[Show abstract][Hide abstract] ABSTRACT: We analyze in this paper the transient behavior of a simplified model for torrents in P2P networks. We consider a large number of peers interested in a file which is initially available at a small fraction of the population. Our model has as parameters the number of interested peers, the rate of arrival of download request, the rate at which peers propose files for upload, the degree of the free riding phenomenon etc. Our goal is to predict the impact of measures against P2P networks on their performance. We provide a Markov model that describes the detailed dynamics of the system. We analyze the model first under the assumption of an infinite population—an approach based on a branching process. This process is shown to provide a bound for the behavior of the system with finite population. We obtain the extinction probabilities for this process as well as approximations to the expected time till extinction. We then study the case of a finite population for which we establish the mean field limit. We show that the limit simplifies to a well studied epidemic model in case of no free riders. The fluid limit allows us to evaluate the behavior of the expected duration of a torrent, the expected number of nodes that eventually receive the file and the maximal availability along with the time at which it is achieved. We finally use these results to evaluate the efficiency of measures against unauthorized file sharing and their impact on file bundling.
[Show abstract][Hide abstract] ABSTRACT: There has been considerable research on the performance analysis of on-demand caching replacement policies like Least-Recently-Used (LRU), First-In-First-Out (FIFO) or Random (RND). Much progress has been made on the analysis of a single cache running these algorithms. However it has been almost impossible to extend the results to networks of caches. In this paper, we introduce a Time-To-Live (TTL) based caching model, that assigns a timer to each content stored in the cache and redraws it every time the content is requested (at each hit/miss). We derive the performance metrics (hit/miss ratio and rate, occupancy) of a TTL-based cache in isolation fed by stationary and ergodic request processes with general TTL distributions. Moreover we propose an iterative procedure to analyze TTL-based cache networks under the assumptions that requests are described by renewal processes (that generalize Poisson processes or the standard IRM assumption). We validate our theoretical findings through event-driven and Monte-Carlo simulations based on the Fourier Amplitude Sensitivity Test to explore the space of the input parameters. We observe that our analytic model predicts remarkably well all metrics of interest with relative errors smaller than 1%1%.
[Show abstract][Hide abstract] ABSTRACT: This paper studies the performance of Peer-to-Peer storage and backup systems (P2PSS). These systems are based on three pillars: data fragmentation and dissemination among the peers, redundancy mechanisms to cope with peers churn and repair mechanisms to recover lost or temporarily unavailable data. Usually, redundancy is achieved either by using replication or by using erasure codes. A new class of network coding (regenerating codes) has been proposed recently. Therefore, we will adapt our work to these three redundancy schemes. We introduce two mechanisms for recovering lost data and evaluate their performance by modeling them through absorbing Markov chains. Specifically, we evaluate the quality of service provided to users in terms of durability and availability of stored data for each recovery mechanism and deduce the impact of its parameters on the system performance. The first mechanism is centralized and based on the use of a single server that can recover multiple losses at once. The second mechanism is distributed: reconstruction of lost fragments is iterated sequentially on many peers until that the required level of redundancy is attained. The key assumptions made in this work, in particular, the assumptions made on the recovery process and peer on-times distribution, are in agreement with the analysis in  and in  respectively. The models are thereby general enough to be applicable to many distributed environments as shown through numerical computations. We find that, in stable environments such as local area or research institute networks where machines are usually highly available, the distributed-repair scheme in erasure-coded systems offers a reliable, scalable and cheap storage/backup solution. For the case of highly dynamic environments, in general, the distributed-repair scheme is inefficient, in particular to maintain high data availability, unless the data redundancy is high. Using regenerating codes overcomes this limitation of the distributed-repair scheme. P2PSS with centralized-repair scheme are efficient in any environment but have the disadvantage of relying on a centralized authority. However, the analysis of the overhead cost (e.g. computation, bandwidth and complexity cost) resulting from the different redundancy schemes with respect to their advantages (e.g. simplicity), is left for future work.
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of estimating the end-to-end latency of intermittently connected paths in disruption/delay tolerant networks. This is useful when performing source routing, in which a complete path is chosen for a packet to travel from source to destination (when intermediate nodes are really low complexity devices that can only forward packets but cannot perform route computations), or in linear network topologies. While computing the time to traverse such a path may be straightforward in fixed, static networks, doing so becomes much more challenging in dynamic networks, in which the state of an edge in one timeslot (i.e., its presence or absence) is random, and may depend on its state in the previous timeslot. The traversal time is due to both time spent waiting for edges to appear and time spent crossing them once they become available. We compute the expected traversal time (ETT) for a dynamic path in a number of special cases of stochastic edge dynamics models, and for three different edge failure models, culminating in a surprisingly nontrivial yet realistic ``hybrid network" setting in which the initial configuration of edge states for the entire path is known. We show that the ETT for this "initial configuration" setting can be computed in quadratic time (as a function of path length), by an algorithm based on probability generating functions. We also give several linear-time upper and lower bounds on the ETT, which we evaluate, along with our ETT algorithm, using numerical simulations.
Proceedings of the 8th ACM MobiCom workshop on Challenged networks; 09/2013
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: In source routing, a complete path is chosen for a packet to travel from
source to destination. While computing the time to traverse such a path
may be straightforward in a fixed, static graph, doing so becomes much
more challenging in dynamic graphs, in which the state of an edge in one
time slot (i.e., its presence or absence) is random, and may depend on
its state in the previous time step. The traversal time is due to both
time spent waiting for edges to appear and time spent crossing them once
they become available. We compute the expected traversal time (ETT) for
a dynamic path in a number of special cases of stochastic edge dynamics
models, and for three edge failure models, culminating in a surprisingly
challenging yet realistic setting in which the initial configuration of
edge states for the entire path is known. We show that the ETT for this
"initial configuration" setting can be computed in quadratic time, by an
algorithm based on probability generating functions. We also give
several linear-time upper and lower bounds on the ETT.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: Two independent Poisson streams of jobs flow into a single-server service
system having a limited common buffer that can hold at most one job. If a
type-i job (i=1,2) finds the server busy, it is blocked and routed to a
separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at
its specific Poisson rate. This creates a system with three dependent queues.
Such a queueing system serves as a model for two competing job streams in a
carrier sensing multiple access system. We study the queueing system using
multi-dimensional probability generating functions, and derive its necessary
and sufficient stability conditions while solving a boundary value problem.
Various performance measures are calculated and numerical results are
Queueing Systems 06/2012; 77(1). DOI:10.1007/s11134-013-9372-8 · 0.60 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Many researchers have been working on the performance analysis of caching in Information-Centric Networks (ICNs) under various replacement policies like Least Recently Used (LRU), FIFO or Random (RND). However, no exact results are provided, and many approximate models do not scale even for the simple network of two caches connected in tandem. In this paper, we introduce a Time-To-Live based policy (TTL), that assigns a timer to each content stored in the cache and redraws the timer each time the content is requested (at each hit/miss). We show that our TTL policy is more general than LRU, FIFO or RND, since it is able to mimic their behavior under an appropriate choice of its parameters. Moreover, the analysis of networks of TTL-based caches appears simpler not only under the Independent Reference Model (IRM, on which many existing results rely) but also with the Renewal Model for requests. In particular, we determine exact formulas for the performance metrics of interest for a linear network and a tree network with one root cache and N leaf caches. For more general networks, we propose an approximate solution with the relative errors smaller than 10-3 and 10-2 for exponentially distributed and constant TTLs respectively.
Performance Evaluation Methodologies and Tools (VALUETOOLS), 2012 6th International Conference on; 03/2012
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: A typical web search engine consists of three principal parts: crawling engine, indexing engine, and searching engine. The present work aims to optimize the performance of the crawling engine. The crawling engine finds new web pages and updates web pages existing in the database of the web search engine. The crawling engine has several robots collecting information from the Internet. We first calculate various performance measures of the system (e.g., probability of arbitrary page loss due to the buffer overflow, probability of starvation of the system, the average time waiting in the buffer). Intuitively, we would like to avoid system starvation and at the same time to minimize the information loss. We formulate the problem as a multi-criteria optimization problem and attributing a weight to each criterion. We solve it in the class of threshold policies. We consider a very general web page arrival process modeled by Batch Marked Markov Arrival Process and a very general service time modeled by Phase-type distribution. The model has been applied to the performance evaluation and optimization of the crawler designed by INRIA Maestro team in the framework of the RIAM INRIA-Canon research project.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: In this paper 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 are likely to be covered at a later time. A
larger area is covered as time continues, 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 characterize the time it takes to detect a randomly
located intruder. For mobile intruders, we take a game theoretic approach and
derive optimal mobility strategies for both sensors and intruders. Our results
show that sensor mobility brings about unique dynamic coverage properties not
present in a stationary sensor network, and that mobility can be exploited to
compensate for the lack of sensors to improve coverage.
IEEE Transactions on Parallel and Distributed Systems 01/2011; abs/1101.0376(2). DOI:10.1109/TPDS.2012.141 · 2.17 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This work investigates distributed transmission scheduling in wireless networks. Due to interference constraints, "neighboring links" cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We follow the model described by Bui, Sanghavi, and Srikant in SBS07,SBS09. We suppose that time is slotted and during each slot we have two phases: one control phase which determines what links will be activated and send data during the second phase. We assume random arrivals on each link during each slot, therefore a queue is associated to each link. Since nodes do not have a global knowledge of the network, our aim (like in SBS07,SBS09) is to design for the control phase, a distributed algorithm which determines a set of non interfering links. To be efficient the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead). In this article we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues); and it needs no knowledge. Indeed contrary to other existing algorithms, we do not need to know the values of the queues of the "neighboring links", which are difficult to obtain in a wireless network with interference. We prove that this algorithm gives a maximal set of active links (in each interference set, there is at least one active edge). We also give sufficient conditions for stability under Markovian assumptions. Finally the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.
[Show abstract][Hide abstract] ABSTRACT: With the introduction of the new generation high speed routers, it becomes possible to improve the Quality of Service, the Quality of Experience for users and the network efficiency for ISPs with the help of "flow-aware" traffic management. An example of the "flow-aware" traffic management is the Alcatel-Lucent framework "Semantic Networking," where short-lived and long-lived TCP flows are treated differently. Short-lived flows are processed with high priority and long-lived flows are controlled in a "flow-aware" fashion. To control efficiently the long-lived flows, one needs to know an estimation of the Round Trip Time (RTT). In the present work, we provide an online RTT estimation algorithm which is passive and can deal with a one-way traffic. The one-way traffic requirement is essential for the application of the algorithm for "flow-aware" traffic management inside the network. To the best of our knowledge, there was no online one-way traffic RTT estimators. Tests on the Internet demonstrate high accuracy of the proposed estimator. The results show that, 75% (resp. 99%) of the time, the RTT estimation is within 10% (resp. 20%) of the RTT at the source.
[Show abstract][Hide abstract] ABSTRACT: The peer-to-peer (P2P) paradigm have emerged as a cheap, scal-able, self-repairing and fault-tolerant storage solution. This solu-tion relies on erasure codes to generate additional redundant frag-ments of each "block of data" in order to increase the reliability and availability and overcome the churn. When the amount of un-reachable fragments attains a predefined threshold, due to perma-nent departures or long disconnections of peers, a recovery process is initiated to compensate the missing fragments, requiring multiple fragments of data of a given "block" to be downloaded in parallel for an enhanced service. Recent modeling efforts that address the availability and the durability of data have assumed the recovery process to follow an exponential distribution, an assumption made mainly in the absence of studies characterizing the "real" distribu-tion of the recovery process. This work aims at filling this gap and better understanding the behavior of these systems through simu-lation while taking into consideration the heterogeneity of peers, the underlying network topologies, the propagation delays and the transport protocol. To that end, the distributed storage protocol is implemented in the NS-2 network simulator. This paper describes a realistic simulation model that captures the behavior of P2P storage systems. We provide some experiments results that show how mod-eling the availability and durability can be impacted by the recovery times distribution which is impacted in turn by the characteristics of the the network and the context.
[Show abstract][Hide abstract] ABSTRACT: Peer-to-peer storage systems rely on data fragmentation and distributed storage. Unreachable fragments are continuously recovered, requiring multiple fragments of data (constituting a ldquoblockrdquo) to be downloaded in parallel. Recent modeling efforts have assumed the recovery process to follow an exponential distribution, an assumption made mainly in the absence of studies characterizing the ldquorealrdquo distribution of the recovery process. This work aims at filling this gap through a simulation study. To that end, we implement the distributed storage protocol in the NS-2 network simulator and run a total of seven experiments covering a large variety of scenarios. We show that the fragment download time follows approximately an exponential distribution. We also show that the block download time and the recovery time essentially follow a hypo-exponential distribution with many distinct phases (maximum of as many exponentials). We use expectation maximization and least square estimation algorithms to fit the empirical distributions. We also provide a good approximation of the number of phases of the hypo-exponential distribution that applies in all scenarios considered. Last, we test the goodness of our fits using statistical (Kolmogorov-Smirnov test) and graphical methods.
[Show abstract][Hide abstract] ABSTRACT: 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.
Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, 2009. WiOPT 2009. 7th International Symposium on; 07/2009
[Show abstract][Hide abstract] ABSTRACT: 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 th-
e 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.
[Show abstract][Hide abstract] ABSTRACT: This report studies the performance of Peer-to-Peer Storage Systems (P2PSS) in terms of data lifetime and availability. Two schemes for recovering lost data are modeled through absorbing Markov chains and their performance are evaluated and compared. The first scheme relies on a centralized controller that can recover multiple losses at once, whereas the second scheme is distributed and recovers one loss at a time. The impact of each system parameter on the performance is evaluated, and guidelines are derived on how to engineer the system and tune its key parameters in order to provide desired lifetime and/or availability of data. We find that, in stable environments such as local area or research laboratory networks where machines are usually highly available, the distributed-repair scheme offers a reliable, scalable and cheap storage/backup solution. This is in contrast with the case of highly dynamic environments, where the distributed-repair scheme is inefficient as long as the storage overhead is kept reasonable. P2PSS with centralized-repair scheme are efficient in any environment but have the disadvantage of relying on a centralized authority. Our analysis also suggests that the use of large size fragments reduces the efficiency of the recovery mechanism.