Dynamic routing in open queueing networks: Brownian models,cut constraints and resource pooling

We present an introductory review of recent work on the control of open queueing networks. We assume that customers of different types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian network models. Our main conclusion is that in many respects dynamic routingsimplifies the behaviour of networks, and that under good control policies it may well be possible to model the aggregate behaviour of a network quite straightforwardly.Supported by SERC grant GR/F 94194.     

Study of discrete automaton models of gene networks of nonregular structure using symbolic calculations

We introduce the discrete automaton models of gene networks with weight functions of vertices accounting for the various forms of the regulatory interaction of agents. We study the discrete mapping that describes the operation of a fragment of the gene network of the bacteria E. coli. For this mapping, we find its fixed points (stationary states) on using the SAT approach. We also study the mappings that are defined by the random graphs of the network which we generate in accordance with the Gilbert-Erdos-Renyi and Watts-Strogatz models. For these mappings, we find the fixed points and the length 2 and 3 cycles. This article can be regarded as a survey of our results on the discrete models of gene networks and the numerical methods for studying their operation.     

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.     

An Approximation Method for Improving Dynamic Network Model Fitting

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, that is, networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a nonnegligible computational burden, is much easier. This article examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail—networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.     

Queueing models for the analysis of communication systems

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.     

Network formation and knowledge gains

Incentive-based models for network formation link micro actions to changes in network structure. Sociologists have extended these models on a number of fronts, but there remains a tendency to treat actors as homogenous agents and to disregard social theory. Drawing upon literature on the strategic use of networks for knowledge gains, we specify models exploring the co-evolution of networks and knowledge gains. Our findings suggest that pursuing transitive ties is the most successful strategy, as more reciprocity and cycling result from this pursuit, thus encouraging learning across the network. We also discuss the role of network size, global network structure, and parameter strength in actors’ attainment of knowledge resources.     

Object oriented modeling of social networks

The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks.We provide a brief introduction into the field of social networks and present an overview of existing network models and methods. Subsequently we introduce an elementary problem field in the social sciences in general, and in studies of organizational change and design in particular: the micro-macro link. We argue that the most appropriate way to hadle this problem is the principle of methodological individualism. For social network analysis, to contribute to this theoretical perspective, it should include an individual choice mechanism and become more dynamically oriented. Subsequently, object oriented modeling is advocated as a tool to meet these requirements for social network analysis. We show that characteristics of social systems that are emphasized in the methodological individualistic approach have their direct equivalences in object oriented models. The link between the micro level where actors act, and the macro level where phenomena occur as a consequence and cause of these actions, can be modelled in a straightforward way.     

Detecting direct associations in a network by information theoretic approaches

Detecting direct associations or inferring networks based on the observed data is an important issue in many fields, including biology, physics, engineering and social studies. In this work, we focus on the information theoretic approaches in the network reconstruction or the direct association detection, in particular,for biological networks. We not only review the traditional approaches or measurements on the associations among the observed variables, such as correlation coefficient, mutual information and conditional mutual information(CMI), but also summarize recently developed theories and methods. The new theoretic works include:information geometry to give a unified framework in detecting causality/association, the partial independence to alleviate the singularity of CMI, and multiscale analysis of CMI to avoid the underestimation issue of CMI.The new methods include part mutual information(PMI) and partial associations(PA), which improve the old measurements in avoiding both overestimation and underestimation. All those theories and methods make important contributions as major advances in the development of network inference.     

Parallel cleaning of a network with brushes

We consider the process of cleaning a network where at each time step, all vertices that have at least as many brushes as incident, contaminated edges, send brushes down these edges and remove them from the network. An added condition is that, because of the contamination model used, the final configuration must be the initial configuration of another cleaning of the network. We find the minimum number of brushes required for trees, cycles, complete bipartite networks; and for all networks when all edges must be cleaned on each step. Finally, we give bounds on the number of brushes required for complete networks.     

Inference of an oscillating model for the yeast cell cycle

High-throughput techniques allow measurement of hundreds of cell components simultaneously. The inference of interactions between cell components from these experimental data facilitates the understanding of complex regulatory processes. Differential equations have been established to model the dynamic behavior of these regulatory networks quantitatively. Usually traditional regression methods for estimating model parameters fail in this setting, since they overfit the data. This is even the case, if the focus is on modeling subnetworks of, at most, a few tens of components. In a Bayesian learning approach, this problem is avoided by a restriction of the search space with prior probability distributions over model parameters.This paper combines both differential equation models and a Bayesian approach. We model the periodic behavior of proteins involved in the cell cycle of the budding yeast Saccharomyces cerevisiae, with differential equations, which are based on chemical reaction kinetics. One property of these systems is that they usually converge to a steady state, and lots of efforts have been made to explain the observed periodic behavior. We introduce an approach to infer an oscillating network from experimental data. First, an oscillating core network is learned. This is extended by further components by using a Bayesian approach in a second step. A specifically designed hierarchical prior distribution over interaction strengths prevents overfitting, and drives the solutions to sparse networks with only a few significant interactions.We apply our method to a simulated and a real world dataset and reveal main regulatory interactions. Moreover, we are able to reconstruct the dynamic behavior of the network.     

Complex dynamics of epidemic models on adaptive networks

There has been a substantial amount of well mixing epidemic models devoted to characterizing the observed complex phenomena (such as bistability, hysteresis, oscillations, etc.) during the transmission of many infectious diseases. A comprehensive explanation of these phenomena by epidemic models on complex networks is still lacking. In this paper we study epidemic dynamics in an adaptive network proposed by Gross et al., where the susceptibles are able to avoid contact with the infectious by rewiring their network connections. Such rewiring of the local connections changes the topology of the network, and inevitably has a profound effect on the transmission of the disease, which in turn influences the rewiring process. We rigorously prove that the adaptive epidemic model investigated in this paper exhibits degenerate Hopf bifurcation, homoclinic bifurcation and Bogdanov–Takens bifurcation. Our study shows that adaptive behaviors during an epidemic may induce complex dynamics of disease transmission, including bistability, transient and sustained oscillations, which contrast sharply to the dynamics of classical network models. Our results yield deeper insights into the interplay between topology of networks and the dynamics of disease transmission on networks.     

Optimal egress time calculation and path generation for large evacuation networks

Finding the optimal clearance time and deciding the path and schedule of evacuation for large networks have traditionally been computationally intensive. In this paper, we propose a new method for finding the solution for this dynamic network flow problem with considerably lower computation time. Using a three phase solution method, we provide solutions for required clearance time for complete evacuation, minimum number of evacuation paths required for evacuation in least possible time and the starting schedules on those paths. First, a lower bound on the clearance time is calculated using minimum cost dynamic network flow model on a modified network graph representing the transportation network. Next, a solution pool of feasible paths between all O-D pairs is generated. Using the input from the first two models, a flow assignment model is developed to select the best paths from the pool and assign flow and decide schedule for evacuation with lowest clearance time possible. All the proposed models are mixed integer linear programing models and formulation is done for System Optimum (SO) scenario where the emphasis is on complete network evacuation in minimum possible clearance time without any preset priority. We demonstrate that the model can handle large size networks with low computation time. A numerical example illustrates the applicability and effectiveness of the proposed approach for evacuation.     

Artificial neural networks in bankruptcy prediction: General framework and cross-validation analysis

In this paper, we present a general framework for understanding the role of artificial neural networks (ANNs) in bankruptcy prediction. We give a comprehensive review of neural network applications in this area and illustrate the link between neural networks and traditional Bayesian classification theory. The method of cross-validation is used to examine the between-sample variation of neural networks for bankruptcy prediction. Based on a matched sample of 220 firms, our findings indicate that neural networks are significantly better than logistic regression models in prediction as well as classification rate estimation. In addition, neural networks are robust to sampling variations in overall classification performance.     

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.     

A Mathematical Model for Optimal Functional Disruption of Biochemical Networks

Biochemical networks are a particular kind of biological networks which describe the cell metabolism and regulate various biological functions, from biochemical pathways to cell growth. The relationship between structure, function and regulation in complex cellular networks is still a largely open question. This complexity calls for proper mathematical models and methods relating network structure and functional properties. In this paper we focus on the problem of drug targets’ identification by detecting network alteration strategies which lead to a cell functionality loss. We propose a mathematical model, based on a bi-level programming formulation, to obtain the minimum cost disruption policy through the identification of specific gene deletions. These deletions represent drug target identification of new drug treatments for hindering bacterial infections.     

Is politics power or policy oriented? A comparative analysis of dynamic access models in policy networks*

We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models.

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points in this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions.

In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor.

Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their “best” requests and learn by experience.

We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to “bolster” their own preference as much as possible.     

Models for planning capacity expansion in local access telecommunication networks

The rapid progress of communications technology has created new opportunities for modeling and optimizing the design of local telecommunication systems. The complexity, diversity, and continuous evolution of these networks pose several modeling challenges. In this paper, we present an overview of the local telephone network environment, and discuss possible modeling approaches. In particular, we (i) discuss the engineering characteristics of the network, and introduce terminology that is commonly used in the communications industry and literature; (ii) describe a general local access network planning model and framework, and motivate different possible modeling assumptions; (iii) summarize various existing planning models in the context of this framework; and (iv) describe some new modeling approaches. The discussion in this paper is directed both to researchers interested in modeling local telecommunications systems and to planners interested in using such models. Our goal is to present relevant aspects of the engineering environment for local access telecommunication networks, and to discuss the relationship between engineering issues and the formulation of economic decision models. We indicate how changes in the underlying switching and transmission technology affect the modeling of the local telephone network. We also review various planning issues and discuss possible optimization approaches for treating them.This research was initiated through a grant from GTE Laboratories, IncorporatedSupported in part by an AT&T research award.Supported in part by Grant No. ECS-8316224 from the Systems Theory and Operations Research Program of the National Science Foundation.     

Stable network topologies using the notion of covering

An alternative perspective to evaluate networks and network evolution is introduced, based on the notion of covering. For a particular node in a network covering captures the idea of being outperformed by another node in terms of, for example, visibility and possibility of information gathering. In this paper, we focus on networks where these subdued network positions do not exist. We call these networks stable. Within this set we identify the minimal stable networks, which frequently have a ‘bubble-like’ structure. Severing a link in such a network results in at least one of the nodes being covered. In a minimal stable network therefore all nodes cooperate to avoid that one of the nodes ends up in a subdued position. Our results can be applied to, for example, the design of (covert) communication networks and the dynamics of social and information networks.     

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.