Layouts for mobility management in wireless ATM networks

In this paper, we present a new model that combines quality of service and mobility aspects in wireless ATM networks. Namely, besides the hop count and load parameters of the basic ATM layouts, we introduce a new notion of distance that estimates the time needed to reconstruct the virtual channel of a wireless user when he moves through the network. Quality of service guarantee dictates that the rerouting phase must be imperceptible, that is, the maximum distance between two virtual channels must be maintained as low as possible. Therefore, a natural combinatorial problem arises in which suitable trade-offs must be determined between the different performance measures. We first show that establishing the existence of a layout with maximum hop count h, load l and distance d is NP-complete, even in the very restricted case h=2, l=1 and d=1. We then provide optimal layout constructions for basic interconnection networks, such as chains and rings.     

Hop Constrained Network Design Problem with Partial Survivability

This paper studies the hop constrained network design problem with partial survivability, namely, given an undirected network, a set of point-to-point demands (commodities), and transmission link costs, identify two node disjoint paths for each demand (commodity) to minimize the total costs subject to the constraints that each demand is routed and traverses at most a specified number of links (or hops) on both the paths.A mathematical programming formulation of the problem is presented and an efficient solution procedure based on the linear programming relaxation is developed. Extensive computational results across a number of networks are reported. These results indicate that the solution procedure is effective for a wide range of problem sizes.     

Virtual Path Design in Service-Specific ATM Networks

This paper addresses the problem of virtual path management in ATM networks, which is the problem of jointly selecting efficient virtual trunk routes and sizing them to meet end-to-end grade-of-service requirements. The problem is posed over capacitated networks and is formulated as a two-level multi-commodity network flow problem with linear side-constraints (physical layer capacity) and non-linear side constraints (end-to-end/link blocking). Through a variety of examples we show the method (i) generates solutions that agree with engineering judgement, (ii) can solve VP layout management for realistic size networks (of up to 200 nodes) in reasonable time and (iii) provides upper bounds on how far the solution strays from the mathematically optimal design.     

ATM network design for corporate networks

Asynchronous transfer mode (ATM) networks play an important role in support of distributed applications and modern corporate systems. The applications that use these architectures transfer high volumes of data in high-speed bursts and have stringent delay requirements. To address these needs, network managers seek cost efficient network solutions that provide network capacity sufficient to support high-speed applications.In this paper we present a new formulation and solution procedure for designing ATM networks to support corporate applications. Given the locations of the application servers and multiple clients we would like to design a minimum cost ATM network by which the clients can access the servers. Most of the previous work done in this area separates the problem into a routing problem (virtual circuit routing) and an assignment (virtual path assignment) problem. Thus, the solutions tend to be sub-optimal in the combined problem. This research optimizes virtual path (VP) assignment and virtual circuit (VC) routing simultaneously. We formulate the combined problem explicitly and develop an effective solution method. The solution method provides the designer with virtual paths and virtual circuits over which the actual communication takes place. Computational results are provided.     

Parameterized complexity of spare capacity allocation and the multicost Steiner subgraph problem

We study the computational complexity of the Spare Capacity Allocation problem arising in optical networks that use a shared mesh restoration scheme. In this problem we are given a network with edge capacities and point-to-point demands, and the goal is to allocate two edge-disjoint paths for each demand (a working path and a so-called restoration path, which is activated only if the working path fails) so that the capacity constraints are satisfied and the total cost of the used and reserved bandwidth is minimized. We focus on the setting where we deal with a group of demands together, and select their restoration paths simultaneously in order to minimize the total cost. We investigate how the computational complexity of this problem is affected by certain parameters, such as the number of restoration paths to be selected, or the treewidth of the network graph. To analyze the complexity of the problem, we introduce a generalization of the Steiner Forest problem that we call Multicost Steiner Subgraph. We study its parameterized complexity, and identify computationally easy and hard cases by providing hardness proofs as well as efficient (fixed-parameter tractable) algorithms.     

Graceful reassignment of excessively long communications paths in networks

Modern broadband telecommunications networks transport diverse classes of traffic through flexible end-to-end communications paths. For instance, Internet Protocol (IP) networks with Multi-Protocol Label Switching (MPLS) carry traffic through label switched paths. These flexible paths are often changed in real, or near-real, time in response to congestion and failures detected in the network. As a result, over time, some of these communications paths become excessively long (referred to as out-of-kilter), leading to poor service performance and waste of network resources. An effective reassignment scheme may require reassignment of communications paths with acceptable length (referred to as in-kilter) in order to generate spare capacity on certain links for the out-of-kilter paths. A graceful reassignment solution provides an ordered sequence of reassignments that satisfies the following: (i) the total number of reassigned communications paths does not exceed a specified limit, (ii) no temporary capacity violations are incurred on any network link during the execution of the sequence of reassignments (reassignments are executed sequentially, one at a time), (iii) a communications path is reassigned only as a unit without being split among multiple alternate routes (iv) all reassigned communications paths will be in-kilter, (v) none of the reassignments of communications paths that were originally in-kilter can be excluded from the specified solution without resulting in some capacity violation, and (vi) the sequence of reassignments approximately optimizes a predefined objective, such as maximizing the number of reassigned out-of-kilter communications paths or maximizing the total load reassigned from out-of-kilter communications paths. The resulting problem is formulated as a multi-period, multi-commodity network flow problem with integer variables. We present a search heuristic that takes advantage of certain problem properties to find subsequences of reassignments that become part of the solution, without performing an exhaustive search. Each subsequence reassigns at least one out-of-kilter communication path.     

Reallocation of paths of ABR services in a multistage interconnection network (MIN)-type ATM switch network

In this paper, we develop algorithms for reallocating paths of available bit rate (ABR) services in an asynchronous transfer mode (ATM) switch network. ATM traffic control for fair share bandwidth allocation is usually performed under the assumption that paths of all services in a switch network are fixed. However, each connection may have multiple paths from an ingress queue to an egress queue since most ATM switch networks have the structure of the multistage interconnection network of switch elements. Therefore, paths already established for ABR connections may have to be changed to enhance throughput of the switch, if the ATM switch has the capability of adjusting paths of ABR connections while they are being served. We present three algorithms, in which throughput for ABR connections is estimated to decide whether or not paths of the connections should be changed. These algorithms are compared with an existing traffic management algorithm through simulation experiments. Results of the experiments show that the suggested algorithms give higher throughput in terms of the number of transmitted ABR cells without increasing the delay time of ABR services as well as quality of service (QoS) guaranteed services or decreasing the number of transmitted cells of QoS guaranteed services.     

A model for the capacitated,hop-constrained,per-packet wireless mesh network design problem

Three critical factors in wireless mesh network design are the number of hops between supply and demand points, the bandwidth capacity of the transport media, and the technique used to route packets within the network. Most previous research on network design has focused on the issue of hop constraints and/or bandwidth capacity in wired networks while assuming a per-flow routing scheme. However, networks that employ per-packet routing schemes in wireless networks involve different design issues that are unique to this type of problem. We present a methodology for designing wireless mesh networks that consider bandwidth capacity, hop constraints, and profitability for networks employing a per-packet routing system.     

Multimodal K-shortest viable path problem in Tehran public transportation network and its solution applying ant colony and simulated annealing algorithms

This paper treats with K-shortest viable path problem in a transportation network including multiple modes. The considered modes are metro, rapid-bus, private and walking. In this network, a viable path is one that the number of mode changes is limited and the traverse time and also the walking, metro and private usage are restricted subjected to some constraints. The traverse time is defined dependent on congestion level. Because constrained shortest path is NP-hard, we extend two metaheuristic algorithms namely GASA and BACS for the given problem. GASA is a Greedy Algorithm Simulated Annealing and BACS is a bi-direction searching Ant Colony System made by two colonies of ants. We evaluate the validation of these algorithms applying several multimodal random networks. In addition, their results are compared with CPLEX 12.1. We find that GASA is appropriate for small networks and BACS has better performance in median and large-scale networks. Our results on Tehran network also demonstrate that BACS provides better objective values than BACS ones because Tehran public transportation is sparse.     

Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.     

Optimal routing in non-geostationary satellite ATM networks with intersatellite link capacity constraints

The trend toward broadband communications in space is foreseeable, and its features predestine ATM as the basic mode of operation. Some of the low and medium earth orbit satellite concepts make use of intersatellite links (ISLs) to provide global connectivity with minimal usage of terrestrial fixed network resources. Interconnecting neighbouring satellites with ISLs results in a partially meshed switching subnetwork in space. The ISLs have a time-varying distance or may even lose sight of each other. This feature of the ISL topology dynamics significantly increases the complexity of connection-oriented network operation and routing. We deal with the routing problem to minimize the virtual path connection handover rate and path delay in the time-varying ISL subnetwork topology with ISL capacity constraints. A heuristic algorithm is proposed to deal with this problem, which is based on Lagrangean relaxation and dynamic programming. When there is sufficient capacity at every ISL, the algorithm produces an optimal solution easily using only dynamic programming. For evaluation of our algorithm, some computational results have been presented. These results show that our optimization algorithm can produce a solution close to an optimal solution when there exist ISL capacity constraints.     

On transmission time through k minimal paths of a capacitated-flow network

The quickest path problem is to minimize the transmission time for sending a specified amount of data through a single minimal path. Two deterministic attributes are involved herein; the capacity and the lead time. However, in many real-life networks such as computer systems, urban traffic systems, etc., the arc capacity should be multistate due to failure, maintenance, etc. Such a network is named a capacitated-flow network. The minimum transmission time is thus not a fixed number. This paper is mainly to evaluate system reliability that d units of data can be transmitted through k minimal paths under time constraint T. A simple algorithm is proposed to generate all minimal capacity vectors meeting the demand and time constraints. The system reliability is subsequently computed in terms of such vectors. The optimal k minimal paths with highest system reliability can further be derived.     

Network design problem with relays: A genetic algorithm with a path-based crossover and a set covering formulation

The network design problem with relays arises in telecommunications and distribution systems where the payload must be reprocessed at intermediate stations called relays on the route from its origin to its destination. In fiber-optic networks, for example, optical signals may be regenerated several times to overcome signal degradation because of attenuation and other factors. Given a network and a set of commodities, the network design problem with relays involves selecting network edges, determining a route for each commodity, and locating relays to minimize the network design cost. This paper presents a new formulation to the problem based on set covering constraints. The new formulation is used to design a genetic algorithm with a specialized crossover/mutation operator which generates a feasible path for each commodity, and the locations of relays on these paths are determined by solving the corresponding set covering problem. Computational experiments show that the proposed approach can outperform other approaches, particularly on large size problems.     

Shortest path games

We study cooperative games that arise from the problem of finding shortest paths from a specified source to all other nodes in a network. Such networks model, among other things, efficient development of a commuter rail system for a growing metropolitan area. We motivate and define these games and provide reasonable conditions for the corresponding rail application. We show that the core of a shortest path game is nonempty and satisfies the given conditions, but that the Shapley value for these games may lie outside the core. However, we show that the shortest path game is convex for the special case of tree networks, and we provide a simple, polynomial time formula for the Shapley value in this case. In addition, we extend our tree results to the case where users of the network travel to nodes other than the source. Finally, we provide a necessary and sufficient condition for shortest paths to remain optimal in dynamic shortest path games, where nodes are added to the network sequentially over time.     

Optimizing the system of virtual paths by tabu search

In an asynchronous transfer mode (ATM) network, given the network topology and traffic demands, the establishment of the system of virtual paths (VPs), and the assignment of connections to them so that the network performance is optimized, entails a number of computationally hard subproblems. The optimization problem discussed here focuses on finding a system of VP routes for a given set of VP terminators and VP capacity demands. Although it has been proven that the existing random path algorithm yields the worst case time bound, the solution performance still depends highly on the number of iterations. In this paper, an exact solution procedure and a heuristic method based on a simple tabu search have been developed for optimizing the system of VPs. Computational results show that the proposed tabu search algorithm is effective in obtaining high quality solutions, and the performance of the proposed algorithm is increasingly attractive as the problem size becomes larger.     

Data envelopment analysis application in sustainability: The origins,development and future directions

Sustainable development and sustainability assessment have been of great interest to both academe and practitioners in the past decades. In this study, we review the literature on data envelopment analysis (DEA) applications in sustainability using citation-based approaches. A directional network is constructed based on citation relationships among DEA papers published in journals indexed by the Web of Science database from 1996 to March 2016. We first draw the citation chronological graph to present a complete picture of literature development trajectory since 1996. Then we identify the local main DEA development paths in sustainability research by assigning an importance index, namely search path count (SPC), to each link in the citation network. The local main path suggests that the current key route of DEA applications in sustainability focus on the environmental sustainability. Through the Kamada–Kawai layout algorithm, we find four research clusters in the literature including corporate sustainability assessment, regional sustainability assessment, sustainability composite indicator construction, and sustainability performance analysis. For each of the clusters, we further identify the key articles based on citation network and local citation scores, demonstrate the developmental trajectory of the literature, and suggest future research directions.     

A deep-submicron steiner tree

An A-Tree is a rectilinear Steiner tree in which every sink is connected to a driver by a shortest length path, while simultaneously minimizing total wire length. This paper presents a polynomial approximation algorithm for the generalized version of an A-Tree problem with upper-bounded delays along each path from the driver to the sinks and with restrictions on the number of Steiner nodes. We refer to it as “Deep-submicron Steiner tree”, as minimizing the number of Steiner nodes is crucial for signal integrity issues in deep-submicron Very-Large-Scaled-Integrated-circuit (VLSI) designs. The idea behind the algorithm is to control two parameters in order to construct a feasible (with respect to the paths delays and the number of Steiner nodes) tree of small cost.The simulation results show the high efficiency of our approach.     

Enumerating several aspects of non-decreasing Dyck paths

A Dyck path is non-decreasing if the $y$-coordinates of its valleys form a non-decreasing sequence. In this paper we give enumerative results and some statistics of several aspects of non-decreasing Dyck paths. We give the number of pyramids at a fixed level that the paths of a given length have, count the number of primitive paths, count how many of the non-primitive paths can be expressed as a product of primitive paths, and count the number of paths of a given height and a given length. We present and prove our results using combinatorial arguments, generating functions (using the symbolic method) and parameterize the results studied here using the Riordan arrays. We use known bijections to connect direct column-convex polyominoes, Elena trees, and non-decreasing Dyck paths.     

Finding K shortest looping paths with waiting time in a time–window network

A time-constrained shortest path problem is a shortest path problem including time constraints that are commonly modeled by the form of time windows. Finding K shortest paths are suitable for the problem associated with constraints that are difficult to define or optimize simultaneously. Depending on the types of constraints, these K paths are generally classified into either simple paths or looping paths. In the presence of time–window constraints, waiting time occurs but is largely ignored. Given a network with such constraints, the contribution of this paper is to develop a polynomial time algorithm that finds the first K shortest looping paths including waiting time. The time complexity of the algorithm is O(rK²|V₁|³), where r is the number of different windows of a node and |V₁| is the number of nodes in the original network.     

Path problems in generalized stars, complete graphs, and brick wall graphs

Path problems such as the maximum edge-disjoint paths problem, the path coloring problem, and the maximum path coloring problem are relevant for resource allocation in communication networks, in particular all-optical networks. In this paper, it is shown that maximum path coloring can be solved optimally in polynomial time for bidirected generalized stars, even in the weighted case. Furthermore, the maximum edge-disjoint paths problem is proved NP-hard for complete graphs (undirected or bidirected), a constant-factor off-line approximation algorithm is presented for the weighted case, and an on-line algorithm with constant competitive ratio is given for the unweighted case. Finally, an open problem concerning the existence of routings that simultaneously minimize the maximum load and the number of colors is solved: an example for a graph and a set of requests is given such that any routing that minimizes the maximum load requires strictly more colors for path coloring than a routing that minimizes the number of colors.