A survey on retrial queues

Queueing systems in which arriving customers who find all servers and waiting positions (if any) occupied may retry for service after a period of time are called retrial queues or queues with repeated orders. Retrial queues have been widely used to model many problems in telephone switching systems, telecommunication networks, computer networks and computer systems. In this paper, we discuss some important retrial queueing models and present their major analytic results and the techniques used. Our concentration is mainly on single-server queueing models. Multi-server queueing models are briefly discussed, and interested readers are referred to the original papers for details. We also discuss the stochastic decomposition property which commonly holds in retrial queues and the relationship between the retrial queue and the queue with server vacations.     

On the Two-Architecture Connected Facility Location Problem

We introduce a new variant of the connected facility location problem that allows for modeling mixed deployment strategies (FTTC/FTTB/FTTH) in the design of local access telecommunication networks. Several mixed integer programming models and valid inequalities are presented. Computational studies on realistic instances from three towns in Germany are provided.     

Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation

Molecular genetics presents an increasingly complex picture of the genome and biological function. Evidence is mounting for distributed function, redundancy, and combinatorial coding in the regulation of genes. Satisfactory explanation will require the concept of a parallel processing signaling network. Here we provide an introduction to Boolean networks and their relevance to present-day experimental research. Boolean network models exhibit global complex behavior, self-organization, stability, redundancy and periodicity, properties that deeply characterize biological systems. While the life sciences must inevitably face the issue of complexity, we may well look to cybernetics for a modeling language such as Boolean networks which can manageably describe parallel processing biological systems and provide a framework for the growing accumulation of data. We finally discuss experimental strategies and database systems that will enable mapping of genetic networks. The synthesis of these approaches holds an immense potential for new discoveries on the intimate nature of genetic networks, bringing us closer to an understanding of complex molecular physiological processes like brain development, and intractable medical problems of immediate importance, such as neurodegenerative disorders, cancer, and a variety of genetic diseases.     

Exploring communication networks to understand organizational crisis using exponential random graph models

In recent social network studies, exponential random graph (ERG) models have been used comprehensively to model global social network structure as a function of their local features. In this study, we describe the ERG models and demonstrate its use in modelling the changing communication network structure at Enron Corporation during the period of its disintegration. We illustrate the modelling on communication networks, and provide a new way of classifying networks and their performance based on the occurrence of their local features. Among several micro-level structures of ERG models, we find significant variation in the appearance of A2P (Alternating k-two-paths) network structure in the communication network during crisis period and non-crisis period. We also notice that the attribute of hierarchical positions of actors (i.e., high rank versus low rank staff) have impact on the evolution process of networks during crisis. These findings could be used in analyzing communication networks of dynamic project groups and their adaptation process during crisis which could lead to an improved understanding how communications network evolve and adapt during crisis.     

Ein Verfahren zur Optimierung von Nachrichtenübertragungsnetzen mit Mehrwegeführung

Within the framework of long-term planning of telecommunication transmission networks, an economic solution has to be calculated for the future network structure. In this structure, the cost of routing the circuits required between the exchanges must be optimized. For reliability reasons, it is necessary to route over several edge-disjoint paths. The paper describes the importance of long-term planning of telecommunication transmission networks. It is shown that this problem can be formulated by a model with a concave objective function and linear constraints. For this model, an algorithm is developed whose numeric behaviour is described. Practical applications of the procedure are indicated.     

Topological design of telecommunication networks-local access design methods

Computer communication networks and telecommunication systems are growing at an explosive rate. Some of the major factors influencing this phenomenal growth rate have been technology driven, deregulation of the telecommunication industry and the breakup of AT&T, product and service introductions and competition, new application areas, price reductions and improved services. Corporations have discovered how to use telecommunication-based systems and computer networks as a strategic competitive weapon. Modern computer networks consist of backbone networks which serve as major highways to transfer large volumes of communication traffic, and local access networks which feed traffic between the backbone network and end user nodes. The design of the local access network is a complex process which builds on many difficult combinatorial optimization problems. This paper surveys many of the problems, presents the state of the art in solving them, and demonstrates a variety of solution procedures. The paper concludes with a list of open problems and areas open for further investigation.This research was partially supported by a Dean's grant for faculty research at the Owen Graduate School of Management, Vanderbilt University, Nashville, TN 37204, USA.     

The Role of Metanetworks in Network Evolution

The question of what structures of relations between actors emerge in the evolution of social networks is of fundamental sociological interest. The present research proposes that processes of network evolution can be usefully conceptualized in terms of a network of networks, or “metanetwork,” wherein networks that are one link manipulation away from one another are connected. Moreover, the geography of metanetworks has real effects on the course of network evolution. Specifically, both equilibrium and non-equilibrium networks located in more desirable regions of the metanetwork are found to be more probable. These effects of metanetwork geography are illustrated by two dynamic network models: one in which actors pursue access to unique information through “structural holes,” and the other in which actors pursue access to valid information by minimizing path length. Finally, I discuss future directions for modeling network dynamics in terms of metanetworks.     

A Branch-and-Bound Algorithm to Solve a Multi-level Network Optimization Problem

Multi-level network optimization problems arise in many contexts such as telecommunication, transportation, and electric power systems. A model for multi-level network design is formulated as a mixed-integer program. The approach is innovative because it integrates in the same model aspects of discrete facility location, topological network design, and dimensioning. We propose a branch-and-bound algorithm based on Lagrangian relaxation to solve the model. Computational results for randomly generated problems are presented showing the quality of our approach. We also present and discuss a real world problem of designing a two-level local access urban telecommunication network and solving it with the proposed methodology.     

Forest management models and combinatorial algorithms: analysis of state of the art

Linear Programming and Mixed Integer Linear Programs have been used for forest planning since the 60's to support decision making on forest harvesting and management. In particular, during the last two decades of forest management there has been an increased interest in spatial issues. Further, new environmental concerns, such as resource sustainability and wildlife protection, impose that increased attention be paid to activities carried out on the ground. Road building needed for access also requires spatial definiton. As a result, more complex models must be used. We discuss the issues which have led to the combinatorial nature of some main forest management problems and the solution algorithms that have been proposed for these problems, including local search heuristics, random search approaches, strengthening of mixed integer model formulations and Lagrangian relaxation. In this survey, we discuss which of the proposed approaches have been used succesfully, the advantages and shortcomings of each and what are still open research problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

General results on preferential attachment and clustering coefficient

This is a review paper that covers some recent results on the behavior of the clustering coefficient in preferential attachment networks and scale-free networks in general. The paper focuses on general approaches to network science. In other words, instead of discussing different fully specified random graph models, we describe some generic results which hold for classes of models. Namely, we first discuss a generalized class of preferential attachment models which includes many classical models. It turns out that some properties can be analyzed for the whole class without specifying the model. Such properties are the degree distribution and the global and average local clustering coefficients. Finally, we discuss some surprising results on the behavior of the global clustering coefficient in scale-free networks. Here we do not assume any underlying model.     

A Heuristic Procedure for Leasing Channels in Telecommunications Networks

Rapid advances in computing and communications technology have made distributed computing an attractive alternative for geographically dispersed organizations. A telecommunication sub-network forms the backbone of these distributed systems. In general, this paper focuses on the assignment of communication channel capacities in the presence of time variant usage patterns. Specifically, we concentrate on long-range capacity planning for organizations that construct networks by leasing communication channels from telecommunication companies. We formulate the capacity assignment problem as a 0-1 integer program that seeks to minimize total leasing cost subject to communication delay restrictions. Unlike previous models that include a single-system wide-average delay constraint, our model allows the flexibility of specifying delay restrictions by communicating node pairs. We propose an efficient heuristic, and a Lagrangian relaxation based procedure to obtain performance guarantees on the solution obtained from the heuristic.     

Evolution of social networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.     

A review of open queueing network models of manufacturing systems

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures — features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches.     

Municipal Water Demand Forecasting: Tools for Intervention Time Series

This article introduces some approaches to common issues arising in real cases of water demand prediction. Occurrences of negative data gathered by the network metering system and demand changes due to closure of valves or changes in consumer behavior are considered. Artificial neural networks (ANNs) have a principal role modeling both circumstances. First, we propose the use of ANNs as a tool to reconstruct any anomalous time series information. Next, we use what we call interrupted neural networks (I-NN) as an alternative to more classical intervention ARIMA models. Besides, the use of hybrid models that combine not only the modeling ability of ARIMA to cope with the time series linear part, but also to explain nonlinearities found in their residuals, is proposed. These models have shown promising results when tested on a real database and represent a boost to the use and the applicability of ANNs.     

Decision support system for planning telecommunication networks: a case study applied to the Andalusian region

Network planning is essential to design real broadband integrated services digital networks (B-ISDN). This paper presents an operations research application to the design of an optic fibre network for the Andalusian region. The economical appraisal is the main consideration in order to take the appropriate decisions: hub location, region sizes and selection of the urban nodes that will receive telecommunication contents. A decision support system with a graphic interface that allows interactive analysis of different scenarios is presented. The system contains a set of mathematical programming models and it has the capability to dynamically construct and solve instances of those models. In addition, it provides data preparation and reports. The system is an integrated, user-friendly and powerful tool to make planning studies by firms developing cable network systems in the telecommunications market.     

A brief survey of the state of mathematical modeling aroung the world

We briefly survey and discuss the issues and perspectives presented in the two special issues of the Zentralblatt für Didaktik der Mathematik on mathematical modeling and pose open questions to the community of researchers interested in this domain of inquiry.     

Agent-based interpretations of classic network models

The paper is aimed at developing agent-based variants of traditional network models that make full use of concurrency. First, we review some classic models of the static structure of complex networks with the objective of developing agent-based models suited for simulating a large-scale, technology-enabled social network. Secondly, we outline the basic properties that characterize such networks. Then, we briefly discuss some classic network models and the properties of the networks they generate. Finally, we discuss how such models can be converted into agent-based models (i) to be executed more easily in heavily concurrent environments and (ii) to serve as basic blocks for more complex agent-based models. We evidence that many implicit assumptions made by traditional models regarding their execution environment are too expensive or outright impossible to maintain in concurrent environments. Consequently, we present the concurrency issues resulting from the violation of such assumptions. Then, we experimentally show that, under reasonable hypothesis, the agent-based variants maintain the main features of the classic models, notwithstanding the change of environment. Eventually, we present a meta-model that we singled out from the individual classic models and that we used to simplify the agent-oriented conversion of the traditional models. Finally, we discuss the software tools that we built to run the agent-based simulations.     

Strong approximations for Markovian service networks

Inspired by service systems such as telephone call centers, we develop limit theorems for a large class of stochastic service network models. They are a special family of nonstationary Markov processes where parameters like arrival and service rates, routing topologies for the network, and the number of servers at a given node are all functions of time as well as the current state of the system. Included in our modeling framework are networks of M _t /M _t /n _t queues with abandonment and retrials. The asymptotic limiting regime that we explore for these networks has a natural interpretation of scaling up the number of servers in response to a similar scaling up of the arrival rate for the customers. The individual service rates, however, are not scaled. We employ the theory of strong approximations to obtain functional strong laws of large numbers and functional central limit theorems for these networks. This gives us a tractable set of network fluid and diffusion approximations. A common theme for service network models with features like many servers, priorities, or abandonment is “non-smooth” state dependence that has not been covered systematically by previous work. We prove our central limit theorems in the presence of this non-smoothness by using a new notion of derivative. This revised version was published online in June 2006 with corrections to the Cover Date.