Showing papers by "Ravi R. Mazumdar published in 2005"

A minimum cost heterogeneous sensor network with a lifetime constraint

Abstract: We consider a heterogeneous sensor network in which nodes are to be deployed over a unit area for the purpose of surveillance. An aircraft visits the area periodically and gathers data about the activity in the area from the sensor nodes. There are two types of nodes that are distributed over the area using two-dimensional homogeneous Poisson point processes; type 0 nodes with intensity (average number per unit area) /spl lambda//sub 0/ and battery energy E/sub 0/; and type 1 nodes with intensity /spl lambda//sub 1/ and battery energy E/sub 1/. Type 0 nodes do the sensing while type 1 nodes act as the cluster heads besides doing the sensing. Nodes use multihopping to communicate with their closest cluster heads. We determine them optimum node intensities (/spl lambda//sub 0/, /spl lambda//sub 1/) and node energies (E/sub 0/, E/sub 1/) that guarantee a lifetime of at least T units, while ensuring connectivity and coverage of the surveillance area with a high probability. We minimize the overall cost of the network under these constraints. Lifetime is defined as the number of successful data gathering trips (or cycles) that are possible until connectivity and/or coverage are lost. Conditions for a sharp cutoff are also taken into account, i.e., we ensure that almost all the nodes run out of energy at about the same time so that there is very little energy waste due to residual energy. We compare the results for random deployment with those of a grid deployment in which nodes are placed deterministically along grid points. We observe that in both cases /spl lambda//sub 1/ scales approximately as /spl radic/(/spl lambda//sub 0/). Our results can be directly extended to take into account unreliable nodes.

Non-convex optimization and rate control for multi-class services in the Internet

Abstract: In this paper, we investigate the problem of distributively allocating transmission data rates to users in the Internet. We allow users to have concave as well as sigmoidal utility functions as appropriate for different applications. In the literature, for simplicity, most works have dealt only with the concave utility function. However, we show that applying rate control algorithms developed for concave utility functions in a more realistic setting (with both concave and sigmoidal types of utility functions) could lead to instability and high network congestion. We show that a pricing-based mechanism that solves the dual formulation can be developed based on the theory of subdifferentials with the property that the prices "self-regulate" the users to access the resources based on the net utility. We discuss convergence issues and show that an algorithm can be developed that is efficient in the sense of achieving the global optimum when there are many users.

Downlink power allocation for multi-class wireless systems

Abstract: In this paper we consider a power allocation problem in multi-class wireless systems. We focus on the downlink of the system. Each mobile has a utility function that characterizes its degree of satisfaction for the received service. The objective is to obtain a power allocation that maximizes the total system utility. Typically, natural utility functions for each mobile are nonconcave. Hence, we cannot use existing convex optimization techniques to derive a global optimal solution. We develop a simple (distributed) algorithm to obtain a power allocation that is asymptotically optimal in the number of mobiles. The algorithm is based on dynamic pricing and consists of two stages. At the mobile selection stage, the base station selects mobiles to which power is allocated. At the power allocation stage, the base station allocates power to the selected mobiles. We provide numerical results that illustrate the performance of our scheme. In particular, we show that our algorithm results in system performance that is close to the performance of a global optimal solution in most cases.

Hybrid sensor networks: a small world

Abstract: In this paper, we investigate the use of limited infrastructure, in the form of wires, for improving the energy efficiency of a wireless sensor network. We call such a sensor network - a wireless sensor network with a limited infrastructural support - a hybrid sensor network. The wires act as short cuts to bring down the average hop count of the network, resulting in a reduced energy dissipation per node. Our results indicate that adding a few wires to a wireless sensor network can not only reduce the average energy expenditure per sensor node, but also the non-uniformity in the energy expenditure across the sensor nodes.

The burstiness behavior of regulated flows in networks

Abstract: In this paper we study the impact of statistical multiplexing on leaky-bucket regulated traffic streams as they pass through the network In particular we show that the burstiness of a flow is randomized as it transits through the nodes with mean equal to its initial burstiness value at the ingress We then show that the random burstiness for a single flow converges to a constant equal to the initial value at the ingress when the flow is multiplexed with a large number of sources The results do not depend on independence or homogeniety between flows We conclude by providing some simulation results that confirm the theory

On product-form stationary distributions for reflected diffusions with jumps in the positive orthant

Abstract: In this paper, we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R n that satisfies certain finiteness conditions, we characterize the Fokker– Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusions with oblique boundary reflections and jumps. To do so, we exploit a recent characterization of the boundary properties of such reflected processes. In particular, we show that the conditions generalize those for semimartingale reflecting Brownian motions and reflected Levy processes. We provide explicit results for some models of interest.

Providing QoS in Large Networks: Statistical Multiplexing and Admission Control

Abstract: In this paper we consider the problem of providing statistical Quality of Service (QoS) guarantees defined in terms of packet loss when independent heterogeneous traffic streams access a network router of high capacity. By using a scaling technique we show how this problem becomes tractable when the server capacity is large and many traffic streams are present. In particular we show that we can define an effective bandwidth for the sources that allows us to map the model onto a multirate loss model. In particular we show several insights on the multiplexing problem as the capacity becomes large. We also provide numerical and simulation evidence to show how the largeness of networks can be used to advantage in providing very simple admission control schemes. The techniques are based on large deviations, local limit theorems, and the product-form associated with co-ordinate convex policies.