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The Internet's TCP/IP stack was not designed with the vagaries of the wireless channel and mobility in mind and is showing signs of age today. TCP has well-known problems over multi-hop wireless networks as it con?ates congestion and loss, performs poorly over time-varying and lossy links, and is fragile in the presence of route changes and disconnections. In this talk, I will present a clean-slate design and implementation of a wireless transport protocol, Hop, that uses reliable per-hop block transfer as a building block. Hop is 1) fast as it eliminates many sources of overhead as well as noisy end-to-end rate control, 2) robust to partitions and route changes because of hop-by-hop control as well as in-network caching, and 3) simple as it obviates complex end-to-end rate control as well as complex interactions across layers. Our experiments over a 20-node multi-hop mesh network show that Hop is dramatically more efficient, achieving better fairness, throughput, delay, and robustness to partitions over several alternate protocols, including gains of over an order of magnitude in median throughput. I will present arguments for why block transfer forms the basis of a simple, robust protocol stack that gracefully degrades in performance across diverse wireless environments such as access point networks, meshes, mobile ad hoc networks, and DTNs. I will outline research challenges and opportunities raised by block transfer in order to realize this vision. ©2009 Microsoft Corporation. All rights reserved.

In this study, we investigate the adaptation and robustness of a packet switching network (PSN), the fundamental architecture of the Internet. We claim that the adaptation introduced by a transmission control protocol (TCP) congestion control mechanism is interpretable as the self-organization of multiple attractors and stability to switch from one attractor to another. To discuss this argument quantitatively, we study the adaptation of the Internet by simulating a PSN using ns-2. Our hypothesis is that the robustness and fragility of the Internet can be attributed to the inherent dynamics of the PSN feedback mechanism called the congestion window size, or \textit{cwnd}. By varying the data input into the PSN system, we investigate the possible self-organization of attractors in cwnd temporal dynamics and discuss the adaptability and robustness of PSNs. The present study provides an example of Ashby's Law of Requisite Variety in action.

A frame relay pseudowire is a mechanism that exists between a provider's edge network nodes and that supports as faithfully as possible frame relay services over an MPLS packet switched network (PSN). This document describes the detailed encapsulation necessary to transport frame relay packets over an MPLS network. [STANDARDS-TRACK]

A frame relay pseudowire is a mechanism that exists between a provider's edge network nodes and that supports as faithfully as possible frame relay services over an MPLS packet switched network (PSN). This document describes the detailed encapsulation necessary to transport frame relay packets over an MPLS network. [STANDARDS-TRACK]

A frame relay pseudowire is a mechanism that exists between a provider's edge network nodes and that supports as faithfully as possible frame relay services over an MPLS packet switched network (PSN). This document describes the detailed encapsulation necessary to transport frame relay packets over an MPLS network. [STANDARDS-TRACK]

Optical burst switching (OBS) is a transporting network for the optical internet in the years ahead vision. As OBS depends on statistical multiplexing, the effect of contention resolution is the main issue to achieve a low probability losing of burst. Basically, there are different ways to resolve contentions in the OBS networks like wavelength conversion, deflection routing, burst segmentation and optical buffering using fiber delay lines. Burst segmentation and deflection routing as well as fiber delay lines technologies, are discussed among the various accessible conflict resolution techniques in this study. However, the main aim of this study is to demonstrate that, the performance of fiber delay line (FDL) is better than other techniques to resolve contention by comparing the performance of these different schemes based on burst losing probabilities and the data handling capability. To evaluate the performance, appropriate mathematical formulae were used. Under the MATLAB environment, the performance was measured based on the probability of burst loss versus incoming traffic (load). The outcomes suggest that deflection routing outperforms fiber delay lines and burst segmentation in the OBS network in terms of resolve the contention.

Mean delay times at certain superposition nodes are found for messages of variable length in a packet-switched network. These improve on some previous approximations. The output from these nodes is such that exact mean delays in some larger networks may be found. (Author)

We report on an astonishing switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high to low resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with our numerical calculations.

Bibliography: p. 46

We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the weakest forms of switching (i.e. along this connection). The form of the global transition maps, and thus the type of the heteroclinic cycle, plays a crucial role in this. We look at two examples in $\mathbb{R}^5$, the House and Bowtie networks, to illustrate complex dynamics that may occur when either of these conditions is broken. For the House network, there is switching along the common connection, while for the Bowtie network we find switching along a cycle.

We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the weakest forms of switching (i.e. along this connection). The form of the global transition maps, and thus the type of the heteroclinic cycle, plays a crucial role in this. We look at two examples in $\mathbb{R}^5$, the House and Bowtie networks, to illustrate complex dynamics that may occur when either of these conditions is broken. For the House network, there is switching along the common connection, while for the Bowtie network we find switching along a cycle.

In this paper, we extend the work of our previous paper "Bounds on monotone switching networks for directed connectivity" by further analyzing the monotone space complexity of directed connectivity. In particular, we analyze the monotone space compexity of directed connectivity for a variety of input graphs, not just minimal YES-instances. We show that the monotone space complexity of input graphs with a very large number of lollipops (vertices $v$ for which there is an edge from $s$ to $v$ or an edge from $v$ to $t$) is low by giving a randomized monotone generalization of Savitch's algorithm which uses a parity argument. This gives us upper bounds for both monotone switching networks and monotone circuits. We then give lower bounds on monotone switching networks for directed connectivity which are tight whenever the input graph is acyclic and does not have any vertices $v$ which are connected to a large number of other vertices by short paths.

An analysis is contained herein that compares circuit with message switching in Military Communications Networks that carry record traffic. Also examined are the effects of system parameters on the attainment and measurement of statistical convergence when Monte Carlo simulation is used to study delays caused by traffic congestion in communication networks.

Part 1 (Threshold Logic) consists of a comprehensive survey of threshold logic, a geometric result relevant to estimating the number of threshold functions, generalizations and strengthening of known bounds on the logical capabilities of threshold gate networks, computer-aided work on the realization of arbitrary functions by networks of three-input majority gates (including a list of realizations for every type of four-argument switching function), and a comparison of two methods for synthesis of very large threshold gates: the well-known Bayesian approach and a geometric alternative. The latter method is shown to be preferable. Part 2 (Reliability of Switching Networks) presents a survey of several important schemes for introducing redundancy into a combinational network for the improvement of reliability. Some extensions of the previous analyses of recursive triangles and initial results on the incorporation of memory and feedback to allow the use of fewer basic gates in a time-shared fashion.

This research project corresponds to one of the first comprehensive studies in multichannel switching. Assuming a broadband communication environment using ATM technology, this work investigates the fundamental characteristics of multichannel switching. Potential benefits of multichannel switching over traditional point to point switching have been identified. A clear theoretical foundation is being developed and theoretical limits on various performance measures are being investigated. Attainable performance objectives in multichannel switches under the current state of technology are being determined, and implementable multichannel switching architectures that satisfy the objectives are being formulated. A comprehensive study of the efficacy of the proposed architectures is being conducted under varying traffic and network conditions. One of the main tasks in this project is to exhibit the feasibility of the proposed switching architectures via prototyping.

Topological method uses the eye as pattern detector to trace path of transmission on truth table. Pathway selection is continually supervised by logician, allowing him to seek planar iterative solution desirable for fabrication of monolithic circuits. Method applies to parity generators, multiple output functions, full adders, and bit comparators.

Packet switching communication networks employ routing protocols to determine the path traversed by each packet as it passes through the network. Routing protocols which are adaptive and can restructure the packet paths in response to localized network congestion are called dynamic routing protocols. Dynamic routing protocols seek to optimize the routing (provide the shortest path) for each packet in the network. Routing protocols which are unaffected by the addition or deletion of any subset of nodes are called distributed routing protocols. The relative performance of two distributed, dynamic routing protocols is determined using computer simulations. The protocols are implemented on four theoretical networks and tested under a range of network traffic loads. (Author)

Neural networks and fuzzy systems have been studied to develop effective means to control highly dynamic high-speed networks in a cost efficient manner. Using the results from a study of robust transfiguring protocols which were designed to recognize changes in assumed network state and adapt to these changing network conditions, a fuzzy control algorithm was implemented.

ADA126790

Bell System Technical Journal, 56: 8. October 1977 pp 1431-1446. On Blocking Probabilities for Switching Networks. (Chung, F.R.K.; Hwang, F.K.)

In this paper, we prove almost tight bounds on the size of sound monotone switching networks accepting permutations sets of directed trees. This roughly corresponds to proving almost tight bounds bounds on the monotone memory efficiency of the directed ST-connectivity problem for the special case in which the input graph is guaranteed to have no path from s to t or be isomorphic to a specific directed tree.

This paper presents a novel framework which combines a non-iterative solution of Real-Time Nonlinear Receding Horizon Control (NRHC) methodology to achieve consensus within complex network topologies with existing time-delays and in presence of switching topologies. In this formulation, we solve the distributed nonlinear optimization problem for multi-agent network systems directly, \emph{in real-time}, without any dependency on iterative processes, where the stability and convergence guarantees are provided for the solution. Three benchmark examples on non-linear chaotic systems provide validated results which demonstrate the significant outcomes of such methodology.

Base station switching (BSS) can results in significant reduction in energy consumption of cellular networks during low traffic conditions. We show that the coverage loss due to BSS can be compensated via coordinated multi-point (CoMP) based transmission in a cluster of base stations. For a BSS with CoMP based system, we propose various BSS patterns to achieve suitable trade-offs between energy savings and throughput. We formulate the CoMP resource allocation and user scheduling as a joint optimization problem. We derive the optimal time fraction and user scheduling for this problem and use it to formulate a simplified BSS with CoMP optimization problem. A heuristic that solves this problem is presented. Through extensive simulations, we show that suitable trade-offs among energy, coverage, and rate can be achieved by appropriately selecting the BSS pattern, CoMP cluster, and rate threshold.

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.

The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose sufficient conditions which guarantee a suboptimal $H_\infty$ level of relative disagreement of estimates in such observer networks. When the status of the network is known globally, these sufficient conditions enable the network gains to be computed by solving certain LMIs. When the nodes are to rely on a locally available information about the network topology, additional rank constraints are used to condition the gains, given this information. The results are complemented by necessary conditions which relate properties of the interconnection graph Laplacian to the mean-square detectability of the plant through measurement and interconnection channels.

An analytic tool in the realization of circuit matrices is presented. The method is based on forming linear trees with each row of a fundamental circuit matrix and combining them to form a tree of the graph. With this method, more difficult problems in the synthesis of contact networks by linear graph theory can be considered. A method of simultaneous synthesis is developed in which two or more switching functions are realized by sharing contacts in an optimal form. Finally the multi-terminal procedures are extended to the synthesis of non-bilateral, 1 port switching networks.

Text Book of Telecommmunication Switching Systems

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a {($\alpha,g$)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.

viii, 357 p. : 25 cm

Bell System Technical Journal, 55: 5. May-June 1976 pp 637-661. Remreed Switching Networks for No. 1 and No. 1A ESS: Transmission Design and Environmental Protection of Remreed Networks. (Klosterman, C.H.; Unrue, J.E. Jr.)

Bell System Technical Journal, 55: 5. May-June 1976 pp 511-535. Remreed Switching Networks for No. 1 and No. 1A ESS: Development of a Remanent Reed Sealed Contact. (Archer, W.E.; Olsen, K.M.; Renaut, P.W.)

Bell System Technical Journal, 59: 7. Sept 1980 pp 1165-1173. On Switching Networks and Block Designs, II. (Chung, F.R.K.)

Automatic Repeat reQuest (ARQ) techniques are often used by a packet switching data communication network to provide an error-free communications link between stations. The ARQ technique ensures consistent data quality under varying link conditions. Unfortunately, the information throughput is link dependent and as the noise or interference on the link increases, the throughput decreases. In an effort to improve the throughput on a short range, RF, packet switching data communications network, an adaptive ARQ strategy applied to Stop- and-Wait (SW) protocols was developed. To provide a system designer with flexibility, different adaptive strategies for different system and link conditions were developed. Examples of information transfer between two stations using the adaptive SW protocol are presented. A simulation to compute the throughput efficiency of several adaptive SW protocols was performed. A comparison of the throughput efficiencies of the simulated adaptive SW protocol with the non-adaptive SW protocol showed good gains could be achieved using the adaptive strategy when the networks are subject to high channel bit error rates. Theses.

In this paper we review the primary characteristics of the U.S. Department of Defense packet switching networks -- ARPANET, AUTODIN II, and WIN. Special requirements for dedicated defense networks are examined. These include privacy and security, precedence, survivability, availability, and interoperability with other networks. Finally, we discuss some architectural concepts for an all digital integrated voice/data network for defense applications in the 1990's. (Author)

In this technical note we address the problem of achieving consensus in a network of homogeneous nonlinear systems. The communication network is supposed to be switching within a finite set of topologies which may be disconnected for finite time intervals. We prove that if the length of the time intervals in which connected topologies are active satisfy an average dwell-time condition consensus is achieved. Lyapunov arguments proposed in the field of hybrid nonlinear systems are adopted to prove the result.

In this technical note we address the problem of achieving consensus in a network of homogeneous nonlinear systems. The communication network is supposed to be switching within a finite set of topologies which may be disconnected for finite time intervals. We prove that if the length of the time intervals in which connected topologies are active satisfy an average dwell-time condition consensus is achieved. Lyapunov arguments proposed in the field of hybrid nonlinear systems are adopted to prove the result.

Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by calculating the spontaneous flipping rate of a symmetric model of a genetic switch consisting of two mutually repressing genes. The rate constant can be obtained orders of magnitude more efficiently than using brute-force simulations. For this model switch, we show that the switching mechanism, and consequently the switching rate, depends crucially on whether the binding of one regulatory protein to the DNA excludes the binding of the other one. Our technique could also be used to study rare events and non-equilibrium processes in soft condensed matter systems.

Bell System Technical Journal, 32: 2. March 1953 pp 406-424. A Study of Non-Blocking Switching Networks. (Clos, Charles)

Bell System Technical Journal, 43: 3. May 1964 pp 965-1004. NEASIM: A General-Purpose Computer Simulation Program for Load-Loss Analysis of Multistage Central Office Switching Networks. (Grantges, R.F.; Sinowitz, N.R.)

Bell System Technical Journal, 52: 6. July-August 1973 pp 991-1007. Switching Networks of Planar Shifting Arrays. (Krupp, R.S.; Tomko, L.A.)

In this paper, stability of linearly coupled dynamical systems with feedback pinning algorithm is studied. Here, both the coupling matrix and the set of pinned-nodes vary with time, induced by a continuous-time Markov chain with finite states. Event-triggered rules are employed on both diffusion coupling and feedback pinning terms, which can efficiently reduce the computation load, as well as communication load in some cases and be realized by the latest observations of the state information of its local neighborhood and the target trajectory. The next observation is triggered by certain criterion (event) based on these state information as well. Two scenarios are considered: the continuous monitoring, that each node observes the state information of its neighborhood and target (if pinned) in an instantaneous way, to determine the next triggering event time, and the discrete monitoring, that each node needs only to observe the state information at the last event time and predict the next triggering-event time. In both cases, we present several event-triggering rules and prove that if the conditions that the coupled system with persistent coupling and control can be stabilized are satisfied, then these event-trigger strategies can stabilize the system, and Zeno behaviors are excluded in some cases. Numerical examples are presented to illustrate the theoretical results.

In this paper, stability of linearly coupled dynamical systems with feedback pinning algorithm is studied. Here, both the coupling matrix and the set of pinned-nodes vary with time, induced by a continuous-time Markov chain with finite states. Event-triggered rules are employed on both diffusion coupling and feedback pinning terms, which can efficiently reduce the computation load, as well as communication load in some cases and be realized by the latest observations of the state information of its local neighborhood and the target trajectory. The next observation is triggered by certain criterion (event) based on these state information as well. Two scenarios are considered: the continuous monitoring, that each node observes the state information of its neighborhood and target (if pinned) in an instantaneous way, to determine the next triggering event time, and the discrete monitoring, that each node needs only to observe the state information at the last event time and predict the next triggering-event time. In both cases, we present several event-triggering rules and prove that if the conditions that the coupled system with persistent coupling and control can be stabilized are satisfied, then these event-trigger strategies can stabilize the system, and Zeno behaviors are excluded in some cases. Numerical examples are presented to illustrate the theoretical results.

This document defines the model and generic mechanisms for Multiprotocol Label Switching on Frame Relay networks. [STANDARDS-TRACK]

NASA LeRC is currently investigating a satellite architecture that incorporates on-board packet switching capability. Because of the statistical nature of packet switching, arrival traffic may fluctuate and thus it is necessary to integrate congestion control mechanism as part of the on-board processing unit. This study focuses on the closed-loop reactive control. We investigate the impact of the long propagation delay on the performance and propose a scheme to overcome the problem. The scheme uses a global feedback signal to regulate the packet arrival rate of ground stations. In this scheme, the satellite continuously broadcasts the status of its output buffer and the ground stations respond by selectively discarding packets or by tagging the excessive packets as low-priority. The two schemes are evaluated by theoretical queuing analysis and simulation. The former is used to analyze the simplified model and to determine the basic trends and bounds, and the later is used to assess the performance of a more realistic system and to evaluate the effectiveness of more sophisticated control schemes. The results show that the long propagation delay makes the closed-loop congestion control less responsive. The broadcasted information can only be used to extract statistical information. The discarding scheme needs carefully-chosen status information and reduction function, and normally requires a significant amount of ground discarding to reduce the on-board packet loss probability. The tagging scheme is more effective since it tolerates more uncertainties and allows a larger margin of error in status information. It can protect the high-priority packets from excessive loss and fully utilize the downlink bandwidth at the same time.

Philip Morris Records; chart; graph; map; report; table; drft, draft

The Internet's TCP/IP stack was not designed with the vagaries of the wireless channel and mobility in mind and is showing signs of age today. TCP has well-known problems over multi-hop wireless networks as it con?ates congestion and loss, performs poorly over time-varying and lossy links, and is fragile in the presence of route changes and disconnections. In this talk, I will present a clean-slate design and implementation of a wireless transport protocol, Hop, that uses reliable per-hop block transfer as a building block. Hop is 1) fast as it eliminates many sources of overhead as well as noisy end-to-end rate control, 2) robust to partitions and route changes because of hop-by-hop control as well as in-network caching, and 3) simple as it obviates complex end-to-end rate control as well as complex interactions across layers. Our experiments over a 20-node multi-hop mesh network show that Hop is dramatically more efficient, achieving better fairness, throughput, delay, and robustness to partitions over several alternate protocols, including gains of over an order of magnitude in median throughput. I will present arguments for why block transfer forms the basis of a simple, robust protocol stack that gracefully degrades in performance across diverse wireless environments such as access point networks, meshes, mobile ad hoc networks, and DTNs. I will outline research challenges and opportunities raised by block transfer in order to realize this vision. ©2009 Microsoft Corporation. All rights reserved.

In this paper, we study the discrete-time consensus problem over networks with antagonistic and cooperative interactions. Following the work by Altafini [IEEE Trans. Automatic Control, 58 (2013), pp. 935--946], by an antagonistic interaction between a pair of nodes updating their scalar states we mean one node receives the opposite of the state of the other and naturally by an cooperative interaction we mean the former receives the true state of the latter. Here the pairwise communication can be either unidirectional or bidirectional and the overall network topology graph may change with time. The concept of modulus consensus is introduced to characterize the scenario that the moduli of the node states reach a consensus. It is proved that modulus consensus is achieved if the switching interaction graph is uniformly jointly strongly connected for unidirectional communications, or infinitely jointly connected for bidirectional communications. We construct a counterexample to underscore the rather surprising fact that quasi-strong connectivity of the interaction graph, i.e., the graph contains a directed spanning tree, is not sufficient to guarantee modulus consensus even under fixed topologies. Finally, simulation results using a discrete-time Kuramoto model are given to illustrate the convergence results showing that the proposed framework is applicable to a class of networks with general nonlinear node dynamics.

Bell System Technical Journal, 37: 6. November 1958 pp 1421-1453. Application of Breakdown Devices to Large Multistage Switching Networks. (Feldman, T.; Rieke, J.W.)