We investigate the problem of covert quickest change detection in a continuous-time setting, where a Brownian motion experiences a drift change at an unknown time. Unlike classical formulations, we consider a covert adversary who adjusts the post-change drift$\mu = \mu (\gamma)$as a function of the false alarm constraint parameter$\gamma$, with the goal of remaining undetected for as long as possible. Leveraging the exact expressions for the average detection delay (ADD) and average time to false alarm (AT2FA) known for the continuous-time CuSum procedure, we rigorously analyze how the asymptotic behavior of ADD evolves as$\mu (\gamma) \to 0$with increasing$\gamma$. Our results reveal that classical detection delay characterizations no longer hold in this regime. We derive sharp asymptotic expressions for the ADD under various convergence rates of$\mu (\gamma)$, identify precise conditions for maintaining covertness, and characterize the total damage inflicted by the adversary. We show that the adversary achieves maximal damage when the drift scales as$\mu (\gamma) = \Theta (1/\sqrt{\gamma })$, marking a fundamental trade-off between stealth and impact in continuous-time detection systems.

We consider assignment policies that allocate resources to users, where both resources and users are located on a one-dimensional line (0, ∞). First, we consider unidirectional assignment policies that allocate resources only to users located to their left. We propose the Move to Right (MTR) policy, which scans from left to right assigning the nearest available resource located to the right of a user, and contrast it to the Unidirectional Gale-Shapley (UGS) matching policy. While both policies among all unidirectional policies, minimize the expected distance traveled by a request, MTR is fairer. Moreover, we show that when user and resource locations are modeled by statistical point processes, and resources are allowed to satisfy more than one user, the spatial system under unidirectional policies can be mapped into bulk service queueing systems, thus allowing the application of many queueing theory results that yield closed form expressions. As we consider a case where different resources can satisfy different numbers of users, we also generate new results for bulk service queues. We also consider bidirectional policies where there are no directional restrictions on resource allocation and develop an algorithm for computing the optimal assignment which is more efficient than known algorithms in the literature when there are more resources than users. Finally, numerical evaluation of performance of unidirectional and bidirectional allocation schemes yields design guidelines beneficial for resource placement.

In this paper, we consider the problem of allocating cache resources among multiple content providers. The cache can be partitioned into slices and each partition can be dedicated to a particular content provider or shared among a number of them. It is assumed that each partition employs the least recently used policy for managing content. We propose utility-driven partitioning, where we associate with each content provide a utility that is a function of the hit rate observed by the content provider. We consider two scenarios: (1) content providers serve disjoint sets of files and (2) there is some overlap in the content served by multiple content providers. In the first case, we prove that cache partitioning outperforms cache sharing as cache size and a number of contents served by providers go to infinity. In the second case, it can be beneficial to have separate partitions for overlapped content. In the case of two providers, it is usually always beneficial to allocate a cache partition to serve all overlapped content and separate partitions to serve the non-overlapped contents of both providers. We establish conditions when this is true asymptotically but also present an example where it is not true asymptotically. We develop online algorithms that dynamically adjust partition sizes in order to maximize the overall utility and prove that they converge to optimal solutions, and through numerical evaluations we show they are effective.

The operation of a wireless network relies extensively on exchanging messages over a universally known channel, referred to as the control channel. The network performance can be severely degraded if a jammer launches a denial-of-service (DoS) attack on such a channel. In this paper, we design quorum-based frequency hopping (FH) algorithms that mitigate DoS attacks on the control channel of an asynchronous ad hoc network. Our algorithms can establish unicast as well as multicast communications under DoS attacks. They are fully distributed, do not incur any additional message exchange overhead, and can work in the absence of node synchronization. Furthermore, the multicast algorithms maintain the multicast group consistency. The efficiency of our algorithms is shown by analysis and simulations.

The paper has two objectives. The first is to study rigorously the transient behavior of some peer-to-peer (P2P) networks whenever information is replicated and disseminated according to epidemic-like dynamics. The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against P2P networks. We first introduce a stochastic model that extends a classical epidemic model and characterize the P2P swarm behavior in presence of free-riding peers. We then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases, the network is shown to exhibit phase transitions: A small change in the parameters causes a large change in the behavior of the network. We show, in particular, how phase transitions affect measures of content providers against P2P networks that distribute nonauthorized music, books, or articles and what is the efficiency of countermeasures. In addition, our analytical framework can be generalized to characterize the heterogeneity of cooperative peers.

We study the dynamic aspects of the coverage of a mobile sensor network resulting from continuous movement of sensors. As sensors move around, initially uncovered locations may be covered at a later time, and intruders that might never be detected in a stationary sensor network can now be detected by moving sensors. However, this improvement in coverage is achieved at the cost that a location is covered only part of the time, alternating between covered and not covered. We characterize area coverage at specific time instants and during time intervals, as well as the time durations that a location is covered and uncovered. We further consider the time it takes to detect a randomly located intruder and prove that the detection time is exponentially distributed with parameter 2\lambda r \bar{v}_s where \lambda represents the sensor density, r represents the sensor's sensing range, and \bar{v}_s denotes the average sensor speed. For mobile intruders, we take a game theoretic approach and derive optimal mobility strategies for both sensors and intruders. We prove that the optimal sensor strategy is to choose their directions uniformly at random between [0, 2\pi ). The optimal intruder strategy is to remain stationary. This solution represents a mixed strategy which is a Nash equilibrium of the zero-sum game between mobile sensors and intruders.

In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary distribution of the walker depends on the walker rate and is difficult to characterize. However, we characterize the stationary distribution in the following cases: i) the walker rate is significantly larger or smaller than the rate in which the graph changes (time-scale separation), ii) the walker rate is proportional to the degree of the node that it resides on (coupled dynamics), and iii) the degrees of node belonging to the same connected component are identical (structural constraints). We provide examples that illustrate our theoretical findings.

The paper has two objectives. The first is to study rigorously the transient behavior of some peer-to-peer (P2P) networks whenever information is replicated and disseminated according to epidemic-like dynamics. The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against P2P networks. We first introduce a stochastic model which extends a classical epidemic model, and characterize the P2P swarm behavior in presence of free riding peers. We then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases the network is shown to exhibit phase transitions: a small change in the parameters causes a large change in the behavior of the network. We show, in particular, how phase transitions affect measures of content providers against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.

No abstract available.

This work focuses on a class of distributed storage systems whose content may evolve over time. Each component or node of the storage system is mobile and the set of all nodes forms a delay tolerant (ad hoc) network (DTN). The goal of the paper is to study efficient ways for distributing evolving files within DTNs and for managing dynamically their content. We specify to dynamic files where not only the latest version is useful but also previous ones; we restrict however to files where a file has no use if another more recent version is available. The DTN is composed of fixed number of nodes including a single source. At some points in time the source makes available a new version of a single file F. We consider both the cases when (a) nodes do not cooperate and (b) nodes cooperate. In case (a) only the source may transmit a copy of F to a node that it meets, while in case (b) any node may transmit a copy of F to a node that it meets. Scenario (a) is studied under the assumption that the source updates F at discrete times t = 0,1,.. .. Within each slot [t,t + 1) there is a fixed probability that a node meets the source. A file management policy is a set of rules specifying when the source transmits a copy of F to a node (say node i) that it meets; this decision only depends on the age of the version of F (if any) that node i is carrying, where the age is k if this version was created k-1 slots ago. We And the optimal static (resp. dynamic) policy which maximizes a general utility function under a constraint on the number of transmissions within a slot. In particular, we show the existence of a threshold dynamic policy. In scenario (b) F is updated at random points in time. Similar to scenerio (a) we assume that each node knows the age of the file it carries (the case where nodes only know the date of creation of a file is studied in (E. Altman et al., 2008)). Under Markovian assumptions regarding nodes mobility and update frequency of F, we study the stability of the system (aging of the nodes) and derive an (approximate) optimal static policy. We then revisit scenario (a) when the source does not know the number of nodes and the probability that the source meets a node in a slot, and we derive a stochastic approximation algorithm which we show to converge to the optimal static policy found in the complete information setting. Numerical results illustrate the respective performance of optimal static and dynamic policies as well as the benefit of node cooperation.

This paper addresses the design and performance evaluation of relay strategies for opportunistic Delay Tolerant Networks (DTNs) augmented with throwboxes. By opportunistic we mean that a node does not have any knowledge regarding its past and future contact opportunities with the other nodes. We consider a network model composed of both mobile relay nodes and throwboxes, where throwboxes are stationary wireless devices acting simply as fixed relays. We propose and evaluate various relay strategies, where the goal is to take advantage of the presence of throwboxes to minimize resources consumption at mobile nodes. Under Markovian assumptions we introduce a mathematical framework which allows us to calculate the main performance metrics (average delivery delay, overhead, etc.) of each proposed relay scheme. The obtained results highlight the various trade-offs that are left to network designers when adding throwboxes to a DTN, and draw insights on the effectiveness of these strategies.

We consider a mobile ad hoc network consisting of three types of nodes: source, destination, and relay nodes. All the nodes are moving over a bounded region with possibly different mobility patterns. We introduce and study the notion of relay throughput, i.e. the maximum rate at which a node can relay data from the source to the destination. Our findings include the results that the relay throughput depends on the node mobility pattern only via its (stationary) node position distribution and that a node mobility pattern that results in a uniform steady-state distribution for all nodes achieves the lowest relay throughput. Random Waypoint and Random Direction mobility models in both one and in two dimensions are studied and approximate simple expressions for the relay throughput are provided. Finally, the behavior of the relay buffer occupancy is examined for the one-dimensional Random Walk, and an explicit form of its mean value is provided in the heavy-traffic case.

Considered is a mobile ad hoc network consisting of three types of nodes (source, destination and relay nodes) and using the two-hop relay routing protocol. Packets at relay nodes are assumed to have a limited lifetime in the network. All nodes are moving inside a bounded region according to some random mobility model. Both closed-form expressions, and asymptotic results are provided for the packet delivery delay and the energy needed to transmit a packet from the source to its destination. Our model is validated through simulations for two mobility models (random waypoint and random direction mobility models), numerical results for the two-hop relay protocols are reported, and the performance of the two-hop routing and of the epidemic routing protocols are compared.

A number of mobility models have been proposed for the purpose of either analyzing or simulating the movement of users in a mobile wireless network. Two of the more popular are the random waypoint and the random direction models. The random waypoint model is physically appealing but difficult to understand. Although the random direction model is less appealing physically, it is much easier to understand. User speeds are easily calculated, unlike for the waypoint model, and, as we observe, user positions and directions are uniformly distributed. The contribution of this paper is to establish this last property for a rich class of random direction models that allow future movements to depend on past movements. To this end, we consider finite oneand two-dimensional spaces. We consider two variations, the random direction model with wrap around and with reflection. We establish a simple relationship between these two models and, for both, show that positions and directions are uniformly distributed for a class of Markov movement models regardless of initial position. In addition, we establish a sample path property for both models, namely that any piecewise linear movement applied to a user preserves the uniform distribution of position and direction provided that users were initially uniformly throughout the space with equal likelihood of being pointed in any direction.

Previous work on the coverage of mobile sensor networks focuses on algorithms to reposition sensors in order to achieve a static configuration with an enlarged covered area. In this paper, we study the dynamic aspects of the coverage of a mobile sensor network that depend on the process of sensor movement. As time goes by, a position is more likely to be covered; targets that might never be detected in a stationary sensor network can now be detected by moving sensors. We characterize the area coverage at specific time instants and during time intervals, as well as the time it takes to detect a randomly located stationary target. Our results show that sensor mobility can be exploited to compensate for the lack of sensors and improve network coverage. For mobile targets, we take a game theoretic approach and derive optimal mobility strategies for sensors and targets from their own perspectives.

A generic stochastic model with only two input parameters is introduced to evaluate the message delay in mobile ad hoc networks (MANETs) where nodes may relay messages. The Laplace-Stieltjes transform (LST) of the message delay is obtained for two protocols: the two-hop and the unrestricted multicopy protocol. From these results we deduce the expected message delays. It is shown that, despite its simplicity, the model accurately predicts the message delay under both relay strategies for a number of mobility models (the random waypoint, random direction and the random walker mobility models).

Peer-to-peer (P2P) systems are complex to analyze due to their large number of users who connect intermittently and to the frequency of requests for files or Web objects. In this paper we propose a mathematical model in which request streams are represented as fluid flows and then apply this model in an analysis of Squirrel: a recent P2P cooperative Web cache. Our fluid model provides a low-complexity means to estimate the performance of Squirrel (hit probability and latency) and exhibits the key qualitative properties of this system. The accuracy of our model is validated by a comparison with discrete-event simulation.

We propose two novel on-line estimation algorithms to determine the size of a dynamic multicast group. We first use a Wiener filter to derive an optimal estimator for the membership size of the session in case the join process is Poisson and the lifetime of participants is distributed exponentially. We next develop the best first-order linear filter from which we derive an estimator that holds for any lifetime distribution. We apply this approach to the case where the lifetime distribution is hyperexponential. Both estimators hold under any traffic regime. Applying both estimators on real traces corresponding to video sessions, we find that both schemes behave well, one of which performs slightly better than the other in some cases. We further provide guidelines on how to tune the parameters involved in both schemes in order to achieve high quality estimation while simultaneously avoiding feedback implosion.

We propose an efficient on-line estimation algorithm for determining the size of a dynamic multicast group. By using diffusion approximation and a Kalman filter, we derive an estimator that minimizes the mean square of the estimation error. As opposed to previous studies, where the size of the multicast group is supposed to be fixed throughout the estimation procedure, we consider a dynamic estimation scheme that updates the estimation at every observation step. The robustness of our estimator to violation of the assumptions under which it has been derived is addressed via simulations. Further validations of our approach are carried out on real audio traces.

The Internet has allowed the creation of huge amounts of data located on many sites. Performing complex operations on some data requires that the data be transferred first to the machine on which the operations are to be executed, which may require a non-negligible amount of bandwidth and may seriously limit performance if it is the bottleneck. However, instead of moving the data to the code, it is possible to move the code to the data, and perform all the operations locally. This simple idea has led to a new paradigm called code-mobility: a mobile object --- sometimes called an agent --- is given a list of destinations and a series of operations to perform on each one of them. The agent will visit all of the destinations, perform the requested operations and possibly pass the result on to another object. Any mobility mechanism must first provide a way to migrate code from one host to another. It must also ensure that any communication following a migration will not be impaired by it, namely that two objects should still be able to communicate even if one of them has migrated. Such a mechanism is referred to as a location mechanism since it often relies on the knowledge of the location of the objects to ensure communications. Two location mechanisms are widely used: the first one uses a centralized server whereas the second one relies on special objects called forwarders.This paper evaluates and compares the performance of an existing implementation of these approaches in terms of cost of communication in presence of migration. Based on a Markov chain analysis, we will construct and solve two mathematical models, one for each mechanism and will use them to evaluate the cost of location. For the purpose of validation, we have developed for each mechanism a benchmark that uses ProActive [2], a Java library that provides all the necessary primitives for code mobility. Experiments conducted on a LAN and on a MAN have validated both models and have shown that the location server always performs better than the forwarders. Using our analytical models we will nevertheless identify situations where the opposite conclusion holds. However, under most operational conditions location servers will perform better than forwarders.

In this work we develop simple inference models based on finite capacity single server queues for estimating the buffer size and the intensity of cross traffic at the bottleneck link of a path between two hosts. Several pairs of moment-based estimators are proposed to estimate these two quantities. The best scheme is then identified through simulation.

The Differentiated services (diffserv) architecture has been proposed as a scalable solution for providing service differentiation among flows without any per-flow buffer management inside the core of the network. It has been advocated that it is feasible to provide service differentiation among a set of flows by choosing an appropriate “marking profile” for each flow. In this paper, we examine (i) whether it is possible to provide service differentiation among a set of TCP flows by choosing appropriate marking profiles for each flow, (ii) under what circumstances, the marking profiles are able to influence the service that a TCP flow receives, and, (iii) how to choose a correct profile to achieve a given service level. We derive a simple, and yet accurate, analytical model for determining the achieved rate of a TCP flow when edge-routers use “token bucket” packet marking and core-routers use active queue management for preferential packet dropping. From our study, we observe three important results: (i) the achieved rate is not proportional to the assured rate, (ii) it is not always possible to achieve the assured rate and, (iii) there exist ranges of values of the achieved rate for which token bucket parameters have no influence. We find that it is not easy to regulate the service level achieved by a TCP flow by solely setting the profile parameters. In addition, we derive conditions that determine when the bucket size influences the achieved rate, and rates that can be achieved and those that cannot. Our study provides insight for choosing appropriate token bucket parameters for the achievable rates.

We show how the analysis of Markov modulated rate processes can be used to address the problem of computing the distribution of W, the stationary workload in the MMPP/GI/1 queue. Using the results of papers by Anick et al. (1982); Mitra (1988); and Elwalid et al. (1991), we present the decomposition properties of the Laplace transform of W and efficient computational algorithms for computing its distribution. The techniques are also applied to compute the bounds on the distribution of W developed by Liu et al. (see JACM, vol.44, no.2, p.366-94, 1997). Numerical results illustrating the usefulness of the methods are given for the case of the superposition of independent, nonidentical sources.

In this paper, we develop a framework for computing upper and lower bounds of an exponential form for a large class of single resource systems with Markov additive inputs. Specifically, the bounds are on quantities such as backlog, queue length, and response time. Explicit or computable expressions for our bounds are given in the context of queuing theory and numerical comparisons with other bounds and exact results are presented. The paper concludes with two applications to admission control in multimedia systems.

There exists a substantial body of work on the problem of providing guaranteed quality of service (QoS) to different service classes in B-ISDNs. We consider a discrete time, single server system in which packets arrive from a finite population of sources. Under the assumption that arrivals from each source are modulated by a Markov process, we examine the following metrics (i) the fraction of an interval during which the queue length exceeds a certain value, and (ii) the fraction of a group of packets from a single source that arrive to find the queue length above a certain value. For both metrics we derive upper and lower bounds on the probabilities that they exceed a threshold. These are important measures because they reflect more accurately the behavior perceived by applications such as networked audio and video. An application of these results to call admission is also given.

The theory of Markov Control Model with Perfect State Information (MCM-PSI) requires that the current state of the system is known to the decision maker at decision instants. Otherwise, one speaks of Markov Control Model with Imperfect State Information (MCM-ISI). In this article, we introduce a new class of MCM-ISI, where the information on the state of the system is delayed. Such an information structure is encountered, for instance, in high-speed data networks.

The behavior of two policies for scheduling customers with deadlines until the beginning of service onto multiprocessors is studied. Both policies attempt to approximate the performance of the minimum laxity (ML) scheduling policy without incurring its complete overhead by dividing the queue in two: one, of maximum size n>0, managed using the minimum laxity policy, and another, of unbounded size, managed in a first-in-first-out manner. One policy, F/ML(n), places the ML queue at the front, i.e. customers finding n or more in the system enter the first-in-first-out (FIFO) queue which in turn feeds the ML queue. The other policy, ML(n)/F, places the ML queue at the back, i.e. arriving customers enter the ML queue and if the total number in the system exceeds n, forces one customer from the ML queue to the FIFO queue. It is shown that these seemingly dissimilar policies exhibit exactly the same behavior for a fixed value of n both when customers are allowed to be discarded when they miss their deadlines before entering service and when they are not allowed to be discarded. Monotonicity properties are established for both policies.>

The server visits N queues in an arbitrary manner. Each queue is visited for a random period of time whose duration is sampled in advance. At the end of a visit period, either all customers of the attended queue leave the system (variant I) or only customers that were present in the queue upon the arrival of the server leave the system (variant II). A scheduling policy is a rule that selects the next queue to be visited by the server. When the controller has no information on the state of the system, it is shown, under homogeneous arrival assumptions, that a cyclic policy minimizes the expected number of customers in the system. When the controller knows the number of customers in each queue, it is shown that the so-called most-customers-first (MCF) policy minimizes, in the sense of strong stochastic ordering, the vector of the number of customers in each queue whose components are arranged in decreasing order. These results hold for variants I and II and are obtained under fairly weak statistical assumptions. This model has potential applications in videotex and time-division multiple-access systems.>

The commenter points out an error made in the paper by P. Nain et al. (see ibid., vol.36, p.806-15, July 1988) and shows that correcting this error requires a state space that has an exponential size. The authors reply that the errors cannot easily be corrected and that their model provides a good approximation model for HYMAP.>

A hybrid multiple access protocol (HYMAP) was proposed by M. Rios and N.D. Georganas (1985), combining the best features of CSMA/CD and of a conflict-free protocol. Control is transferred from one protocol to the other according to state information sensed on the channel. The performance of HYMAP was evaluated by computer simulation. An exact analysis of this hybrid protocol is presented. Since HYMAP permits free access of new arrivals during collision resolution, the mean length of the conflict-free period is determined by solving a large system of linear equations. The basic mean performance measures (throughput, delay) can then be easily computed and compared to the performance of CSMA/CD.>

Considered are optimal dynamic policies for multiplexing Κ + 1 heterogeneous traffic types onto a single communication channel. The packet types arrive to the channel according to independent Poisson processes. The service requirements are exponential with type dependent means. The optimization criterion is to minimize a linear combination of the average delays for packet types 1 to Κ, while simultaneously subjecting the average delay of type-0 packets to a hard constraint. The optimal multiplexing policy is shown to be a randomized modification of the “μc rule”. The optimization problem is thereby reduced to a problem of finding the optimal randomization factor; an algorithm, which can be implemented in real time, is given to do this for two particular cases.

We define and evaluate two policies (NA-policy, A-policy) for parallel execution of program tree structures. Via a probabilistic model we analytically determine, for each policy, the Laplace-Stieltjes transform for the tree processing time distribution. The acceleration of the program execution time achieved when adding processors to a single processor environment, is computed and plotted for each policy.