Luoyi Fu

Recognizing Exponential Inter-Contact Time in VANETs

Inter-contact time between moving vehicles is one of the key metrics in vehicular ad hoc networks (VANETs) and central to forwarding algorithms and the end-to-end delay. Due to prohibitive costs, little work has conducted experimental study on inter-contact time in urban vehicular environments. In this paper, we carry out an extensive experiment involving thousands of operational taxies in Shanghai city. Studying the taxi trace data on the frequency and duration of transfer opportunities between taxies, we observe that the tail distribution of the inter-contact time, that is the time gap separating two contacts of the same pair of taxies, exhibits a light tail such as one of an exponential distribution, over a large range of timescale. This observation is in sharp contrast to recent empirical data studies based on human mobility, in which the distribution of the inter-contact time obeys a power law. By performing a least squares fit, we establish an exponential model that can accurately depict the tail behavior of the inter-contact time in VANETs. Our results thus provide fundamental guidelines on design of new vehicular mobility models in urban scenarios, new data forwarding protocols and their performance analysis.

Impact of Traffic Influxes: Revealing Exponential Intercontact Time in Urban VANETs

Intercontact time between moving vehicles is one of the key metrics in vehicular ad hoc networks (VANETs) and central to forwarding algorithms and the end-to-end delay. Due to prohibitive costs, little work has conducted experimental study on intercontact time in urban vehicular environments. In this paper, we carry out an extensive experiment involving thousands of operational taxies in Shanghai city. Studying the taxi trace data on the frequency and duration of transfer opportunities between taxies, we observe that the tail distribution of the intercontact time, that is, the time gap separating two contacts of the same pair of taxies, exhibits an exponential decay, over a large range of timescale. This observation is in sharp contrast to recent empirical data studies based on human mobility, in which the distribution of the intercontact time obeys a power law. By analyzing a simplified mobility model that captures the effect of hot areas in the city, we rigorously prove that common traffic influxes, where large volume of traffic converges, play a major role in generating the exponential tail of the intercontact time. Our results thus provide fundamental guidelines on design of new vehicular mobility models in urban scenarios, new data forwarding protocols and their performance analysis.

Multicast performance with hierarchical cooperation

It has been shown in a previous version of this paper that hierarchical cooperation achieves a linear throughput scaling for unicast traffic, which is due to the advantage of long-range concurrent transmissions and the technique of distributed multiple-input-multiple-output (MIMO). In this paper, we investigate the scaling law for multicast traffic with hierarchical cooperation, where each of the <i>n</i> nodes communicates with <i>k</i> randomly chosen destination nodes. Specifically, we propose a new class of scheduling policies for multicast traffic. By utilizing the hierarchical cooperative MIMO transmission, our new policies can obtain an aggregate throughput of Ω(( [( <i>n</i>)/( <i>k</i>)])^1-ε) for any ε >; 0. This achieves a gain of nearly √{[( <i>n</i>)/( <i>k</i>)]} compared to the noncooperative scheme in Li s work (Proc. ACM MobiCom, 2007, pp. 266-277). Among all four cooperative strategies proposed in our paper, one is superior in terms of the three performance metrics: throughput, delay, and energy consumption. Two factors contribute to the optimal performance: multihop MIMO transmission and converge-based scheduling. Compared to the single-hop MIMO transmission strategy, the multihop strategy achieves a throughput gain of ( [( <i>n</i>)/( <i>k</i>)])^[(<i>h</i>-1)/( <i>h</i>(2<i>h</i>-1))] and meanwhile reduces the energy consumption by <i>k</i>^{[( α-2)/ 2]} times approximately, where <i>h</i> >; 1 is the number of the hierarchical layers, and α >; 2 is the path-loss exponent. Moreover, to schedule the traffic with the converge multicast instead of the pure multicast strategy, we can dramatically reduce the delay by a factor of about ( [( <i>n</i>)/( <i>k</i>)])^[(<i>h</i>)/ 2]. Our optimal cooperative strategy achieves an approximate delay-throughput tradeoff <i>D</i>(<i>n</i>,<i>k</i>)/<i>T</i>(<i>n</i>,<i>k</i>)=Θ(<i>k</i>) when <i>h</i>→ ∞. This tradeoff ratio is identical to that of noncooperative scheme, while the throughput is greatly improved.

Speed Improves Delay-Capacity Trade-Off in MotionCast

In this paper, we study a unified mobility model for mobile multicast (MotionCast) with n nodes, and k destinations for each multicast session. This model considers nodes which can either serve in a local region or move around globally, with a restricted speed R. In other words, there are two particular forms: Local-based Speed-Restricted Model (LSRM) and Global-based Speed-Restricted Model (GSRM). We find that there is a special turning point when mobility speed varies from zero to the scale of network. For LSRM, as R increases, the delay-capacity trade-off ratio decreases iff R is greater than the turning point θ(√1/k); For GSRM, as R increases, the trade-off ratio decreases R R is smaller than the turning point, where the turning point is located at Θ(k√nn25) when k = o(n2/3), and at θ(k/n) when k = ω(n2/3). As k increases from 1 ton -1, the region that mobility can improve delay-capacity trade-off is enlarged. When R = θ(1), the optimal delay-capacity trade-off ratio is achieved. This paper presents a general approach to study the performance of wireless networks under more flexible mobility models.

Asymptotic Analysis on Secrecy Capacity in Large-Scale Wireless Networks

Since wireless channel is vulnerable to eavesdroppers, the secrecy during message delivery is a major concern in many applications such as commercial, governmental, and military networks. This paper investigates information-theoretic secrecy in large-scale networks and studies how capacity is affected by the secrecy constraint where the locations and channel state information (CSI) of eavesdroppers are both unknown. We consider two scenarios: 1) noncolluding case where eavesdroppers can only decode messages individually; and 2) colluding case where eavesdroppers can collude to decode a message. For the noncolluding case, we show that the network secrecy capacity is not affected in order-sense by the presence of eavesdroppers. For the colluding case, the per-node secrecy capacity of Θ([1/(√n)]) can be achieved when the eavesdropper density ψe(n) is O(n-β), for any constant β > 0 and decreases monotonously as the density of eavesdroppers increases. The upper bounds on network secrecy capacity are derived for both cases and shown to be achievable by our scheme when ψe(n)=O(n-β) or ψe(n)=Ω(log[(α-2)/(α)]n), where α is the path-loss gain. We show that there is a clear tradeoff between the security constraints and the achievable capacity. Furthermore, we also investigate the impact of secrecy constraint on the capacity of dense network, the impact of active attacks and other traffic patterns, as well as mobility models in the context.

Converge Cast: On the Capacity and Delay Tradeoffs

In this paper, we define an ad hoc network where multiple sources transmit packets to one destination as Converge-Cast network. We will study the capacity delay tradeoffs assuming that n wireless nodes are deployed in a unit square. For each session (the session is a dataflow from k different source nodes to 1 destination node), k nodes are randomly selected as active sources and each transmits one packet to a particular destination node, which is also randomly selected. We first consider the stationary case, where capacity is mainly discussed and delay is entirely dependent on the average number of hops. We find that the per-node capacity is Θ (1/√(n log n)) (given nonnegative functions f(n) and g(n): f(n) = O(g(n)) means there exist positive constants c and m such that f(n) ≤ cg(n) for all n ≥ m; f(n)= Ω (g(n)) means there exist positive constants c and m such that f(n) ≥ cg(n) for all n ≥ m; f(n) = Θ (g(n)) means that both f(n) = Ω (g(n)) and f(n) = O(g(n)) hold), which is the same as that of unicast, presented in (Gupta and Kumar, 2000). Then, node mobility is introduced to increase network capacity, for which our study is performed in two steps. The first step is to establish the delay in single-session transmission. We find that the delay is Θ (n log k) under 1-hop strategy, and Θ (n log k/m) under 2-hop redundant strategy, where m denotes the number of replicas for each packet. The second step is to find delay and capacity in multisession transmission. We reveal that the per-node capacity and delay for 2-hop nonredundancy strategy are Θ (1) and Θ (n log k), respectively. The optimal delay is Θ (√(n log k)+k) with redundancy, corresponding to a capacity of Θ (√((1/n log k) + (k/n log k)). Therefore, we obtain that the capacity delay tradeoff satisfies delay/rate ≥ Θ (n log k) for both strategies.

Throughput and Delay Analysis for Convergecast with MIMO in Wireless Networks

This paper investigates throughput and delay based on a traffic pattern, called convergecast, where each of the n nodes in the network acts as a destination with k randomly chosen sources corresponding to it. Adopting Multiple-Input-Multiple-Output (MIMO) technology, we devise two many-to-one cooperative schemes under convergecast for both static and mobile ad hoc networks (MANETs), respectively. We call them Convergimo Schemes. In static networks, our Convergimo scheme highly utilizes hierarchical cooperation MIMO transmission. This feature overcomes the bottleneck which hinders convergecast traffic from yielding ideal performance in traditional ad hoc network, by turning the originally interfering signals into interference-resistant ones. It helps to achieve an aggregate throughput up to Ω(n1-ϵ) for any ϵ >;0. In the mobile ad hoc case, our Convergimo scheme characterizes on joint transmission from multiple nodes to multiple receivers. With optimal network division where the number of nodes per cell is constantly bounded, the achievable per-node throughput can reach Θ(1) with the corresponding delay reduced to Θ(k). The gain comes from the strong and intelligent cooperation between nodes in our scheme, along with the maximum number of concurrent active cells and the shortest waiting time before transmission for each node within a cell. This increases the chances for each destination to receive the data it needs with minimum overhead on extra transmission. Moreover, our converge-based analysis well unifies and generalizes previous work since the results derived from convergecast in our schemes can also cover other traffic patterns. Last but not the least, our schemes are of interest not only from a theoretical perspective but also provide useful theoretical guidelines to future design of MIMO schemes in wireless networks.

Percolation Degree of Secondary Users in Cognitive Networks

A cognitive network refers to the one where two overlaid structures, called primary and secondary networks coexist. The primary network consists of primary nodes who are licensed spectrum users while the secondary network comprises unauthorized users that have to access the licensed spectrum opportunistically. In this paper, we study the percolation degree of the secondary network to achieve k-percolation in large scale cognitive radio networks. The percolation degree is defined as the number of nearest neighbors for each secondary user when there are at least k vertex-disjoint paths existing between any two secondary relays in the percolated cluster. The percolated cluster is formed when there are an infinite number of mutually connected secondary users spanning the whole network. Each user in the cluster is possibly connected to several neighbors, inducing more communication links between any two of them. Since nodes located near the boundary have fewer neighbors, the boundary effect becomes a bottleneck in determining the percolation degree. For cognitive networks, when the primary node density becomes considerably large, the boundary effect spreads inside the network. The transmission area of most secondary users who are located near the primary nodes decreases due to the restriction of the primary network. Therefore, to ensure k-connectivity in the percolated cluster, each secondary user must be connected to more neighbors, and the percolation degree of the secondary network yields a function of the primary node density. We specify the relationship into three regimes regarding the topology variation of the cognitive network. A closed-form expression of the percolation degree under different primary node densities is presented. The expression characterizes the connectivity strength in the secondary percolated cluster, therefore providing analytical insight on fault tolerance improvement in cognitive networks.

Converge-cast with MIMO

This paper investigates throughput and delay based on a newly predominant traffic pattern, called converge-cast, where each of the n nodes in the network act as a destination with k randomly chosen sources corresponding to it. Adopting Multiple-Input-Multiple-Output (MIMO) technology, we devise two many-to-one cooperative schemes under converge-cast for both static and mobile ad hoc networks (MANETs), respectively. In a static network, our scheme highly utilizes hierarchical cooperation MIMO transmission. This feature overcomes the bottleneck which hinders converge-cast traffic from yielding ideal performance in traditional ad hoc network, by turning the originally interfering signals into interference-resistant ones. It helps to achieve an aggregate throughput up to Ω(n1−ε) for any ε > 0. In the mobile ad hoc case, our scheme characterizes on joint transmission from multiple nodes to multiple receivers. With optimal network division where the number of nodes per cell is constant bounded, the achievable per-node throughput can reach Θ(1) with the corresponding delay reduced to Θ(k). The gain comes from the strong and intelligent cooperation between nodes in our scheme, along with the maximum number of concurrent active cells and the shortest waiting time before transmission for each node within a cell. This, to a great extent, increases the chances for each destination to receive the data it needs with minimum overhead on extra transmission. Moreover, our converge-based analysis well unifies and generalizes previous work since the results derived from converge-cast in our schemes can also cover other traffic patterns. Last but not least, our cooperative schemes are of interest not only from a theoretical perspective but also shed light on future design of MIMO schemes in wireless networks.

Distributed Multicast Tree Construction in Wireless Sensor Networks

Multicast tree is a key structure for data dissemination from one source to multiple receivers in wireless networks. Minimum length multica modeled as the Steiner tree problem, and is proven to be NP-hard. In this paper, we explore how to efficiently generate minimum length multi wireless sensor networks (WSNs), where only limited knowledge of network topology is available at each node. We design and analyze a simple algorithm, which we call toward source tree (TST), to build multicast trees in WSNs. We show three metrics of TST algorithm, i.e., running and energy efficiency. We prove that its running time is