By Christos Panayiotou, Christos G. Cassandras (auth.), Sophie Tarbouriech, Chaouki T. Abdallah, John Chiasson (eds.)
The region of verbal exchange and desktop networks has develop into a truly energetic box of study by way of the keep watch over platforms group within the final years. instruments from convex optimization and keep an eye on concept are enjoying expanding roles in effective community usage, reasonable source allocation, and verbal exchange hold up lodging and the sphere of Networked regulate structures is speedy changing into a mainstay of keep watch over structures examine and functions. This rigorously edited publication brings jointly solicited contributions from specialists within the numerous parts of communication/control networks bearing on either networks lower than keep watch over (control in networks) in addition to networked regulate structures (control over networks). the purpose of this publication is to opposite the fashion of fragmentation and specialization in verbal exchange regulate Networks connecting a variety of interdisciplinary examine fields together with keep watch over, verbal exchange, utilized arithmetic and computing device science.
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The only effect is that queueing delay steadily decreases. 6 Simulation results In this section, we present a simulation experiment to validate the stability results established in Sections 3 and 4. The experiments all use the topology shown in Figure 4, with a single bottleneck link shared by N TCP sources. The access links between sources (or destinations) and their router are nonbottlenecks with zero latency, and the link between the two routers is the only bottleneck link with capacity c units and round-trip propagation delay d units.
N, be the value in (0, π/2) that satisﬁes ωr Tr tan ωr Tr = ar , r ≥ 0. (20) Clearly ω0 ≤ ωr for all r. Here ωr , r ≥ 1, is the critical frequency when the eigenvalue Λr ( jω) has a phase lag of −π. Hence, for ω < ω0 ≤ ωr , the convex combination of Λr ( jω) cannot encircle −1 because phase(Λr ( jω)) > −π for all r. We now show that, for ω ≥ ω0 , all Λr ( jω) are in the unit circle and hence their convex combination cannot encircle −1 either. For ω ≥ ω0 , since k0 Tr ≥ T0 , we have |Λr ( jω)| = ≤ k ωTr ω2 Tr2 + a2r kk02 ω0 T0 ω20 T02 + a20 = kk02 1 · · a0 ω0 T0 = kk02 · sinc θ(a0 ) a0 a0 ω20 T02 + a20 where the last equality follows from (20) and the deﬁnition of θ(·) in (14).
9, 11, 14, 16, 18]. These models mostly focus on the equilibrium structure, and do not adequately deal with network delay. To complement this series of work, we use here a multi-link multi-source model, described in Section 2, that explicitly includes heterogeneous forward and backward delays to analyze the linear stability of Vegas around an equilibrium. In comparison with previous analytical work, we sacriﬁce global (nonlinear) dynamics in order to understand the effect of delay on stability of Vegas, and how to stabilize it.
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