Bidirectional Rings Research Articles

Free axisymmetric vibrations of heated non-uniform Bi-directional FGM Mindlin rings employing quadrature approaches

The present article investigates the axisymmetric vibrations of non-uniform bi-directional functionally graded rings under two-dimensional temperature distribution on the basis of first-order shear deformation theory. The linear variation of thickness along the radial direction is controlled by a taper parameter. The temperature-dependent mechanical properties are assumed to be graded in thickness as well as radial direction. The separation of variables method is applied to obtain the classical solution of two-dimensional heat conduction equation by imposing the thermal boundary conditions. The governing differential equations of thermoelastic equilibrium and axisymmetric motion together with boundary conditions are extracted from Hamilton’s principle. The quadrature technique is used to obtain the frequency equations and then the lowest three roots of these equations are calculated by MATLAB. After validating the results for the present approach, numerical results are given to analyze the effects of thermal environment, taper parameter, volume fraction index, heterogeneity and density parameters on the frequency parameter. Mode shapes for the specified rings are illustrated.

Optimal design of a 5th generation district heating and cooling network based on seawater heat pumps

This work presents the design and the thermo-economic optimization of a novel layout of a 5th generation district heating and cooling network, for a residential district located in the Pantelleria island (South of Italy). The research focuses on a novel arrangement based on two bidirectional low-temperature neutral rings. For both rings, the fluid temperature is controlled by means of two groups of heat pumps cooled by seawater. The investigated layout also includes wind turbines and photovoltaic panels for power production. This layout will be used as a driver to promote the transition from the present centralized energy paradigm to a novel one, based on small-scale distributed generation integrated with renewables. The paper aims at evaluating the energy, economic and environmental savings achieved by this novel layout. A thermo-economic optimization is also implemented in order to determine the set of design/operating variables, maximizing system economic profitability. To this scope, a detailed approach is implemented, developing a dynamic simulation model of the system in TRNSYS 17. The developed simulation tool is able to mimic the real time operation of the system, for whatever weather condition, boundary and/or design variable. The results of the simulations show that the proposed layout achieves significantly positive results, with a primary energy saving and avoided greenhouse gases emissions equal to 133% and 134%, respectively. The economic profitability of the system is limited with the payback period close to 15 years, due to the high capital cost of the plant. The renewable electric production of the plant meets 57% of the district demand, although only 37% of this amount is self-consumed by the district. The study also includes a sensitivity analysis suggesting to limit the capacities of solar and wind fields to reduce the electricity in excess sold to the grid.

Topology-Specific Synthesis of Self-Stabilizing Parameterized Systems with Constant-Space Processes

This paper investigates the synthesis of parameterized systems that are self-stabilizing by construction. To this end, we present several significant results. First, we show a counterintuitive result that despite the undecidability of verifying self-stabilization for parameterized unidirectional rings, synthesizing self-stabilizing unidirectional rings is decidable! This is surprising because it is known that, in general, the synthesis of distributed systems is harder than their verification. Second, we present a topology-specific synthesis method (derived from our proof of decidability) that generates the state transition system of template processes of parameterized self-stabilizing systems with elementary unidirectional topologies (e.g., rings, chains, trees). We also provide a software tool that implements our synthesis algorithms and generates interesting self-stabilizing parameterized unidirectional rings in less than 50 microseconds on a regular laptop. We validate the proposed synthesis algorithms for decidable cases in the context of several interesting distributed protocols. Third, we show that synthesis of self-stabilizing bidirectional rings remains undecidable.

An optical packet metro architecture for Fixed Mobile Convergence in the cloud era

The present paper addresses future network architectures considered for Fixed Mobile Convergence, where users can access resources transparently either through fixed access technologies or through the mobile RAN. Optical technologies rely on Wavelength Division Multiplexing (WDM) to meet continuously growing bandwidth demands. However, although in the core network optical circuit switching may efficiently support huge traffic aggregates, closer to the access, in future Metropolitan Area Networks (MAN), it is necessary to provide a finer granularity, and a dynamical bandwidth control, to very heterogeneous traffic demands. This is supported by Optical Packet Switching (OPS) relying on WDM slotted Add/Drop Multiplexing (WSADM). A flow-based transfer mode, compatible with SDN control is first specified, and applied to bi-directional MAN rings. This mode is shown to provide several methods for supporting both local and global repair in case of failure. Mathematical models are derived to assess optical packet insertion performance and are used to illustrate how WSADM rings can support MAN performance requirements. Lastly the impact of locating the IP edge, and Data Centres closer to the users than in legacy architectures, within the MAN is addressed.

Shadow/Puppet Synthesis: A Stepwise Method for the Design of Self-Stabilization

This paper presents a novel two-step method for automated design of self-stabilization. The first step enables the specification of legitimate states and an intuitive (but imprecise) specification of the desired functional behaviors in the set of legitimate states (hence the term “shadow”). After creating the shadow specifications, we systematically introduce the main variables and the topology of the desired self-stabilizing system. Subsequently, we devise a parallel and complete backtracking search towards finding a self-stabilizing solution that implements a precise version of the shadow behaviors, and guarantees recovery to legitimate states from any state. To the best of our knowledge, the shadow/puppet synthesis is the first sound and complete method that exploits parallelism and randomization along with the expansion of the state space towards generating self-stabilizing systems that cannot be synthesized with existing methods. We have validated the proposed method by creating both a sequential and a parallel implementation in the context of a software tool, called Protocon. Moreover, we have used Protocon to automatically design three new self-stabilizing protocols that we conjecture to require the minimal number of states per process to achieve stabilization (when processes are deterministic): 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, and 3-state token passing on bidirectional chains.

A Note on the Ring Loading Problem

The Ring Loading Problem is an optimal routing problem arising in the planning of optical communication networks which use bidirectional SONET rings. In mathematical terms, it is an unsplittable multicommodity flow problem on undirected ring networks. We prove that any split routing solution to the Ring Loading Problem can be turned into an unsplittable solution while increasing the load on any edge of the ring by no more than $+\frac{19}{14} D$, where $D$ is the maximum demand value. This improves upon a classical result of Schrijver, Seymour, and Winkler (1998), who obtained a slightly larger bound of $+\frac32 D$. We also present an improved lower bound of $\frac{11}{10} D$ (previously $\frac{101}{100} D$) on the best possible bound and disprove a famous long-standing conjecture of Schrijver, Seymour, and Winker in this context.

Symmetry analysis of coupled scalar systems under time delay

We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based on the equivariant degree method and its computational packages, we perform a symmetry classification of destabilizing bifurcations in bidirectional rings of coupled units. Both stationary and oscillatory bifurcations are discussed. We also introduce the concept of secondary dominating orbit types to capture bifurcating solutions of submaximal nature.

The uniqueness property for networks with several origin–destination pairs

We consider congestion games on networks with nonatomic users and user-specific costs. We are interested in the uniqueness property defined by Milchtaich (2005) as the uniqueness of equilibrium flows for all assignments of strictly increasing cost functions. He settled the case with two-terminal networks. As a corollary of his result, it is possible to prove that some other networks have the uniqueness property as well by adding common fictitious origin and destination. In the present work, we find a necessary condition for networks with several origin–destination pairs to have the uniqueness property in terms of excluded minors or subgraphs. As a key result, we characterize completely bidirectional rings for which the uniqueness property holds: it holds precisely for nine networks and those obtained from them by elementary operations. For other bidirectional rings, we exhibit affine cost functions yielding to two distinct equilibrium flows. Related results are also proven. For instance, we characterize networks having the uniqueness property for any choice of origin–destination pairs.

Evaluation of asynchronous multi‐swarm particle optimization on several topologies

SUMMARYParticle swarm optimization is a population‐based stochastic optimization technique that is easy to implement and has been successfully applied in many areas. However, its performance often deteriorates as the dimensionality of the problem increases. Recently, parallel strategies based on multiple swarms (multi‐swarm) have been investigated as an alternative to overcome this problem. In this paper, we evaluate the impact of the topology on multi‐swarm systems, considering that swarms are independent, and interact by means of particle migration. We focus on asynchronous communication, that is, only when an improvement occurs on the best particle that the solution migrates among swarms. The goal is to check how different communication strategies affect the parallel execution of the optimization tasks. Several different topologies and communication strategies have been evaluated, including broadcast and gossip on fully connected networks, unidirectional and bidirectional rings, hypercubes, and a dynamic topology. Extensive experimental results were obtained and are reported using several traditional benchmark functions. We evaluated the impact of the topologies in terms of the number of iterations and the communication overhead. With the results, a ranking of the different topologies is presented. The impact of the number of swarms on the optimization process is also evaluated. Copyright © 2012 John Wiley & Sons, Ltd.

ROADM optimization in WDM ring networks

Reconfigurable optical add–drop multiplexers (ROADMs) and tunable transceivers play an important role in optical network reconfigurability and cost saving. ROADMs provide support to dynamic traffic demands, enable new services, and save capital expenditure (CapEx) along with the operational expenditure (OpEx). Limiting the range of wavelengths that can be accessed at a node reduces costs, and possibly reduces flexibility in reconfigurability. The limited range (band size) of wavelengths is a result of the limited add/drop range of the ROADMs and/or limited tuning range of transceivers. In either case, limited reconfigurability introduces a new constraint in the wavelength assignment of connections called as the wavelength termination constraint. Limited ROADMs (L-ROADMs) can add and drop only a subset of (contiguous) wavelengths (a waveband) and are less costly than fully reconfigurable OADMs (F-ROADMs). In order to quantify the trade-offs between the number of L-ROADMs and their band sizes and compare those with F-ROADMs, optimization solutions must be obtained. In this paper, we consider two models of L-ROADMs and present optimization problems specific to each model under all-to-all traffic for ring networks. We consider two ring topologies, uni- and bi-directional rings. We give integer linear programming formulations and present heuristic solutions to minimize the worst-case band size and the total number of wavebands for the two L-ROADM types. For the uni-directional ring in the first model, we present a lower bound of ⌈ ( W + 2 ) / 2 ⌉ for the band size of ROADMs, where W is the number of wavelengths. For the upper bound, our results show that the worst-case band size of L-ROADMs is only about 65% of the full range for large network sizes. For the bi-directional ring of N nodes, our heuristic algorithm, Algorithm-Min-Bi, produces a worst-case band size of b ( w ) = N 2 − 4 N + 19 8 . This produces a reduction of 10% to 20% in the band size for typical network sizes. When the band size b s is fixed under the second model, we observe the trade-off between the total band size of L-ROADMs and the number of L-ROADMs. For both uni- and bi-directional ring networks, our results are close to optimal. We also examine the performance of our models under dynamic traffic.

Traffic grooming in bidirectional WDM ring networks

AbstractWe study the minimization of ADMs (Add‐Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all‐to‐all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor C and N, the size of the ring. We first study exhaustively the cases C = 1, C = 2, and C = 3, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case C > 3, focusing specifically on the case C = k(k + 1)/2 for some k ≥ 1. We give optimal decompositions for several congruence classes of N using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 58(1), 20–35 2011

Quasi-periodic states in coupled rings of cells

We study some dynamical features of certain coupled cell networks that consist of two (unidirectional or bidirectional) rings of cells coupled through a ‘buffer’ cell. Depending on how the rings and the buffer cell are coupled, the full network may have a non-trivial group of symmetries or a non-trivial group of ‘interior’ symmetries. This group is Zp×Zq in the unidirectional case and Dp×Dq in the bidirectional case. We are interested in finding quasi-periodic motion in these networks, motivated by an example presented by Golubitsky, Nicol and Stewart (Some curious phenomena in coupled cell systems, J Nonlinear Sci 2004;14(2):207–36). In the examples considered here, we obtain quasi-periodic states through a sequence of Hopf bifurcations. Interestingly, we observe relaxation oscillation phenomena appearing further away from the last Hopf bifurcation point. We use XPPAUT and MATLAB to compute numerically the relevant states.

Bifurcations from regular quotient networks: A first insight

We consider regular (identical-edge identical-node) networks whose cells can be grouped into classes by an equivalence relation. The identification of cells in the same class determines a new network — the quotient network. In terms of the dynamics, this corresponds to restricting the coupled cell systems associated with a network to flow-invariant subspaces given by equality of certain cell coordinates. Assuming a bifurcation occurs for a coupled cell system restricted to the quotient network, we ask how that bifurcation lifts to the overall space. Surprisingly, for certain networks, new branches of solutions occur besides the ones that occur in the quotient network. To investigate this phenomenon we develop a systematic method that enumerates all networks with a given quotient. We also prove necessary conditions for the existence of solution branches not predicted by the quotient. We then apply our method to two particular quotient networks; namely, two- and three-cell bidirectional rings. We show there are no additional bifurcating solution branches when the quotient network is a two-cell bidirectional ring. However, two of the 12 five-cell networks that have the three-cell bidirectional ring as a quotient network exhibit bifurcating solutions that do not occur in the quotient itself. Thus, network architecture sometimes forces the existence of bifurcating branches in addition to the ones determined by the quotient.

On the capacity of optical networks: A framework for comparing different transport architectures

We compare three optical transport network architectures - optical packet switching (OPS), optical flow switching (OFS), and optical burst switching (OBS) - based on a notion of network capacity as the set of exogenous traffic rates that can be stably supported by a network under its operational constraints. We characterize the capacity regions of the transport architectures, and show that the capacity region of OPS dominates that of OFS, and that the capacity region of OFS dominates that of OBS. We then apply these results to two important network topologies - bidirectional rings and Moore graphs - under uniform all-to-all traffic. Motivated by the incommensurate complexity/cost of comparable transport architectures, we also investigate the dependence of the relative capacity performance of the switching architectures on the number of switch ports per fiber at core nodes.

A performance study on optical burst switched networks: the ring topology

Existing performance studies on optical burst switched (OBS) networks have been focusing on channel blocking, i.e., when the required wavelength is not available on a link along a burst’s route. However, we identify another type of blocking as the receiver blocking, i.e., when the receiver at a burst’s destination node is occupied by another burst. Receiver blocking may account for the much larger part of total burst blocking. Receiver blocking has been largely ignored in existing research. In this paper we propose using multiple receivers or fiber delay lines (FDL) in front of the receivers in order to reduce the receiver blocking probability. Extensive simulation results on bi-directional OBS rings are presented to illustrate the problem and the performance of our proposed approaches. The results indicate that receiver blocking can be almost eliminated by using as little as three receivers and can be reduced by using a FDL of small length. To our knowledge, this is the first performance study that covers both channel and receiver blocking for OBS networks.

On the multicast capacity of unidirectional and bidirectional packet-switched WDM ring networks

In this paper we examine the relationship between the effective capacity (stability limit) of unidirectional and bidirectional packet-switched wavelength division multiplexing (WDM) ring networks for multicast traffic. We consider both bidirectional rings with one packet copy transmission per wavelength channel and two packet copy transmissions. We first prove bounds for the ratio of the multicast capacity of the bidirectional ring to the multicast capacity of the unidirectional ring. Specifically, we show that this ratio is at least two for two copy transmission in the bidirectional ring, and at most two for one copy transmission. We derive closed form expressions of the multicast capacity ratios for networks with a large number of nodes and from these expressions show that the ratios tend to two for a large number of multicast destinations. We demonstrate that for the bidirectional ring with two copy transmission the ratio becomes as large as 2.276. We also find that in the bidirectional ring, the capacity gain with two copy transmission over one copy transmission reaches 30.4%

Long-lifetime capacity upgrades of ring networks for unpredictable traffic

Traffic forecasting is an important means to facilitate network capacity planning by predicting necessary link upgrades and link additions, but it is generally unable to take into account events that are hard to predict, e.g., breaking news, denial-of-service attacks, and failures. These events, which may be typically short-lived but whose impact on the network traffic load is significant, together with the hard to predict traffic due to the server farm based architecture of the Internet will increase the amount of unpredictable traffic. The so-called network lifetime metric, which measures the ability of a network to sustain unexpected changes and shifts in traffic load, is becoming increasingly important. Very recently reported preliminary results show that the widely deployed bidirectional rings provide the smallest network lifetime, whereas chordal rings perform best in terms of network lifetime. In this paper, we first provide extensive numerical investigations of the network lifetime of bidirectional rings for realistic initial traffic scenarios. We then provide more detailed insights into the network lifetime of chordal rings and show that chordal rings not necessarily outperform bidirectional rings. Finally, we examine meshed rings and a novel hybrid ring-star network which clearly outperform not only bidirectional but also chordal rings in terms of network lifetime for a wide range of unexpected traffic changes and shifts

A RANDOMIZED 1-LATENT, TIME-ADAPTIVE AND SAFE SELF-STABILIZING MUTUAL EXCLUSION PROTOCOL

For bidirectional rings, there have been proposed self-stabilizing mutual exclusion protocols, which are either time-adaptive (i.e., efficient in recovery) or 1-latent (i.e., efficient in legal execution) but not both. This paper proposes a randomized self-stabilizing mutual exclusion protocol that inherits both of the advantages from them: It is 1-latent in the sense that the privilege is circulated in a linear round (i.e., very intuitively, the privilege is transferred from a process to another by a "step"), provided that the system always stays in legitimate configurations, and is weakly time-adaptive in the sense that the system stabilizes from any configuration c in O(f) steps with a high probability, where f is the number of corrupted processes in c. It also guarantees with a high probability that there is at most one privilege even while converging to a legitimate configuration.

Data Redistribution Algorithms for Heterogeneous Processor Rings

We consider the problem of redistributing data on homogeneous and heterogeneous rings of processors. The problem arises in several applications, after each invocation of a load-balancing mechanism (but we do not discuss the load-balancing mechanism itself). We provide algorithms that aim at optimizing the data redistribution, both for unidirectional and bidirectional rings. One major contribution of the paper is that we are able to prove the optimality of the proposed algorithms in all cases except that of a bidirectional heterogeneous ring, for which the problem remains open.

Grooming of non-uniform traffic on unidirectional and bidirectional rings

Traffic grooming in WDM networks is obtained by intelligently allocating the traffic onto a given set of wavelengths. This paper presents heuristics for grooming of non-uniform general traffic demands onto a given set of wavelengths available on a unidirectional or bidirectional ring. The objective is to minimize the number of higher layer equipment, like SONET Add/Drop Multiplexers (ADMs), or MPLS routers. We map the unidirectional ring onto a linear topology and develop a generalized two-step approach to solve the grooming problem on the mapped topology. In the first step, we allocate the traffic while minimizing the possible number of strings (each string being a collection of non-overlapping traffic streams) in a manner that yields the optimal number of strings in the linear topology case. We also prove the optimality of this step in the number of the strings (wavelengths). In the second step we employ a grouping technique to efficiently combine g strings onto a wavelength while minimizing the total number of the ADMs. We also address the problem of grooming the non-uniform traffic on a bidirectional ring by mapping it onto unidirectional rings, and applying the two-step approach. Moreover, in the case of bidirectional rings we propose an approach to route the traffic that reduces the total number of the required wavelengths and ADMs. The time complexity of our technique is at least an order of n less than other proposed approaches, where n is the total number of nodes in the network. The efficacy of the proposed technique has been demonstrated through a large number of experiments.