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APPENDIX 11B: PROOF OF THEOREM 11.2 ON STABILITY REGION OF STOCHASTIC PHYSICAL LAYER Necessary Condition. The random process describing the behavior of the entire system is given by S(t) S(t ) = {(U i 1 (t ), . . . , U iQi (t ) (t )), m(t ), i = 1, . . . , K} where Qi(t) is the queue length of user i at time t and Uik(t) is the current delay of the kth packet in the queue of user i at time t. Let Di(t) = min(Qi(t), mim(t)) be the number of packets for user i served at time t. Hence, we have Qi (t + 1) = Qi (t ) - Di (t ) + Ai (t + 1) " i By stability of the system, we mean that the Markov chain S(t) is stable.7 Consider a scheduling policy static service split (SSS) parameterized by a aj(S ). When the system is in state S, the SSS rule chooses for rate vector rjm with probability aj(S). Assume that the stability of the system is achievable. For any xed timeslot t, we have

Table 71 Trace of rgcd(15,123)

rgcd(123, 15) rgcd(15, 3) rgcd(3, 0) 3

2. Strip about 3 4" of the insulation off of each end (see Figure 9-3).

A Markov chain S(t) is stable if the set of positive recurrent states is nonempty and contains a nite subset that is reached with probability 1 from any initial state [71]. In this context the term stability implies the existence of a stationary probability distribution. In addition, if all positive recurrent states are connected, the stationary distribution is unique.

The last call,

rgcd(3,0)

satisfies the stopping condition It returns the greatest common denominator, 3 This value successively becomes the return value of each prior call The value is said to percolate upward until the execution returns to the function that called rgcd in the first place

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6.7.1 Multiuser Physical Layer Model with Imperfect CSIT 6.7.2 System Utility Function 248 6.7.3 The Scheduling Problem Formulation 249 6.7.4 The Optimal Scheduling Solution 249 6.7.5 Suboptimal Solution 251 6.7.6 Numerical Results 253 6.8 Summary 253 Appendix 6A: Proof of Lemma 6.2 257 Appendix 6B: Calculation of Weights 257 Appendix 6C: Proof of Lemma 6.3 258 Appendix 6D: Proof of Lemma 6.4 259 Appendix 6E: Proof of Lemma 1.10 259 Appendix 6F: Proof of Lemma 6.5 259 Appendix 6G: Optimal Power Allocation for Network Capacity Utility 261 Appendix 6H: Asymptotic Distribution of Sk 262 Exercises 264

C++ Primer, Fourth Edition By Stanley B Lippman,Jos e Lajoie, Barbara E Moo Publisher:Addison Wesley Professional Pub Date: February 14, 2005 Print ISBN: 0-201-72148-1 Pages: 912

This popular tutorial introduction to standard C++ has been completely updated, reorganized, and rewritten to help programmers learn the language faster and use it in a more modern, effective wayJust as C++ has evolved since the last Exercise Rewritefactorial as an iterative function edition, so has the authors' approach to teaching it They now introduce the C++ standard library from the beginning, giving 720: readers the means to write useful programs without first having to master every language detail Highlighting today's best practices, they show how to write programs that are safe, can be built quickly, and yet offer outstanding performance Exercise What would happen if the stopping condition in factorial Examples that take advantage of the library, and explain the features of C++, also show how to make the best use of the 721: were: language As in its previous editions, the book's authoritative discussion of fundamental C++ concepts and techniques makes it a valuable resource even for more experienced programmersProgram Faster and More Effectively with This Rewritten Classic Restructured for quicker learning, using the C++ standard library Updated to teach the most current programming if (val != 0) styles and program design techniques Filled with new learning aids that emphasize important points, warn about common pitfalls, suggest good programming practices, and provide general usage tips Complete with exercises that reinforce skills learned Authoritative and comprehensive in its coverageThe source code for the book's extended examples is available on the Web at the address below

C++ Primer, Fourth Edition By Stanley 74 Function EB Lippman,Jos e Lajoie, Barbara Declarations Moo

7 Review of MAC Layer Design for Wireless Systems 269 7.1 Overview 269 7.2 TDMA-Based MAC Layer Design 272 7.2.1 ALOHA 272 7.2.2 Slotted ALOHA 272 7.2.3 PRMA 273 7.2.4 TDMA with Request Subframe 273 7.3 CDMA-Based MAC Layer Design 275 7.4 Issues in Request Scheduling 277 7.5 Design Example a Jointly Adaptive TDMA MAC Protocol 279 7.5.1 Overview of TDMA MAC Protocol Design 279 7.5.2 Synergistic Channel-Adaptive Multiple Access 280 7.6 Design Example a Jointly Adaptive CDMA MAC Protocol 290 7.6.1 Channel Adaptation in CDMA Systems 290 7.6.2 Optimal and Near-Optimal Approaches 291 7.6.3 Approaches that Maintain Fairness 293 7.6.4 User-Oriented Heuristics 294 7.7 Performance Comparisons 295 7.8 Summary 303 Exercises 303

Just as variablesPublisher:Addison Wesley they are used, a function must be declared before it is must be declared before called As with aProfessional variable definition (Section 235, p 52), we can declare a function separately Pub Date: February be defined only once but may be declared multiple times from its definition; a function may14, 2005

3. Slip a 1" section of heat-shrink tubing over one of the wires (see Figure 9-4).

Print ISBN: 0-201-72148-1

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