J. Mammen

Throughput-delay trade-off in wireless networks

Gupta and Kumar (2000) introduced a random network model for studying the way throughput scales in a wireless network when the nodes are fixed, and showed that the throughput per source-destination pair is /spl otimes/(1//spl radic/nlogn). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant or /spl otimes/(1) throughput scaling per source-destination pair. The focus of this paper is on characterizing the delay and determining the throughput-delay trade-off in such fixed and mobile ad hoc networks. For the Gupta-Kumar fixed network model, we show that the optimal throughput-delay trade-off is given by D(n) = /spl otimes/(nT(n)), where T(n) and D(n) are the throughput and delay respectively. For the Grossglauser-Tse mobile network model, we show that the delay scales as /spl otimes/(n/sup 1/2//v(n)), where v(n) is the velocity of the mobile nodes. We then describe a scheme that achieves the optimal order of delay for any given throughput. The scheme varies (i) the number of hops, (ii) the transmission range and (iii) the degree of node mobility to achieve the optimal throughput-delay trade-off. The scheme produces a range of models that capture the Gupta-Kumar model at one extreme and the Grossglauser-Tse model at the other. In the course of our work, we recover previous results of Gupta and Kumar, and Grossglauser and Tse using simpler techniques, which might be of a separate interest.

Optimal throughput-delay scaling in wireless networks: part I: the fluid model

Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per source-destination pair is Theta(1/radic(nlogn)). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per source-destination pair. In most applications, delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughput-delay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughput-delay tradeoff is given by D(n)=Theta(nT(n)), where T(n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of Theta(1) for the Grossglauser-Tse scheme is given and the associated delay scaling is shown to be Theta(nlogn). The optimal throughput-delay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random-walk (RW) model for node mobility is assumed. It is shown that for throughput of Oscr(1/radic(nlogn)), which can also be achieved in static networks, the throughput-delay tradeoff is the same as in static networks, i.e., D(n)=Theta(nT(n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be Theta(nlogn), which is the delay for throughput of Theta(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in real-world networks would necessitate an abrupt and very large increase in delay.

Throughput and Delay in Random Wireless Networks With Restricted Mobility

Grossglauser and Tse (2001) introduced a mobile random network model where each node moves independently on a unit disk according to a stationary uniform distribution and showed that a throughput of Theta(1) is achievable. El Gamal, Mammen, Prabhakar, and Shah (2004) showed that the delay associated with this throughput scales as Theta(nlogn), when each node moves according to an independent random walk. In a later work, Diggavi, Grossglauser, and Tse (2002) considered a random network on a sphere with a restricted mobility model, where each node moves along a randomly chosen great circle on the unit sphere. They showed that even with this one-dimensional restriction on mobility, constant throughput scaling is achievable. Thus, this particular mobility restriction does not affect the throughput scaling. This raises the question whether this mobility restriction affects the delay scaling. This correspondence studies the delay scaling at Theta(1) throughput for a random network with restricted mobility. First, a variant of the scheme presented by Diggavi, Grossglauser, and Tse (2002) is presented and it is shown to achieve Theta(1) throughput using different (and perhaps simpler) techniques. The exact order of delay scaling for this scheme is determined, somewhat surprisingly, to be of Theta(nlogn), which is the same as that without the mobility restriction. Thus, this particular mobility restriction does not affect either the maximal throughput scaling or the corresponding delay scaling of the network. This happens because under this 1-D restriction, each node is in the proximity of every other node in essentially the same manner as without this restriction

Relay Networks With Delays

The paper investigates the effect of link delays on the capacity of relay networks. The relay-with-delay is defined as a relay channel with relay encoding delay d isin Z of units, or equivalently, a delay of units on the link from the sender to the relay, zero delay on the links from the transmitter to the receiver and from the relay to the receiver, and zero relay encoding delay. Two special cases are studied. The first is the relay-with-unlimited look-ahead, where each relay transmission can depend on its entire received sequence, and the second is the relay-without-delay, where the relay transmission can depend only on current and past received symbols, i.e., d=0. Upper and lower bounds on capacity for these two channels that are tight in some cases are presented. It is shown that the cut-set bound for the classical relay channel, corresponding to the case where d=1, does not hold for the relay-without-delay. Further, it is shown that instantaneous relaying can be optimal and can achieve higher rates than the classical cut-set bound. Capacity for the classes of degraded and semi-deterministic relay-with-unlimited-look-ahead and relay-without-delay are established. These results are then extended to the additive white Gaussian noise (AWGN) relay-with-delay case, where it is shown that for any dles0, capacity is achieved using amplify-and-forward when the channel from the sender to the relay is sufficiently weaker than the other two channels. In addition, it is shown that a superposition of amplify-and-forward and decode-and-forward can achieve higher rates than the classical cut-set bound. The relay-with-delay model is then extended to feedforward relay networks. It is shown that capacity is determined only by the relative delays of paths from the sender to the receiver and not by their absolute delays. A new cut-set upper bound that generalizes both the classical cut-set bound for the classical relay and the upper bound for the relay-without-delay on capacity is established.

The Simplest Solution to an Underdetermined System of Linear Equations

Consider a d times n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has infinitely many solutions (if there are any). Given y, the minimum Kolmogorov complexity solution (MKCS) of the input x is defined to be an input z (out of many) with minimum Kolmogorov-complexity that satisfies y = Az. One expects that if the actual input is simple enough, then MKCS will recover the input exactly. This paper presents a preliminary study of the existence and value of the complexity level up to which such a complexity-based recovery is possible. It is shown that for the set of all d times n binary matrices (with entries 0 or 1 and d < n), MKCS exactly recovers the input for an overwhelming fraction of the matrices provided the Kolmogorov complexity of the input is O(d). A weak converse that is loose by a log n factor is also established for this case. Finally, we investigate the difficulty of finding a matrix that has the property of recovering inputs with complexity of O(d) using MKCS

Optimal Hopping in Ad Hoc Wireless Networks

Gupta and Kumar showed that throughput in a static random wireless network increases with the amount of hopping. In a subsequent paper (2004), it was shown that although throughput benefits from a large number of hops, this comes at the expense of higher delay. Separately, several studies have shown that in ad hoc networks, transmission energy decreases as hopping increases. However, when transceiver circuit energy is also taken into account, hopping as much as possible no longer maximizes energy efficiency and the optimal amount of hopping depends on the topology and size of the network. This paper attempts to unify these earlier results by estab- lishing the optimal hopping for energy efficiency along with throughput and delay. A random network model with n nodes in area A(n) is considered. The effect of interference is captured by the Physical model and the signal is assumed to decay with distance r as r �δ ,δ> 1. Both transmission and transceiver circuit energy are taken into account. Optimal trade-offs between throughput, delay and energy-per-bit scaling for this random network model are established. These results show that the amount of hopping still determines the optimal trade-off and yield the amount of hopping that should be used to achieve any point of the optimal trade-off. In a constant area network, where A(n )=1 , Θ(1) hops result in the best energy and delay scaling

Simultaneous Tracking of Both Hands by Estimation of Erroneous Observations.

Thearticulate motionof thehandmakesit very difficult to track thehands while performing a gesture.Simultaneoustrackingof both hands needsto dealwith largeinterframevariationsin shape,clutterandmutual occlusion. In this paper , we presenta robustmethodfor localizing thehandregion by tracking even in the presence of severe occlusion.We develop a model for tracking two rectangularwindows,eachboundingoneof thehands,usingthe condensationalgorithm. We proposea new methodfor dealingwith occlusionsby estimatingtheoccludedobservations in termsof thenon-occluded obser vationsandtheirpredictedvalues,yielding very reliableresults.

Throughput-delay trade-off in energy constrained wireless networks

The random network model assumed in this paper is a generalization of the model that incorporates transmission energy consumption. The throughput, delay and energy-per-bit for a communication scheme are related through the schemes average transmission range, i.e., average hop distance is considered. For mobile networks, the same model with additional feature that each node moves with velocity according to an independent Brownian motion is considered.

Throughput and delay in random wireless networks: 1-D mobility is just as good as 2-D

In this paper, we study the delay scaling for a mobile network with 1-D mobility restriction and show, that the delay scales as /spl Theta/(/spl radic/n/v(n)). Thus, this particular mobility restriction does not affect the throughput or the delay performance of the network.

Hierarchical recognition of dynamic hand gestures for telerobotic application

In this paper a scheme is presented for recognizing hand gestures using the output of a hand tracker which tracks a rectangular window bounding the hand region. A hierarchical scheme for dynamic hand gesture recognition is proposed based on the dominant feature trajectories using an a priori knowledge of the way in which each gesture is performed. A state representation is obtained from the dominant feature trajectories, where the states correspond to perceptually important segments of hand movement characterizing the gesture.