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Traf c engineering for a multiservice network handling both stream and elastic traf c is still a largely unexplored eld. In this section we suggest how it may be possible to generalize the methods and tools developed over the years for dimensioning the telephone network. 16.6.1 Provisioning for Stream Traf c
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To determine the network capacity required to meet a target blocking probability for stream ows, it is necessary to make assumptions about the arrival process of new demands, their rate, and their duration. For illustration purposes, we consider a simple traf c model consisting of one link receiving traf c from a very large population of users. Details and more general models may be found in Roberts et al. [26] for example. First assume that it is possible to identify m distinct homogeneous classes, ows of each class having a common rate distribution. Flows from class i arrive according to a Poisson process of intensity li (requests per second) and have an expected duration of 1=mi seconds. Their peak rate is pi . For a xed (fairly large) link capacity c, the impact of a ow of class i on the probability of data loss can be summarized in a single gure, the effective bandwidth: the effective bandwidth ei is such that the P probability of data loss is negligible (less than a target value) as long as ni ei c, where ni is the number of class i ows in progress. Although measurement-based admission control does not rely on the identi cation of the different classes (a new ow is denied access if its peak rate is greater than a real-time estimate of available bandwidth), for dimensioning purposes we can P assume a ow of class j will be blocked if ni ei > c ej . With this blocking condition and the assumption of Poisson arrivals, the distribution of the ni has a wellknown product form enabling computation of the blocking probability. Note that blocking probabilities and data loss rates are insensitive to the distribution of ow duration. A reasonable approximation for the blocking probability of a ow with peak rate pi when c is large with respect to the ei is given by Bi % where a P ei li =mi , d P pi E a=d; c=d ; d 16:1
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e2 li =mi =a and i E a; n an . P ai n! i n i!
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is Erlang's formula. Formula (16.1) is a simpli cation of the formulas given by Lindberger [20]. It is less accurate but more clearly demonstrates the structural relationship between performance and traf c characteristics. Instead of identifying traf c classes with
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common traf c characteristics, it may prove more practical to estimate the essential parameters a and d directly. It is well known that application of Erlang's formula leads to scale economies: to achieve a low blocking probability and high utilization (a=c), it is necessary to have a large capacity c. For multirate traf c with blocking probabilities given by Eq. (16.1), the same requirement implies a high value of c=d. The line labeled ``stream'' in Fig. 16.3 shows how achievable utilization a=c in a simple Erlang loss system varies with c for a target blocking probability of 0.01. 16.6.2 Provisioning for Elastic Traf c
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Following the simple service model introduced in Section 16.5, we assume throughput quality of service is satis ed by limiting the number of elastic ows on a link and seek to dimension link capacity such that the blocking probability is less than some low target value E. Consider rst an isolated link handling only elastic ows. Assuming Poisson arrivals, a minimum throughput requirement y, exact fair shares (i.e., processor sharing service), and a link bandwidth of c ny, the probability of blocking is equal to the saturation probability in an M =G=1 processor sharing queue of capacity n: Be rn 1 r = 1 rn 1 where r is the link load. 16:2
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