (lambs), “The Simpsons” (simpsons), “Asterix” (asterix), “Mr Bean” (Mr Bean), “Formula 1 Car Race” (race). Table 8 lists the mean rate, peak rate and Hurst parameter for each of these traces. The Hurst parameter (H) is useful to determine the long-range dependence of a trace: values of H close to 1 indicate a high degree of LRD, whereas the absence of LRD is denoted by H ˆ 0:5 (see Ref. [10]). Further details on the MPEG sequences used in this paper can be obtained from Ref. [21]. Since it would be unrealistic to transmit video traces over a 10 Mb/s link, m is increased to 155 Mb/s, thus allowing a higher degree of statistical multiplexing. The ON/OFF source model is identical to the heterogeneous source

Fig. 9. Comparison of fixed-window and adaptive-window admission schemes-heterogeneous sources 1 video traces.

model used in previous Sections. The call arrival rate is still rs ˆ 10 calls=s; and traffic from a new call is generated by either an ON/OFF source (with probability p s ) or by a video trace (with probability p n ). The video traces driving the traffic generation process for a video call are randomly chosen among the five traces listed above. Call holding times for video traces are fixed and equal to 1666 s (corresponding to 40 000 frames). Call holding times for ON/OFF sources are as in the previous sections, i.e. about 10 times shorter than for the video traces, on average. Note that with this choice of parameters the network operates in constant overload. The algorithm’s parameters used in these simulations are the same as in Section 5.1, the target commitment period was 12 h, the delay bound was 16 ms and the trigger was initialized to 145 Mb/s. Unless otherwise stated, we use ps ˆ 9=10 and pn ˆ 1=10: Table 9 shows the performance of the algorithm for different target values. It can be seen that, while values higher than 0.1% can be easily reached, values lower than 0.1% miss their target. We conclude that non-stationarity affects the algorithm’s performance for very small targets in a greater way than it does for less tight guarantees. Also, comparing Tables 4, 5 and 9, it can be observed that the algorithm had to use a larger window size (see “Avg. window size” in the tables) for video traces so as to lessen the impact of sudden traffic bursts; moreover, the increased level of statistical multiplexing allowed by the higher link bandwidth …m ˆ 155 Mb=s for video traces vs. m ˆ 10 Mb=s for ON/OFF sources only) was reflected by the higher utilization achieved using video traces. As in the previous section, we can compare fixed and adaptive window algorithms (Fig. 9), again using 0.5% as target percentage of late bits. The TSpecs used by the Admission Control algorithm were s ˆ 1 and r ˆ peak rate: While comparing Figs. 6 and 9, we observe how the fixed window algorithm yields substantially different values of delay violations and utilization for the same

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Table 10 Adaptive-window algorithm-heterogeneous sources 1 video traces. Different values of p v-target: 0.5% of delay violations

pv

Avg. window size

Percentage of adm. flows

Percentage of late bits

Utilization (%)

0.10 0.15 0.20 0.30 0.40

5.36 14.78 16.35 19.46 33.70

31.2 17.3 13.3 9.2 6.7

0.550 0.557 0.677 0.410 0.128

89.92 82.70 82.71 80.59 76.75

window length under different traffic conditions. For example, if we wish to achieve the 0.5% target using the fixed window algorithm, a window is required that is twice as large as the one needed for a population of heterogeneous ON/OFF sources. On the other hand, the adaptive window admission algorithm achieves the same target under both scenarios without having to adjust either window shaping factors or trigger increments. We also examined scenarios with a different mix of video traces and ON/OFF sources, namely with different values of p n and p s. Table 10 illustrates the performance of the adaptive algorithm for p n ranging from 0.1 to 0.4, with a target of 0.5% of delay violations. These results underscore the impact of the increased number of video traces: while the target commitments were, generally, kept, the utilization appears to become much lower as p n is increased, indicating that the algorithm has to be especially cautious in the admission process (as proved by the larger average window sizes and the low percentage of admitted flows). Notice also how the violation percentage for p n ˆ 0:4 is way below the target, showing that early violations were so frequent that the adaptive algorithm was forced to use a very large window to become more conservative. In order to justify the need for this “cautiousness”, we simulated the pn ˆ 0:4 case using the fixed-window algorithm. The results, shown in Table 11, are quite surprising: not only is the delay violation percentage higher than 0.5% using the selected range of window sizes, but the utilization is also lower than for the adaptive window scheme, something we have not observed so far.

Fig. 10. Percentage of late bits, as a function of time, for different delay targets; 24-h commitment period only.

proposing should be operational for much longer, so a provision for the extension of the target commitment period should be put in place. In our opinion, simply resetting every measured quantity at the end of the commitment period is not the correct choice. As shown in Fig. 4, a transient rise of delay bound violation can be expected if the measure of the long-range percentage of late bits is reset. Earlier, we observed that this transient rise is determined by a lack of information available to the algorithm. Therefore, the solution is to extend the coverage of the algorithm without devoiding it of the useful metrics it has been gathering up until that moment. However, a simple “indefinite” extension of the target commitment period is not a sensible alternative, either, as it would result in the algorithm relying on stale data that might be of little use, if not misleading. A possible solution would be to let the algorithm “gradually” forget older data as new ones become available, without ever emptying its memory. There are several ways to implement this solution. One would be introducing a filter weighing less and less older samples; or, a sliding window

6. Extending the target commitment period So far, our results were limited to relatively short time spans, i.e. 12 h. Conceivably, the CAC scheme we are Table 11 Fixed-window algorithm-heterogeneous sources 1 video traces. pv ˆ 0:4 Window size

Percentage of late bits

Utilization (%)

1.00 10.00 100.00 500.00

47.5597 32.3581 14.0324 3.7743

96.86 96.09 89.77 73.46

Fig. 11. Percentage of overall late bits, as a function of time, for different delay targets-1 week.

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Table 12 Overall utilization Target (%)

Utilization (%)

0.05 0.10 0.50 1.00

74.53 75.23 80.54 82.22

several hundreds samples long could be introduced. For the sake of simplicity, we followed the second approach. In our scheme, every ts seconds (we will refer to this time period as ‘Tslot’), metrics are stored in a circular buffer of size ns, each buffer position holding two separate metrics referring to the last Tslot: the number of transmitted bits in the last ts seconds, and the number of late bits observed in the queue during the same Tslot. Let xi denote the number of bits transmitted in a generic ith Tslot and, similarly, li the number of late bits observed in the queue in the same Tslot. Clearly, after filling the circular buffer with data from ns Tslots, older metrics are replaced by newer ones. At the nth Tslot, we can define Xn as the sum of all the bits transmitted in the last ns Tslots; similarly, we can define Ln as the sum of all late bits observed in the last ns Tslots. More precisely: Xn ˆ

n X

xi if n # ns

…4†

iˆ1

Xn ˆ

n X

xi if n . ns

…5†

iˆn 2 ns

Ln ˆ

n X

li if n # ns

…6†

iˆ1

Ln ˆ

n X

li if n . ns

…7†

iˆn 2 ns

Fig. 13. Percentage of late bits, as a function of time-sliding window coverage ˆ 12 h commitment period only.

delay violation percentage”, used by our second-level algorithm, as the percentage of late bits observed in the last ns Tslots, rather than since time 0. When implementing this solution, we are faced with choosing two additional parameters, ts and ns, which together define a new ‘sliding’ target commitment period. However, the choice of these parameters is not as difficult as the choice of the other parameters of our algorithm. Common sense, supported by preliminary experiments, indicates that the “right” choice is to use a very small ts granularity with respect to the length of the commitment period, so as to soften the impact when data from a Tslot are erased. The choice of ns appears to be more critical, although a sufficiently long sliding window provides a better averaging effects and smooths out oscillations. In our simulations, the “natural” choice was to pick ts and ns yielding a sliding window 24 h long, although we also show results for different lengths and with some traffic fluctuations. The first set of results uses the same settings found in Section 5.1, with heterogeneous Pareto sources, and a sliding window defined by ts ˆ 200 s and ns ˆ 432 Tslots. Figs. 10 and 11 refer to the simulation of a week’s worth of data

The quantities Ln and Xn are used to redefine the “long term

Fig. 12. Percentage of late bits, as a function of time-sliding window coverage ˆ 6 h commitment period only.

Fig. 14. Percentage of late bits, as a function of time-sliding window coverage ˆ 24 h commitment period only.

C. Casetti et al. / Computer Communications 23 (2000) 1363–1376

Fig. 15. Percentage of late bits, as a function of time-sliding window coverage ˆ 48 h commitment period only.

showing the percentage of late bits output by the node in the commitment period only and during the whole week, for different delay targets. More precisely, each point in Fig. 10 represents the long-term delay violation percentage (computed through Xn and Ln) and refers to observations spanning the past 24 h (or less, as in the first day). Points in Fig. 11 instead refer to percentages collected since time 0, hence the smoother profile. Table 12 reports the overall utilization (like before, without admission control we would have achieved a near 100% utilization). One of the most interesting conclusions that can be drawn from these results is that by letting the algorithm run for long periods of time and exploiting the sliding window technique, some shortcomings, such as the presence of the initial transient peak, can be reduced, if not overcome. As the network traffic often exhibits fluctuations depending on the time of day, we tried to gauge the algorithm’s response to a scenario where the node was underloaded for an average of 12 h a day, and overloaded for the remaining 12 h (again, on average). Overload traffic corresponds to the same traffic pattern we used above, while underload conditions were simulated using a call arrival rate 10 times lower. Figs. 12–15 show the results for sliding windows whose parameters are ts ˆ 200s and ns equal to 108, 216, 432 and 864 Tslots, respectively yielding a coverage of 6, 12, 24 and 48 h. It is interesting to observe that short sliding windows (i.e. 6 and 12 h) still show transient rises when traffic switches from underload to overload, while the problem almost completely disappears when sliding windows are longer than the underload period. It can be concluded that, when the algorithm is allowed to keep a sufficiently long memory of the past network behavior, sudden traffic fluctuations are less disruptive.

7. Conclusions This paper addressed the topic of measurement-based admission control. Through the use of simulation, we have

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addressed the problem of what source characterization and what measured quantities best suit a measurement-based admission control scheme for predictive service. This enabled us to devise a simple admission algorithm, relying on rate measures only and using only the source peak rate as TSpec. A delay bounding scheme was used together with the admission algorithm to provide delay guarantees over a period of time. The analysis of our results have shown the algorithm and the bounding scheme to perform well under high loads and different traffic conditions, including empirical traffic patterns such as video traces. Comparisons with a fixed-window scheme have shown that our adaptivewindow algorithm provides a similar performance, without the uncertainty related to the choice of the window size. We also tested it with traffic fluctuations, which have proved to be more difficult to handle, particularly under tight guarantees, unless a sufficiently long memory of network behavior is made available to the CAC algorithm.

Acknowledgements The authors would like to thank Francesco Lo Presti for many valuable discussions on the subject of fluid models and admission control. This work was supported in part under NSF grant NCR-9508274.

References [1] B. Braden, D. Clark, S. Shenker. Integrated Services in the Internet Architecture: An Overview, RFC 1633, June 1994. [2] D. Clark, S. Shenker, L. Zhang, Supporting real-time applications in an integrated packet services network, in: Proceedings of IEEE SIGCOMM’92, Baltimore, MD, USA, August 1992. [3] A. Demers, S. Keshav, S. Shenker, Analysis and simulation of a fair queueing algorithm, in: Proceedings of ACM SIGCOMM’89, Austin, TX, USA, September 1989. [4] Z. Dziong, B. Shukhman, L.G. Mason, Estimation of aggregate effective bandwidth for traffic admission in ATM networks, in: Proceedings of IEEE INFOCOM’95, Boston, MA, USA, May 1995. [5] I. Elwalid, D. Mitra, Analysis and design of rate-based congestion control of high speed networks. I: stochastic fluid models, access regulation, Queueing Systems 9 (1991) 29–64. [6] D. Ferrari, A. Banerjea, H. Zhang, Network support for multimedia: a discussion of the tenet approach, Computer Networks and ISDN Systems 10 (1994) 1267–1280. [7] G.S. Fishman, Principles of Discrete Event Simulation, Wiley, New York, 1991. [8] S. Floyd, Comments on measurement-based admission control for controlled-load services. URL: ftp://ftp.ee.lbl.gov/papers/admit.ps.z. [9] S. Floyd, V. Jacobson, Link-sharing and resource management models for packet networks, IEEE/ACM Transactions on Networking 3 (4) (1995) 365–386. [10] M.K. Garrett, W. Willinger, Analysis, modeling and generation of self-similar VBR video traffic, in: Proceedings of the ACM SIGCOMM’94, London, UK, August 1994. [11] R.J. Gibbens, F.P. Kelly, Measurement-based connection admission control, in: Proceedings of the 15th International Teletraffic Congress, June 1997. [12] S. Golestani, A self-clocked fair queueing scheme for broadband

1376

[13]

[14]

[15]

[16]

[17]

[18]

C. Casetti et al. / Computer Communications 23 (2000) 1363–1376 applications, in: Proceedings of IEEE INFOCOM’94, Toronto, Canada, June 1994. M. Grossglauser, D. Tse, A Framework for robust measurementbased admission control, in: Proceedings of ACM SIGCOMM’97, Cannes, France, September 1997. M. Grossglauser, D. Tse, Measurement-based call admission control: analysis and simulation, in: Proceedings of IEEE INFOCOM’97, Kobe, Japan, April 1997. J. Hyman, A.A. Lazar, G. Pacifici, Joint scheduling with quality of service constraints, IEEE Journal on Selected Areas in Communications 9 (7) (1991) 1052–1063. S. Jamin, P.B. Danzig, S. Shenker, Comparison of measurementbased admission control algorithms for controlled-load service, in: Proceedings of IEEE INFOCOM’97, Kobe, Japan, April 1997. S. Jamin, P.B. Danzig, S. Shenker, L. Zhang, A measurement-based control algorithm for integrated services packet networks, in: Proceedings of ACM SIGCOMM’95, Cambridge, MA, USA, August 1995. S. Jamin, P.B. Danzig, S. Shenker, L. Zhang, Measurement-based admission control algorithm for integrated services packet networks, IEEE/ACM Transactions on Networking 5 (1) (1997) 56–70.

[19] J. Kurose, Open issues and challenges in providing quality of service guarantees in high speed networks, ACM Computer Communication Review 23 (1) (1993) 6–15. [20] A.K. Parekh, R.G. Gallager, Generalized processor sharing approach to flow control in integrated service networks: the single node case, IEEE/ACM Transactions on Networking 1 (1993) 344–357. [21] O. Rose, Statistical properties of MPEG video traffic and their impact on traffic modeling in ATM systems, Research Report 101, University of Wuerzburg, Germany, February 1995. [22] S. Shenker, Fundamental design issues for the future internet, IEEE Journal on Selected Areas in Communications, September (1995). [23] S. Shenker, C. Partridge, R. Guerin, Specification of the guaranteed quality of service, RFC 2212, September 1997. [24] T.E. Tedijanto, L. Guen, Effectiveness of dynamic bandwidth management mechanisms in ATM networks, in: Proceedings of IEEE INFOCOM’93, San Francisco, CA, USA, March 1993. [25] H.M. Vin, A. Goyal, P. Goyal, An observation-based admission control algorithm for multimedia servers, in: Proceedings of ICMCS’94, Boston, MA, USA, April 1994. [26] J. Wroclawski, Specification of the controlled-load network element service, RFC 2211, September 1997.