A Markov Renewal Based Model for Wireless Networks

We propose a queueing network model which can be used for the integration of the mobility and teletraffic aspects that are characteristic of wireless networks. In the general case, the model is an open network of infinite server queues where customers arrive according to a non-homogeneous Poisson process. The movement of a customer in the network is described by a Markov renewal process. Moreover, customers have attributes, such as a teletraffic state, that are driven by continuous time Markov chains and, therefore, change as they move through the network. We investigate the transient and limit number of customers in disjoint sets of nodes and attributes. These turn out to be independent Poisson random variables. We also calculate the covariances of the number of customers in two sets of nodes and attributes at different time epochs. Moreover, we conclude that the arrival process per attribute to a node is the sum of independent Poisson cluster processes and derive its univariate probability generating function. In addition, the arrival process to an outside node of the network is a non-homogeneous Poisson process. We illustrate the applications of the queueing network model and the results derived in a particular wireless network.     

Optimal seamless self-assembly of files in linear networks

A file F is sited at one end (the root) of a path in some network. Each non-root node in the path is able to cache part or all of F, and each node may also have a client wanting to download F. Links between neighbors on the path have given transmission delays associated with them, but the delay from a node to its own client, if it has one, is zero. In the seamless, self-assembly paradigm all clients issue requests simultaneously at time 0, each starts to receive segments of F immediately, and continues to receive them until F is fully downloaded. The process must be implemented by means of a distributed self-assembly protocol which is unaware of network structure beyond links to immediate neighbors. We exhibit such a protocol, and show how to assign segments of F to the node caches in such a way that, no matter which nodes are chosen as clients, seamless self-assembly is realized and, simultaneously, the total cache size achieves a lower bound determined solely by the link delays. The paper concludes with a brief discussion of the many open problems arising in systems requiring seamless, or nearly seamless, self assembly of files.     

Mathematical model on malicious attacks in a mobile wireless network with clustering

A mathematical model has been formulated for the analysis of a wireless epidemic on a clustered heterogeneous network. The model introduces mobility into the epidemic framework assuming that the component nodes have a tendency to be attached with a frequently visited home cluster. This underlines the inherent regularity in the mobility pattern of mobile nodes in a wireless network. The analysis focuses primarily on features that arise because of the mobility considerations compared in the larger scenario formed by the epidemic aspects. A result on the invariance of the home cluster populations with respect to time provides an important view-point of the long-term behavior of the system. The analysis also focuses on obtaining a basic threshold condition that guides the epidemic behavior of the system. Analytical as well as numerical results have also been obtained to establish the asymptotic behavior of the connected components of the network, and that of the whole network when the underlying graph turns out to be irreducible. Applications to proximity based attacks and to scenarios with high cluster density have also been outlined.     

Travel times in queueing networks and network sojourns

We first describe expected values of sojourn times for semi-stationary (or synchronous) networks. This includes sojourn times for units and sojourn times for the entire network. A typical sojourn time of a unit is the time it spends in a sector (set of nodes) while it travels through the network, and a typical network sojourn time is the busy period of a sector. Our results apply to a wide class of networks including Jackson networks with general service times, general Markov or regenerative networks, and networks with batch processing and concurrent movement of units. The results also shed more light on when Little's law for general systems, holds for expectations as well as for limiting averages. Next, we describe the expectation of a unit's travel time on a general route in a basic Markov network process (such as a Jackson process). Examples of travel times are the time it takes for a unit to travel from one sector to another, and the time between two successive entrances to a node by a unit. Finally, we characterize the distributions of the sojourn times at nodes on certain overtake-free routes and the travel times on such routes for Markov network processes.This research was supported in part by the Air Force Office of Scientific Research under contract 89-0407 and NSF grant DDM-9007532.     

Recent advances on failure and recovery in networks of networks

Until recently, network science has focused on the properties of single isolated networks that do not interact or depend on other networks. However it has now been recognized that many real-networks, such as power grids, transportation systems, and communication infrastructures interact and depend on other networks. Here, we will present a review of the framework developed in recent years for studying the vulnerability and recovery of networks composed of interdependent networks. In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This is also the case when some nodes, like for example certain people, play a role in two networks, i.e. in a multiplex. Dependency relations may act recursively and can lead to cascades of failures concluding in sudden fragmentation of the system. We review the analytical solutions for the critical threshold and the giant component of a network of n interdependent networks. The general theory and behavior of interdependent networks has many novel features that are not present in classical network theory. Interdependent networks embedded in space are significantly more vulnerable compared to non-embedded networks. In particular, small localized attacks may lead to cascading failures and catastrophic consequences. Finally, when recovery of components is possible, global spontaneous recovery of the networks and hysteresis phenomena occur. The theory developed for this process points to an optimal repairing strategy for a network of networks. Understanding realistic effects present in networks of networks is required in order to move towards determining system vulnerability.     

On Cost Allocation in Hub-Like Networks

We consider telecommunication network design in which each pair of nodes can communicate via a direct link and the communication flow can be delivered through any path in the network. The cost of flow through each link is discounted if and only if the amount of flow exceeds a certain threshold. This exploitation of economies of scale encourages the concentration of flows and use of relatively small number of links. We will call such networks hub-like networks. The cost of services delivered through a hub-like network is distributed among its users who may be individuals or organizations with possibly conflicting interests. The cooperation of these users is essential for the exploitation of economies of scale. Consequently, there is a need to find a fair distribution of the cost of providing the service among users of such network. In order to describe this cost allocation problem we formulate the associated cooperative game, to be referred to as the hub-like game. Special attention is paid to users' contribution to economies of scale. We then demonstrate that certain cost allocation solutions (the core and the nucleolus of the hub-like game), which provide users with the incentive to cooperate, can be efficiently characterized.     

Critical Thresholds for Dynamic Routing in Queueing Networks

This paper studies dynamic routing in a parallel server queueing network with a single Poisson arrival process and two servers with exponential processing times of different rates. Each customer must be routed at the time of arrival to one of the two queues in the network. We establish that this system operating under a threshold policy can be well approximated by a one-dimensional reflected Brownian motion when the arrival rate to the network is close to the processing capacity of the two servers. As the heavy traffic limit is approached, thresholds which grow at a logarithmic rate are critical in determining the behavior of the limiting system. We provide necessary and sufficient conditions on the growth rate of the threshold for (i) approximation of the network by a reflected Brownian motion (ii) positive recurrence of the limiting Brownian diffusion and (iii) asymptotic optimality of the threshold policy.     

Location tracking in mobile ad hoc networks using particle filters

Mobile ad hoc networks (MANETs) are dynamic networks formed on-the-fly as mobile nodes move in and out of each others' transmission ranges. In general, the mobile ad hoc networking model makes no assumption that nodes know their own locations. However, recent research shows that location-awareness can be beneficial to fundamental tasks such as routing and energy-conservation. On the other hand, the cost and limited energy resources associated with common, low-cost mobile nodes prohibits them from carrying relatively expensive and power-hungry location-sensing devices such as GPS. This paper proposes a mechanism that allows non-GPS-equipped nodes in the network to derive their approximated locations from a limited number of GPS-equipped nodes. In our method, all nodes periodically broadcast their estimated location, in terms of a compressed particle filter distribution. Non-GPS nodes estimate the distance to their neighbors by measuring the received signal strength of incoming messages. A particle filter is then used to estimate the approximated location, along with a measure of confidence, from the sequence of distance estimates. Simulation studies show that our solution is capable of producing good estimates equal or better than the existing localization methods such as APS-Euclidean for the more difficult scenario when the network connectivity is low.     

Random Walk Analysis in Antagonistic Stochastic Games

Abstract

This article deals with two “antagonistic random processes” that are intended to model classes of completely noncooperative games occurring in economics, engineering, natural sciences, and warfare. In terms of game theory, these processes can represent two players with opposite interests. The actions of the players are manifested by a series of strikes of random magnitudes imposed onto the opposite side and rendered at random times. Each of the assaults is aimed to inflict damage to vital areas. In contrast with some strictly antagonistic games where a game ends with one single successful hit, in the current setting, each side (player) can endure multiple strikes before perishing. Each player has a fixed cumulative threshold of tolerance which represents how much damage he can endure before succumbing. Each player will try to defeat the adversary at his earliest opportunity, and the time when one of them collapses is referred to as the “ruin time”. We predict the ruin time of each player, and the cumulative status of all related components for each player at ruin time. The actions of each player are formalized by a marked point process representing (an economic) status of each opponent at any given moment of time. Their marks are assumed to be weakly monotone, which means that each opposite side accumulates damages, but does not have the ability to recover. We render a time-sensitive analysis of a bivariate continuous time parameter process representing the status of each player at any given time and at the ruin time and obtain explicit formulas for related functionals.     

The first K shortest unique-arc walks in a traffic-light network

In this article, we present an algorithm to find the first K shortest unique-arc walks in a traffic-light network. Each node of the present network is associated with a repeated sequence of different windows to model operations of traffic signals and intersection movements. Unlike conventional simple or looping paths, we refer to the paths in this paper as unique-arc walks because they may include repeated nodes but will exclude repeated arcs. Using the heap structure, we develop an algorithm to find the first K shortest unique-arc walks in time O(Kr|V|³|A|), where |V| is the number of nodes, |A| is the number of arcs, and r represents the number of different windows associated with a node.     

Emergency path restoration problems

We consider the problem of optimally scheduling the restoration of edges of a transportation network destroyed/damaged by a disaster. The restoration is performed by service units (servers) which have fixed restoration speeds. If several servers work simultaneously at the same point of the network, their collective restoration speed is the sum of their individual restoration speeds. The servers are initially located at some nodes. Each server can travel within the already restored part of the network with infinite speed, that is, at any time can immediately relocate to another point of the same connected component of the already restored part of the network. It is required to minimize a scheduling objective that can be expressed as the maximum or the sum of nondecreasing functions of the recovery times of the nodes, where the recovery time of a node is the time when the node is reached for the first time by a server. We present polynomial-time algorithms on path networks for problems with fixed initial locations of the servers. For problems with flexible locations that should also be optimized, we present polynomial-time algorithms for the case of equal restoration speeds of the servers, and prove that the problems are strongly NP-hard if the restoration speeds of the servers can be different.     

A branch and price solution approach for order acceptance and capacity planning in make-to-order operations

Make-to-order (MTO) operations have to effectively manage their capacity to make long-term sustainable profits. This objective can be met by selectively accepting available customer orders and simultaneously planning for capacity. We model a MTO operation of a job-shop with multiple resources having regular and non-regular capacity. The MTO firm has a set of customer orders at time zero with fixed due-dates. The process route, processing times, and sales price for each order are given. Since orders compete for limited resources, the firm can only accept some orders. In this paper a Mixed-Integer Linear Program (MILP) is proposed to aid an operational manager to decide which orders to accept and how to allocate resources such that the overall profit is maximized. A branch-and-price (B&P) algorithm is devised to solve the MILP effectively. The MILP is first decomposed into a master problem and several sub-problems using Dantzig-Wolfe decomposition. Each sub-problem is represented as a network flow problem and an exact procedure is proposed to solve the sub-problems efficiently. We also propose an approximate B&P scheme, Lagrangian bounds, and approximations to fathom nodes in the branch-and-bound tree. Computational analysis shows that the proposed B&P algorithm can solve large problem instances with relatively short time.     

New algorithms for generalized network flows

This paper, of which a preliminary version appeared in ISTCS'92, is concerned with generalized network flow problems. In a generalized network, each edgee = (u, v) has a positive flow multipliera _e associated with it. The interpretation is that if a flow ofx _e enters the edge at nodeu, then a flow ofa _e x _e exits the edge atv. The uncapacitated generalized transshipment problem (UGT) is defined on a generalized network where demands and supplies (real numbers) are associated with the vertices and costs (real numbers) are associated with the edges. The goal is to find a flow such that the excess or deficit at each vertex equals the desired value of the supply or demand, and the sum over the edges of the product of the cost and the flow is minimized. Adler and Cosares [Operations Research 39 (1991) 955–960] reduced the restricted uncapacitated generalized transshipment problem, where only demand nodes are present, to a system of linear inequalities with two variables per inequality. The algorithms presented by the authors in [SIAM Journal on Computing, to appear result in a faster algorithm for restricted UGT.Generalized circulation is defined on a generalized network with demands at the nodes and capacity constraints on the edges (i.e., upper bounds on the amount of flow). The goal is to find a flow such that the excesses at the nodes are proportional to the demands and maximized. We present a new algorithm that solves the capacitated generalized flow problem by iteratively solving instances of UGT. The algorithm can be used to find an optimal flow or an approximation thereof. When used to find a constant factor approximation, the algorithm is not only more efficient than previous algorithms but also strongly polynomial. It is believed to be the first strongly polynomial approximation algorithm for generalized circulation. The existence of such an approximation algorithm is interesting since it is not known whether the exact problem has a strongly polynomial algorithm.Corresponding author. Research was done while the first author was attending Stanford University and IBM Almaden Research Center. Research partially supported by ONR-N00014-91-C-0026 and by NSF PYI Grant CCR-8858097, matching funds from AT&T and DEC.Research partially supported by ONR-N00014-91-C-0026.     

Isodistant points in competitive network facility location

An isodistant point is any point on a network which is located at a predetermined distance from some node. For some competitive facility location problems on a network, it is verified that optimal (or near-optimal) locations are found in the set of nodes and isodistant points (or points in the vicinity of isodistant points). While the nodes are known, the isodistant points have to be determined for each problem. Surprisingly, no algorithm has been proposed to generate the isodistant points on a network. In this paper, we present a variety of such problems and propose an algorithm to find all isodistant points for given threshold distances associated with the nodes. The number of isodistant points is upper bounded by nm, where n and m are the number of nodes and the number of edges, respectively. Computational experiments are presented which show that isodistant points can be generated in short run time and the number of such points is much smaller than nm. Thus, for networks of moderate size, it is possible to find optimal (or near-optimal) solutions through the Integer Linear Programming formulations corresponding to the discrete version of such problems, in which a finite set of points are taken as location candidates.     

Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda

The identification of key players in a terrorist organization aids in preventing attacks, the efficient allocation of surveillance measures, and the destabilization of the corresponding network. In this paper, we introduce a game theoretic approach to identify key players in terrorist networks. In particular we use the Shapley value as a measure of importance in cooperative games that are specifically designed to reflect the context of the terrorist organization at hand. The advantage of this approach is that both the structure of the terrorist network, which usually reflects a communication and interaction structure, as well as non-network features, i.e., individual based parameters such as financial means or bomb building skills, can be taken into account. The application of our methodology to the analysis results in rankings of the terrorists in the network. We illustrate our methodology through two case studies: Jemaah Islamiyah’s Bali bombing and Al Qaedas 9/11 attack, which lead to new insights in the operational networks responsible for these attacks.     

Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm

We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision “produces” a certain vector of “commodities”; it also has associated “traditional” queueing control effect, i.e., it determines traffic (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to find a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable.We introduce a dynamic control algorithm, which we call Greedy Primal-Dual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traffic sources and network processing nodes may be randomly time-varying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traffic rate constraints.     

Threshold analysis of the susceptible-infected-susceptible model on overlay networks

In this paper, we study epidemic spreading on overlay networks in which n multiple sets of links interconnect among the same nodes. By using the microscopic Markov-chain approximation (MMA) approach, we establish the conditions of epidemic outbreak for two kinds of spreading mechanisms in such an overlay network: the concatenation case and the switching case. When a uniform infection rate is set in all the subnetworks, we find the epidemic threshold for the switching case is just n times as large as that of concatenation case. We also find that the overlay network with a uniform infection rate can be considered as an equivalent (in the sense of epidemic dynamics and epidemic threshold) weighted network. To be specific, the concatenation case corresponds to the integer weighted network, while the switching case corresponds to the fractional weighted network. Interestingly, the time-varying unweighted network can be mapped into the static weighted network. Our analytic results exhibit good agreement with numerical simulations.     

On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank; hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.     

Limit laws for coverage in backbone-sensor networks

We study coverage in sensor networks having two types of nodes, namely, sensor nodes and backbone nodes. Each sensor is capable of transmitting information over relatively small distances. The backbone nodes collect information from the sensors. This information is processed and communicated over an ad hoc network formed by the backbone nodes, which are capable of transmitting over much larger distances. We consider two models of deployment for the sensor and backbone nodes. One is a Poisson–Poisson cluster model and the other a dependently thinned Poisson point process. We deduce limit laws for functionals of vacancy in both models using properties of association for random measures.     

Scheduling networks of queues: Heavy traffic analysis of a simple open network

We consider a queueing network with two single-server stations and two types of customers. Customers of type A require service only at station 1 and customers of type B require service first at station 1 and then at station 2. Each server has a different general service time distribution, and each customer type has a different general interarrival time distribution. The problem is to find a dynamic sequencing policy at station 1 that minimizes the long-run average expected number of customers in the system.The scheduling problem is approximated by a dynamic control problem involving Brownian motion. A reformulation of this control problem is solved, and the solution is interpreted in terms of the queueing system in order to obtain an effective sequencing policy. Also, a pathwise lower bound (for any sequencing policy) is obtained for the total number of customers in the network. We show via simulation that the relative difference between the performance of the proposed policy and the pathwise lower bound becomes small as the load on the network is increased toward the heavy traffic limit.