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A t generated by a ow in an interval of length t satis es a constraint of the form: A t rt s. If the link serves this ow at a rate at least equal to r, then the maximum buffer content from this ow is s. Loss can therefore be completely avoided and delay bounded by providing a buffer of size s and implementing a scheduling discipline that ensures the service rate r [7]. The constraint on the input rate can be enforced by means of a leaky bucket, as discussed below. 16.3.2 The Leaky Bucket Traf c Descriptor
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Open-loop control in both ATM and Internet service models relies on the leaky bucket to describe traf c ows. Despite this apparent convergence, there remain serious doubts about the ef cacy of this choice. For present purposes, we consider a leaky bucket as a reservoir of capacity s emptying at rate r and lling due to the controlled input ow. Traf c conforms to the leaky bucket descriptor if the reservoir does not over ow and then satis es the inequality A t rt s introduced above. The leaky bucket has been chosen mainly because it simpli es the problem of controlling input conformity. Its ef cacy depends additionally on being able to choose appropriate parameter values for a given ow and then being able to ef ciently guarantee quality of service by means of admission control. The leaky bucket may be viewed either as a statistical descriptor approximating (or more exactly, providing usefully tight upper bounds on) the actual mean rate and burstiness of a given ow or as the de nition of an envelope into which the traf c must be made to t by shaping. Broadly speaking, the rst viewpoint is appropriate for stream traf c, for which excessive shaping delay would be unacceptable, while the second would apply in the case of (aggregates of) elastic traf c. Stream traf c should pass transparently through the policer without shaping by choosing large enough bucket rate and capacity parameters. Experience with video traces shows that it is very dif cult to de ne a happy medium solution between a leak rate r close to the mean with an excessively large capacity s, and a leak rate close to the peak with a moderate capacity [25]. In the former case, although the overall mean rate is accurately predicted, it is hardly a useful traf c characteristic since the rate averaged over periods of several seconds can be signi cantly different. In the latter, the rate information is insuf cient to allow signi cant statistical multiplexing gains. For elastic ows it is, by de nition, possible to shape traf c to conform to the parameters of a leaky bucket. However, it remains dif cult to choose appropriate leaky bucket parameters. If the traf c is long-range dependent, as in the case of an aggregation of ows, the performance models studied in this book indicate that queueing behavior is particularly severe. For any choice of leak rate r less than the peak rate and a bucket capacity s that is not impractically large, the majority of traf c will be smoothed and admitted to the network at rate r. The added value of a nonzero bucket capacity is thus extremely limited for such traf c. We conclude that, for both stream and elastic traf c, the leaky bucket constitutes an extremely inadequate descriptor of traf c variability.
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To perform admission control based solely on the parameters of a leaky bucket implies unrealistic worst-case traf c assumptions and leads to considerable resource allocation inef ciency. For statistical multiplexing, ows are typically assumed to independently emit periodic maximally sized peak rate bursts separated by minimal silence intervals compatible with the leaky bucket parameters [8]. Deterministic delay bounds are attained only if ows emit the maximally sized peak rate bursts simultaneously. As discussed above, these worst-case assumptions bear little relation to real traf c characteristics and can lead to extremely inef cient use of network resources. An alternative is to rely on historical data to predict the statistical characteristics of know own types. This is possible for applications like the telephone, where an estimate of the average activity ratio is suf cient to predict performance when a set of conversations share a link using bufferless multiplexing. It is less obvious in the case of multiservice traf c, where there is generally no means to identify the nature of the application underlying a given ow. The most promising admission control approach is to use measurements to estimate currently available capacity and to admit a new ow only if quality of service would remain satisfactory assuming that ow were to generate worst-case traf c compatible with its traf c descriptor. This is certainly feasible in the case of bufferless multiplexing. The only required ow traf c descriptor would be the peak rate with measurements performed in real-time to estimate the rate required by existing ows [11, 14]. Without entering into details, a suf ciently high level of utilization is compatible with negligible overload probability, on condition that the peak rate of individual ows is a small fraction of the link rate. The latter condition ensures that variations in the combined input rate are of relatively low amplitude, limiting the risk of estimation errors and requiring only a small safety margin to account for the most likely unfavorable coincidences in ow activities. For buffered multiplexing, given the dependence of delay and loss performance on complex ow traf c characteristics, design of ef cient admission control remains an open problem. It is probably preferable to avoid this type of multiplexing and to instead use reactive control for elastic traf c.
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