By Christos Panayiotou, Christos G. Cassandras (auth.), Sophie Tarbouriech, Chaouki T. Abdallah, John Chiasson (eds.)
The sector of communique and laptop networks has develop into a truly energetic box of study via the keep an eye on structures group within the final years. instruments from convex optimization and keep watch over concept are taking part in expanding roles in effective community usage, reasonable source allocation, and communique hold up lodging and the sector of Networked keep watch over platforms is quick turning into a mainstay of keep watch over platforms examine and functions. This rigorously edited publication brings jointly solicited contributions from specialists within the quite a few components of communication/control networks concerning either networks less than keep watch over (control in networks) in addition to networked keep an eye on platforms (control over networks). the purpose of this e-book is to opposite the craze of fragmentation and specialization in conversation keep an eye on Networks connecting a variety of interdisciplinary study fields together with keep watch over, communique, utilized arithmetic and laptop science.
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Hence, for all r, (31) Stabilized Vegas |Λ( jωTr )| ≤ Λ jω1 = µk0 ω1 T1 ≤ µk0 φ 39 T1 k0 (ω1 T1 )2 + (ak0)2 (ω1 T1 )2 + µ2(ak0 )2 φ2 + (ak0)2 . φ2 + µ2 (ak0 )2 The last inequality follows from Lemma 1 below which implies that, for all r, ωr Tr ≥ 1−µ π − tan−1 √ = φ 2 2 µ where φ is deﬁned in the theorem. The condition (28) in the theorem then guarantees that (31) holds. Since x∗r q∗r = α, the conditions (27) and (28) are equivalent. Hence the proof is complete with the following lemma. Lemma 1.
015) 90 80 propagation delay [ms] 70 60 50 40 30 20 10 0 0 100 200 300 400 500 600 link capacity [pkts/ms] 700 800 900 1000 Fig. 2. Stability regions of Examples 1 and 2: single-link shared by homogeneous sources. The stability condition is only sufﬁcient. Indeed, less conservative values can be used for a and µ. For instance, the Nyquist plots of (MTr /q∗r ) · Λ( jωTr ) for MTr /q∗r = 42 Hyojeong Choe and Steven H. Low 100 are shown in Fig. 015]. 2 Real Axis Fig. 3. 015]. Even though these a and µ values do not satisfy the stability condition of Theorem 2, the network is indeed stable, as shown by the Nyquist plots.
Y. Le Boudec. A note on the fairness of TCP Vegas. In Proceedings of International Zurich Seminar on Broadband Communications, pages 163–170, February 2000.  Lawrence S. Brakmo and Larry L. Peterson. TCP Vegas: end-to-end congestion avoidance on a global Internet. IEEE Journal on Selected Areas in Communications, 13(8):1465–80, October 1995. ps.  C. A. Desoer and Y. T. Yang. On the generalized Nyquist stability criterion. IEEE Trans. on Automatic Control, 25:187–196, 1980.  U. Hengartner, J.