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This equation basically states that the sum of the average number of customers in all stations must equal the total number of customers. If we know the functions fi, the nonlinear equation ( 11.70) in X(K) can be solved numerically. Let us now first focus on the determination of the functions fi before we discuss the numerical solution of (11.70) in Section 11.5.3. For ease in notation, we use pi = Xi/(mipi). One problem in the determination of the functions f; is that they should be valid in the finite-customer domain. Normal functional relationships, e.g., those derived from MIMI1 analysis, are valid for open QNs, hence for infinite customer populations, We first address the type 1 queueing stations with m = 1. For the infinite-buffer singleserver case, we know from M) MI 1 analysis that (11.67) holds. Observe that limpZ,r E[.A i] = 00 in this case. However, if we introduce a correction factor (K- 1)/K in the denominator, we obtain E[Aq = pi (11.71) l- !$2pi* This equation has a limiting value of K when pi -+ 1, which is intuitively appealing: when the utilisation approaches lOO%, all K customers will reside in this node. Due to the insensitivity property in BCMP queueing networks (see 13) this result can also be used for nodes of type 2 (PS) and type 4 (LCFSPR). Note that the above result can also be derived from the Bard-Schweitzer approximation discussed in Section 11.4.2, in particular, by rewriting (11.56). When we deal with an MJMlmi-FCFS station, we have to adapt the result so as to account for the multiserver behaviour. Maintaining the same line of thinking, we obtain: E[Ni] = miPi + P,(Pi) X 1 _ ~ ~~-1 . Kerni Pi (11.72)

Table 2-3: (continued) PLATFORM VPN Router 1010 VPN Router 1050 VPN Router 1100 VPN Router 1700 VPN Router 1740 VPN Router 1750 VPN Router 2700 VPN Router 5000 ADSL No No Yes Yes Yes Yes Yes Yes SSL No No No No Yes Yes Yes Yes ACCELERATOR No No No Yes Yes Yes Yes Yes V.90 MODEM No No Yes Yes Yes Yes Yes Yes ISDN BRI No No Yes Yes Yes Yes Yes Yes

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One subject that digital camera and lens manufacturers are reluctant to discuss is a somewhat obscure technical issue called the Nyquist frequency (also known as the Nyquist theorem). When applied to digital photography, Nyquist frequency means that when a lens s resolving power (the ability to distinguish fine detail and render black lines black and not simply dark) is less than twice the resolution of an image sensor, visual aliasing can occur (usually in the form of moir patterns). This wasn t an issue when megapixel counts were relatively low, because most lenses were far sharper than image sensor density requirements. With the advent of DSLRs came higher megapixel image sensors coupled with larger photoreceptor sites, which require either a blur filter to reduce aliasing, significantly better lenses, or both. Blur filter and sharpening algorithms help improve image definition, but only up to a point. That s when superior optics make a significant image quality difference. However, although the newest, state-of-the-art digital lenses may match image sensor resolution, more megapixels do not necessarily produce sharper images or greater detail and may even reduce overall image sharpness. It s a conundrum that lens designers and image sensor fabricators are trying to deal with in a number of ways, such as by not placing microlenses in front of the image sensor or by coating the front elements of lenses so that they are fully apochromatic (color-corrected for all primary colors). The only way that you, the photographer, can know whether a lens you are considering buying has a correspondingly higher resolving power than your DSLR s image sensor is to study technical reviews of the lens on such Web sites as www.dpreview.com.

. . . . .

are equivalent. When the true distributions are ri , the best choice of i is a (i) = d log ri (s). ds

1 = 1 -0

i2(/)

For example, if you wanted to specify a telephone number with a format like (212) 555-1212, you would enter (000) 000-0000 in the Pattern field of the Property inspector with the Format set to Custom Pattern. If the Enforce Pattern option is selected, the open parenthesis appears after the first number is entered and the other non-numeric characters appear as the user enters the numbers; non-numbers are not accepted.

The Extended Server-Side Include (XSSI) extension, developed by Webmonkey authors Alx Ladygo, Nadav Savio, and Taylor for Adobe, includes a translator that brings the Apache-served code right into the Document window. Developed by Pervasive Software, the Tango translator compensates for differences between database-oriented code and standard HTML. Additionally, Tango includes a manually controlled Sample Data translator that enables the Web designer to view the page complete with an example database.

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