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We let the macroscopic level process fL t : t ! 0g be a semi-Markov process (SMP) as in Cinlar [9, Chap. 10]; that is, the level process is constant except for jumps, with the jump transitions governed by a Markov process, while the level holding times (times between jumps) are allowed to have general distributions depending on the originating level and the next level. Given a transition from level j to level k, the holding time in level j has cumulative distribution function (cdf) Fjk . Conditional on the sequence of successive levels, the holding times are mutually independent. To

BCX-1812), had also been in Phase III trials in Europe. All three compounds showed remarkable antiviral activity in cell cultures and in the mouse model against H5N1, H9N2, and many other avian in uenza viruses.314 317 H5N1 strains are resistant to the traditional in uenza drugs amantadine 58 and rimantadine 59.312,318

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obtain models compatible with traf c measurements cited earlier, we allow the holding-time cdf's Fjk to have heavy tails We assume that the within-level variation process fW t : t ! 0g is a zero-mean piecewise-stationary process During each holding-time interval in a level, the within-level variation process is an independent segment of a zero-mean stationary process, with the distribution of each segment being allowed to depend on the level We allow the distribution of the stationary process segment to depend on the level, because it is natural for the variation about any level to vary from level to level We will require only a limited characterization of the within-level variation process; it turns out that the ne structure of the within-level variation process plays no role in our analysis Indeed, that is one of our main conclusions.

the organisms begin to exhibit increased stimulation in corticosteroid secretion. However, at slightly higher doses, a compensatory response occurs whereby corticosteroid secretion is decreased in order to maintain homeostasis within the organism. Overcompensation may actually result in a decrease in corticosteroid secretion at certain toxicant dosages. Finally the compensatory abilities of the organism are overcome by the high doses of the toxicant at the pseudo threshold dose, above which the standard dose-response relationship occurs. Nonconventional dose-response relationships have been observed with respect to both acute and chronic toxicity and are particularly relevant to the risk assessment process when establishing levels of exposure that are anticipated to pose no harm.

In several examples of processes that we envisage modeling by these methods, there will only be the level process First, the level process may be some smoothed functional of a raw bandwidth process This is the case with algorithms for smoothing stored video by converting into piecewise constant rate segments in some optimal manner subject to buffering and delay constraints; see Salehi et al [25] With such smoothing, the input rate will directly be a level process as we have de ned it Alternatively, the level process may stem from rate reservation over the period between level-shifts, rather than the bandwidth actually used This would be the case for RCBR previously mentioned In this situation we act as if the reservation level is the actual demand, and thus again have a level process.

TABLE 3.6 1997: 1999: 2002: 2003: 2004: Recent Human Clinical Isolates of In uenza A Viruses of Avian Origin

An exhaustive review of the mechanisms by which chemicals cause acute toxicity is beyond the scope of this chapter. However, certain mechanisms of toxicity are relevant since they are common to many important classes of toxicants. Some of these mechanisms of acute toxicity are discussed.

A key to being able to analyze the system with such complex sources represented by our traf c model is exploiting asymptotics associated with multiplexing a large number of sources The ever-increasing network bandwidth implies that more and more sources will be able to be multiplexed This gain is generally possible, even in the presence of heavy-tailed distributions and more general long-range dependence; for example, see Duf eld [12, 13] for demonstration of the multiplexing gains available for long-range dependent traf c in shared buffers As the scale increases, describing the detailed behavior of all sources become prohibitively dif cult, but fortunately it becomes easier to describe the aggregate, because the large numbers produce statistical regularity As the size increases, the aggregate demand can be well described by laws of large numbers, central limit theorems, and large deviation principles.

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