A geometrically random network of sensors is obtained by modeling sensors as random points in the unit disc equipped with a local sensing capability and the ability to communicate with other sensors in their vicinity. Node extinctions in the network representing the finite battery lifetimes of the sensors are modeled as a sequence of independent random variables governed by a common probability distribution parametrized by the sensing and communication radii of the sensor nodes. Following its establishment, the devolution of the network with time is characterized by the appearance first of isolated nodes, then the growth of sensory lacunae or dead spots in the sensor field, and, eventually, a breakdown in connectivity between survivors. It is shown that these phenomena occur very sharply in time, these phase transitions occurring at times characteristic of the underlying probability law governing lifetimes. More precisely, it is shown that as the number of sensors grows there exists a critical point in time determined solely by the lifetime distribution at which the number of emergent lacunae of a given size is asymptotically Poisson

In this paper we model the channel access delay experienced by a message in a wireless ad-hoc network and study the effect of network parameters on the channel access delay. We first derive a simple model to study the channel access delay for ad-hoc networks. We then show that the channel access delay experienced is a function of four network parameters: 1) channel access probability, 2) transmission power or radius, 3) network load and 4) density of nodes. We study the effect of each of these parameters on the delay and show that delay guarantees in wireless networks require careful choice of the network parameters.

The inefficiency of a TCP connection in the presence of high bandwidth links due to the constant multiplicative decrease factor has been well documented in recent literature. In this paper we look at the effect of fiber error rates on the throughput of a TCP connection. We propose a congestion controller that removes the ill-effects of fiber error rates on TCP throughput by lower bounding the marking probability. We show that this congestion controller can achieve extremely high utilizations in high bandwidth links. We also discuss the TCP friendliness of this congestion controller and present simulation results that validate our analysis.

As batteries fail in wireless sensor networks there is an inevitable devolution of the network characterised by a breakdown in connectivity between the surviving nodes of the network. A sharp limit theorem characterising the time at which this phenomena makes an appearance is derived.

Virtual queue-based marking schemes have been recently proposed for Active Queue Management (AQM) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: its stability in the presence of feedback delays, its ability to maintain small queue lengths, and its robustness in the presence of extremely short flows (the so-called web mice). Using a linearized model of the system dynamics, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several well-known AQM schemes such as RED, REM, Proportional Integral (PI) controller, and a nonadaptive virtual queue algorithm. With a view toward implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code.

In this paper we describe a simple scheme that uses feedback from underutilized high capacity links to allow a TCP connection to aggressively increase its sending rate. The feedback is in the form of a single bit in the packet header and is given per packet. The scheme uses aggregate information to provide feedback and does not require the routers to maintain per flow state. We show through simulations that such a scheme allow TCP connections to efficiently utilize high capacity links without increasing the implementation complexity at the routers.

We present a framework for designing end-to-end congestion control schemes in a network where each user may have a different utility function and may experience noncongestion-related losses. We first show that there exists an additive-increase-multiplicative-decrease scheme using only end-to-end measurable losses such that a socially optimal solution can be reached. We incorporate round-trip delay in this model, and show that one can generalize observations regarding TCP-type congestion avoidance to more general window flow control schemes. We then consider explicit congestion notification (ECN) as an alternate mechanism (instead of losses) for signaling congestion and show that ECN marking levels can be designed to nearly eliminate losses in the network by choosing the marking level independently for each node in the network. While the ECN marking level at each node may depend on the number of flows through the node, the appropriate marking level can be estimated using only aggregate flow measurements, i.e., per-flow measurements are not required.

Fair resource allocation in high-speed networks such as the Internet can be viewed as a constrained optimization program. Kelly and his co-workers have shown that an unconstrained penalty function formulation of this problem can be used to design congestion controllers that are stable. In this paper, we examine the question of providing feedback from the network such that the congestion controllers derived from the penalty function formulation lead to the solution of the original unconstrained problem. This can be viewed as the decentralized design of early congestion notification (ECN) marking rates at each node in the Internet to ensure global loss-free operation of a fluid model of the network. We then look at the stability of such a scheme using a time-scale decomposition of the system. This results in two separate systems which are stable individually and we show that under certain assumptions the entire system is semi-globally stable and converges to the equilibrium point exponentially fast.

Virtual Queue-based marking schemes have been recently proposed for AQM (Active Queue Management) in Internet routers. We consider a particular scheme, which we call the Adaptive Virtual Queue (AVQ), and study its following properties: stability in the presence of feedback delays, its ability to maintain small queue lengths and its robustness in the presence of extremely short flows (the so-called web mice). Using a mathematical tool motivated by the earlier work of Hollot et al, we present a simple rule to design the parameters of the AVQ algorithm. We then compare its performance through simulation with several well-known AQM schemes such as RED, REM, PI controller and a non-adaptive virtual queue algorithm. With a view towards implementation, we show that AVQ can be implemented as a simple token bucket using only a few lines of code.

Fair resource allocation in high-speed networks such as the Internet can be viewed as a constrained convex program. Kelly, Maulloo and Tan (see Journal of the Operational Research Society, vol.49, p.237-52, 1998) have shown that an unconstrained penalty function formulation of this problem can be used to design congestion controllers that are stable. We examine the question of providing feedback from the network such that the congestion controllers derived from the penalty function formulation lead to the solution of the original unconstrained problem. This can be viewed as the decentralized design of early congestion notification (ECN) marking rates at each node in the Internet to ensure global loss-free, socially-optimal operation of a fluid model of the network.

We present a framework for designing end-to-end congestion control schemes in a network where each user may have a different utility function. We first show that there exists an additive increase-multiplicative decrease scheme using only end-to-end measurable losses such that a socially-optimal solution can be reached. We incorporate non-congestion-related random losses and round-trip delay in this model, and show that one can generalize observations regarding TCP-type congestion avoidance to more general window flow control schemes. We then consider explicit congestion notification (ECN) as an alternate mechanism (instead of losses) for signaling congestion and show that ECN marking levels can be designed to nearly eliminate losses in the network by choosing the marking level independently for each node in the network. While the ECN marking level at each node may depend on the number of flows through the node, the appropriate marking level can be estimated using only aggregate flow measurements, i.e., per-flow measurements are not required.