Do Young Eun

Crossing over the bounded domain: from exponential to power-law inter-meeting time in MANET

Inter-meeting time between mobile nodes is one of the key metrics in a Mobile Ad-hoc Network (MANET) and central to the end-to-end delay and forwarding algorithms. It is typically assumed to be exponentially distributed in many performance studies of MANET or numerically shown to be exponentially distributed under most existing mobility models in the literature. However, recent empirical results show otherwise: the inter-meeting time distribution in fact follows a power-law. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the exponential distribution ofthe inter-meeting time, and thus calls for further study on the power-law inter-meeting time including its fundamental cause, mobility modeling, and its effect. In this paper, we rigorously prove that a finite domain, on which most of the current mobility models are defined, plays an important role in creating the exponential tail of the inter-meeting time. We also prove that by simply removing the boundary in a simple two-dimensional isotropic random walk model, we are able to obtain the empirically observed power-law decay of the inter-meeting time. We then discuss the relationship between the size of the boundary and the relevant time scale of the network scenario under consideration. Our results thus provide guidelines on the design of new mobility models with power-law inter-meeting time distribution, new protocols including packet forwarding algorithms, as well as their performance analysis.

Crossing over the bounded domain: from exponential to power-law intermeeting time in mobile ad hoc networks

Intermeeting time between mobile nodes is one of the key metrics in a mobile ad hoc network (MANET) and central to the end-to-end delay of forwarding algorithms. It is typically assumed to be exponentially distributed in many performance studies of MANET or numerically shown to be exponentially distributed under most existing mobility models in the literature. However, recent empirical results show otherwise: The intermeeting time distribution, in fact, follows a power-law. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the exponential distribution of the intermeeting time and, thus, calls for further study on the power-law intermeeting time including its fundamental cause, mobility modeling, and its effect. In this paper, we rigorously prove that a finite domain, on which most of the current mobility models are defined, plays an important role in creating the exponential tail of the intermeeting time. We also prove that by simply removing the boundary in a simple two-dimensional isotropic random walk model, we are able to obtain the empirically observed power-law decay of the intermeeting time. We then discuss the relationship between the size of the boundary and the relevant timescale of the network scenario under consideration. Our results thus provide guidelines on the mobility modeling with power-law intermeeting time distribution, new protocols including packet-forwarding algorithms, as well as their performance analysis.

Multicast Scheduling in Cellular Data Networks

Multicast is an efficient means of transmitting the same content to multiple receivers while minimizing network resource usage. Applications that can benefit from multicast such as multimedia streaming and download, are now being deployed over 3G wireless data networks. Existing multicast schemes transmit data at a fixed rate that can accommodate the farthest located users in a cell. However, users belonging to the same multicast group can have widely different channel conditions. Thus existing schemes are too conservative by limiting the throughput of users close to the base station. We propose two proportional fair multicast scheduling algorithms that can adapt to dynamic channel states in cellular data networks that use time division multiplexing: Inter-group Proportional Fairness (IPF) and multicast proportional fairness (MPF). These scheduling algorithms take into account (1) reported data rate requests from users which dynamically change to match their link states to the base station, and (2) the average received throughput of each user inside its cell. This information is used by the base station to select an appropriate data rate for each group. We prove that IPF and MPF achieve proportional fairness among groups and among all users in a group inside a cell respectively. Through extensive packet-level simulations, we demonstrate that these algorithms achieve good balance between throughput and fairness among users and groups.

Beyond random walk and metropolis-hastings samplers: why you should not backtrack for unbiased graph sampling

Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random walk with re-weighting (SRW-rw) and Metropolis-Hastings (MH) algorithm have been popular in the literature for such unbiased graph sampling. However, an unavoidable downside of their core random walks -- slow diffusion over the space, can cause poor estimation accuracy. In this paper, we propose non-backtracking random walk with re-weighting (NBRW-rw) and MH algorithm with delayed acceptance (MHDA) which are theoretically guaranteed to achieve, at almost no additional cost, not only unbiased graph sampling but also higher efficiency (smaller asymptotic variance of the resulting unbiased estimators) than the SRW-rw and the MH algorithm, respectively. In particular, a remarkable feature of the MHDA is its applicability for any non-uniform node sampling like the MH algorithm, but ensuring better sampling efficiency than the MH algorithm. We also provide simulation results to confirm our theoretical findings.

A measurement-analytic approach for QoS estimation in a network based on the dominant time scale

In this paper, we describe a measurement-analytic approach for estimating the overflow probability, an important measure of the quality of service (QoS), at a given multiplexing point in the network. A multiplexing point in the network could be a multiplexer or an output port of a switch or router where resources such as bandwidth and buffers are shared. Our approach impinges on using the notion of the dominant time scale (DTS), which corresponds to the most probable time scale over which overflow occurs. The DTS provides us with a measurement window for the statistics of the traffic, but is in fact itself defined in terms of the statistics of the traffic over all time. This, in essence, results in a chicken-and-egg type of unresolved problem. For the DTS to be useful for on-line measurements, we need to be able to break this chicken-and-egg cycle, and to estimate the DTS with only a bounded window of time over which the statistics of the traffic are to be measured. In this paper, we present a stopping criterion to successfully break this cycle and find a bound on the DTS. Thus, the result has significant implications for network measurements. Our approach is quite different from other works in the literature that require off-line measurements of the entire trace of the traffic. In our case, we need to measure only the statistics of the traffic up to a bound on the DTS. We also investigate the characteristics of this upper bound on the DTS, and provide numerical results to illustrate the utility of our measurement analytic approach.

Multicast scheduling in cellular data networks

Multicast is an efficient means of transmitting the same content to multiple receivers while minimizing network resource usage. Applications that can benefit from multicast such as multimedia streaming and download, are now being deployed over 3G wireless data networks. Existing multicast schemes transmit data at a fixed rate that can accommodate the farthest located users in a cell. However, users belonging to the same multicast group can have widely different channel conditions. Thus existing schemes are too conservative by limiting the throughput of users close to the base station. We propose two proportional fair multicast scheduling algorithms that can adapt to dynamic channel states in cellular data networks that use time division multiplexing: inter-group proportional fairness (IPF) and multicast proportional fairness (MPF). These scheduling algorithms take into account (1) reported data rate requests from users which dynamically change to match their link states to the base station, and (2) the average received throughput of each user inside its cell. This information is used by the base station to select an appropriate data rate for each group. We prove that IPF and MPF achieve proportional fairness among groups and among all users inside a cell respectively. Through extensive packet-level simulations, we demonstrate that these algorithms achieve good balance between throughput and fairness among users and groups.

Superdiffusive Behavior of Mobile Nodes and Its Impact on Routing Protocol Performance

Mobility is the most important component in mobile ad hoc networks (MANETs) and delay-tolerant networks (DTNs). In this paper, we first investigate numerous GPS mobility traces of human mobile nodes and observe superdiffusive behavior in all GPS traces, which is characterized by a ¿faster-than-linear¿ growth rate of the mean square displacement (MSD) of a mobile node. We then investigate a large amount of access point (AP) based traces, and develop a theoretical framework built upon continuous time random walk (CTRW) formalism, in which one can identify the degree of diffusive behavior of mobile nodes even under possibly heavy-tailed pause time distribution, as in the case of reality. We study existing synthetic models and trace-based models in terms of the capability of producing various degrees of diffusive behavior, and use a set of Levy walk models due to its simplicity and flexibility. In addition, we show that diffusive properties make a huge impact on contact-based metrics and the performance of routing protocols in various scenarios, and that existing models such as random waypoint, random direction model, or Brownian motion lead to overly optimistic or pessimistic results when diffusive properties are not properly captured. Our work in this paper, thus, suggests that the diffusive behavior of mobile nodes should be correctly captured and taken into account for the design and comparison study of network protocols.

Aging rules: what does the past tell about the future in mobile ad-hoc networks?

The study in mobile ad-hoc networks (MANET) is facing challenges brought by recent discovery of non-exponential behavior of the inter-contact time distribution of mobile nodes. In this paper, we analyze various characteristics of the relative mobility of a random pair of nodes in MANET to show that they produce inter-contact time with different aging properties. First, by fixing one node and resorting to the random walks on directed graphs, we mathematically prove that under four classes of stochastic mobility patterns, the resulting inter-contact times have constant/decreasing/increasing failure rate and new-better-than-used property. Then, we consider the case when both nodes are mobile and use simulation results to uncover the aging property of their inter-contact times under random waypoint models and random walk mobility models. This aging property tells us how to correctly relate the past experience of mobile nodes with their future behavior, thereby allowing tremendous opportunities brought by the memory structure in the non-exponential inter contact time, which would be impossible under the widely assumed exponentially distributed (memoryless) inter-contact time. As an application of our results, we establish for the first time that the approach based on exponential inter-contact time assumption can either under-estimate or over-estimate the actual system performance, under different stochastic mobility patterns indexed by their aging properties. Our results on aging properties also provide theoretic guidelines on how to exploit the memory structure toward better design of protocols under general mobility.

Optimal CSMA: A survey

Carrier Sense Multiple Access (CSMA) has been widely used as a medium access control (MAC) scheme in wireless networks mainly due to its simple and totally distributed operations. Recently, it has been reported in the community that even such simple CSMA-type algorithms can achieve optimality in terms of throughput and utility, by smartly controlling its operational parameters such as backoff and holding times. In this survey paper, we summarize the recent research efforts in this area with main focus on the key intuitions and rationales, and conclude by presenting some open problems.

Network decomposition: theory and practice

We show that significant simplicities can be obtained for the analysis of a network when link capacities are large enough to carry many flows. We develop a network decomposition approach in which network analysis can be greatly simplified. We prove that the queue length at the downstream queue converges to that of a single queue obtained by removing the upstream queue, as the capacity and the number of flows at the upstream queue increase. The precise modes of convergence vary depending on the type of input traffic, i.e., from regulated traffic arrivals to point process inputs. Our results thus help simplify network analysis by decomposing the original network into a simplified network in which all the nodes with large capacity have been eliminated. By means of extensive numerical investigation under various network scenarios, we demonstrate different aspects and implications of our network decomposition approach. Some of our findings are that our techniques perform well especially for the cases when: i) many flows are multiplexed as they enter the queue and/or ii) departing flows are routed to different downstream nodes, i.e., no single flow dominates at any node.