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In the previous subsections, we have focused on characterization of the stability region for the system. Given an arrival rate vector l within the stability region, we know that there exists a scheduler that can achieve stability. In other words, not all schedulers can achieve stability in the system. In the following paragraphs, we focus on the connection between the scheduling objectives and system stability. De nition 11.3 (Throughput Optimal Scheduler) A scheduler is throughputoptimal if it can maintain the stability of the system without knowing the arrival rate vector l as long as l is within the system s stability region S. In fact, there is quite a wide class of scheduling rules that are throughputoptimal (i.e., they guarantee that all the queues remain stable in the system as long as the vector of arrival rates is within the system stability region). For example, the max-weight scheduler (MW), the modi ed max-weight scheduler (MMW), and the exponential scheduler (EXP) are all throughput-optimal. We shall elaborate these schedulers below. Max-Weight Scheduler (MW). The MW scheduling rule is summarized in the following de nition. De nition 11.4 [Max-Weight (MW) Scheduler] At any time t, the MW scheduler selects the user(s) with the largest Q(t) r(t), where Q(t) = [Q1(t), . . . ,QK(t)] is the vector of queue lengths (number of untransmitted bits at time t) of K users and r(t) = [r1(t), . . . , rK(t)] is the data rate vector within the instantaneous feasible capacity region C(t) in the underlying multiuser physical layer

SAS published an IT Governance maturity model depicted in Exhibit 4.1. This model reflects the approach most IT organizations use to gain process maturity and incorporates the best of IT thought leadership. However, most current research and surveys indicate that IT maturity still lags despite a recent emphasis on process management. This particular process model advocates that all IT organizations build from the bottom up in sequential

max Q(t ) r(t )

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product in a neutral or positive way so we can tally your reach. Simple tools like Google Alerts can keep you apprised of mentions of speci c keywords in the blogs, as can Technorati. More sophisticated services like Hitwise and comScore can do so much more, but will also deliver the goods on how many people are talking about you out there. But don t stop at Twitter and Blogs. Keep your eyes and ears open to photos posted about you on Flickr, Twitpic, Yfrog, videos on YouTube and many, many others. Fortunately, there are a myriad of services like Buzzlogic and Blogscope to help you do just that. There are also a number of walled gardens that deserve your attention the social networking sites.

where denotes vector dot product. We have the following theorem regarding the stability property of the MW scheduler. Theorem 11.3 (Throughput Optimiality of MW Scheduler) Suppose that at any timeslot t, the channel state is m(t). The MW scheduler choosing the rate vector r C(m) that optimizes Q(t) r(t) achieves stability for all vector of arrival rates l strictly dominated by (11.16) for some f. In other words, the MW scheduler picks the most favorable rate allocation r within the capacity region of the physical layer such that it optimizes the weighted sum of the queue length and data rate. Users with longer queue and/or higher instantaneous data rate will be given priority. Such a scheduling

steps and not skip any steps along the way. The model is a practical, stepby-step maturity process. The main premise here is that the CIO must build IT organization maturity and business value on top of a solid, predictable infrastructure. We at SAS and our IT customers agree with this premise. So would our friends in the symphony orchestra. IT begins to part ways with the orchestra as the other dimensions of IT maturity add complexity to the problem of maturing IT and adding business value. An example of complexity is the implementation of process management to move from stabilization to business alignment. One such process management framework is the IT Infrastructure Library (ITIL). ITIL is gaining rapid acceptance in the United States after an excellent track record in Europe. Another source of complexity is the extensive automation required for IT operations and management. Orchestras do not need to trade in their violins every other year for a newer, more powerful, more capable, more musical violin. Just how far along the maturity index have most IT organizations developed According to a Gartner survey of CIOs in 2005, only 12 percent of

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