Nikhil Singh

Rethinking Indoor Wireless Mesh Design: Low Power, Low Frequency, Full-Duplex

Existing indoor WiFi networks in the 2.5GHz and 5 GHz use too much transmit power, needed because the high carrier frequency limits signal penetration and connectivity. Instead, we propose a novel indoor wireless mesh design paradigm, based on Low Frequency, using the newly freed white spaces previously used as analogue TV bands, and Low Power - 100 times less power than currently used. Preliminary experiments show that this maintains a similar level of connectivity and performance to existing networks. It also yields more uniform connectivity, thus simplifies MAC and routing protocol design. We also advocate full-duplex networking in a single band, which becomes possible in this setting (because we operate at low frequencies). It potentially doubles the throughput of each link and eliminates hidden terminals.

On Tractable Instances of Modular Supervisory Control

An instance of a modular supervisory control problem involves a plant automaton, described either as a monolithic, finite-state automaton (SUP1M), or as the synchronous product of several finite-state automata (SUPMM), along with a set of finite state, specification automata on a common alphabet. The marked language of the synchronous product of these automata represents the desired specification. A supervisory policy that solves the instance selectively disables certain events, based on the past history of event-occurrences, such that the marked behavior of the supervised system is a non-empty subset of the desired specification. Testing the existence of a supervisory policy for a variety of in stances of modular supervisory control is PSPACE-complete [1]. This problem remains intractable even when the plant is a monolithic finite state automaton and the specification automata are restricted to have only two states with a specific structure [2]. We refer to this intractable class as SU P1Ω in this paper. After introducing complement sets for events in a plant automaton, we identify a subclass of SUP1Ω that can be solved in polynomial time. Using this class as the base, inspired by a family of subclasses of SAT (cf. section 4.2, [3]) that can be solved in polynomial time [4], we develop a family of subclasses of SUP1Ω that can be solved in polynomial time. The results of this paper are also used to identify a polynomial time hierarchy for certain intractable subclasses of SUPMM identified in this paper.

On a Non-Linear Optimization Approach for Proportional Fairness in Ad-Hoc Wireless Networks

In this paper we present a partially asynchronous, fully distributed flow-based access scheme for slotted-time protocols, that guarantees proportional-fairness in ad hoc wireless networks. This problem of providing fairness in wireless networks is considered in the framework of non-linear optimization. We say a medium access control algorithm is proportionally fair with respect to individual end-to-end flows in a network, if the product of the end-to-end flow-success probabilities is maximized.

On Distributed Algorithms that Enforce Proportional Fairness in Ad-hoc Wireless Networks

In this paper we present a distributed flow-based access scheme for slotted-time protocols, that provides proportional- fairness in ad hoc wireless networks based on the local two- hop information of nodes. We say a medium access control algorithm is proportionally fair with respect to individual end- to-end flows in a network, if the product of the end-to-end flow-success probabilities is maximized. The proposed scheme is implemented using a slotted-time protocol - ST-MAC [14]. We then present the preliminary results evaluating the fairness properties of the ST-MAC protocol using ns2 simulations [12].

Wireless Networks: An Instance of Tandem Discrete-Time Queues

We model end-to-end flows in an ad-hoc wireless network using a tandem of finite-size, discrete-time queues, located at the nodes along the routes used by the flows, with appropriate restrictions that capture the first- and second-order interference constraints. In addition, we assume there are no capture effects, that is, there is at most one arrival into a queue at any discrete-time instant. The half-duplex nature of communication also supposes there cannot be a simultaneous arrival and departure from a discrete-time queue. These queues are characterized by the channel access probabilities of the node. If the objective is to bound the buffer overflow probability at each queue along a flow, we show that is not necessary to maintain separate queues for each flow that is routed through a node. We present simulation results to support our conclusions. This observation significantly eases the implementation of the distributed algorithm that enforces end-to-end proportional fairness subject to constraints on the buffer overflow probabilities (Singh N, Sreenivas R, Shanbhag U (2008) Enforcing end-to-end proportional fairness with bounded buffer overflow probabilities. Technical Report UILU-ENG-08-2211, Aug 2008, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana).

Inferring algebraic gene networks using local decoding

Modeling the coupled dynamics of gene expression patterns is an important task in systems biology. It is most accurately performed via systems of coupled differential equations, derived by analyzing involved biochemical reactions of the cell cycle (bottom-up approach). Probabilistic Boolean networks (PBN) represent stochastic extensions of Boolean models [5, 7] that allow inference by reverse engineering from a given data set (top-down approach). In a PBN, a list of Boolean functions is associated with each node in the network, and each time the state of a gene is updated, only one of these functions is randomly chosen to compute the new state of the gene [7]. Recently [1], we presented a constructive approach for reverse engineering gene expression dynamics casted within the algebraic framework developed in [6] that can be seen as a generalization of PBN. We showed that, in a probabilistic framework, reverse engineering under this model is closely related to problems arising in coding theory. In particular, we applied list-decoding of Reed-Muller codes to address randomness, measurement errors, and small sample size issues. In this contribution we show how the concept of local decoding can be used to reduce the decoding complexity and aid experimental design.

Approximating Flow-Based Proportional Fairness in Ad-hoc Wireless Networks

This paper presents a distributed flow-based access scheme for slotted-time protocols that approximates proportional-fairness in ad hoc wireless networks and does not have a significant implementation overhead. We say a medium access control algorithm is proportionally fair with respect to individual end-to-end flows in a network, if the product of the end-to-end flow-success probabilities is maximized. The proposed scheme is implemented using a slotted-time protocol - ST-MAC (Singh, 2004). The authors then compare the performance of the ST-MAC protocol with that of the 802.11-MAC using ns2 simulations of random networks of various sizes. For dense-networks, in terms of packet-delivery-ratios and throughput, the ST-MAC protocol presents an improvement over 802.11-MAC, with comparable end-to-end delay.