Chandramani Kishore Singh

Performance evaluation of an IEEE 802.15.4 sensor network with a star topology

One class of applications envisaged for the IEEE 802.15.4 LR-WPAN (low data rate—wireless personal area network) standard is wireless sensor networks for monitoring and control applications. In this paper we provide an analytical performance model for a network in which the sensors are at the tips of a star topology, and the sensors need to transmit their measurements to the hub node so that certain objectives for packet delay and packet discard are met. We first carry out a saturation throughput analysis of the system; i.e., it is assumed that each sensor has an infinite backlog of packets and the throughput of the system is sought. After a careful analysis of the CSMA/CA MAC that is employed in the standard, and after making a certain decoupling approximation, we identify an embedded Markov renewal process, whose analysis yields a fixed point equation, from whose solution the saturation throughput can be calculated. We validate our model against ns2 simulations (using an IEEE 802.15.4 module developed by Zheng [14]). We find that with the default back-off parameters the saturation throughput decreases sharply with increasing number of nodes. We use our analytical model to study the problem and we propose alternative back-off parameters that prevent the drop in throughput. We then show how the saturation analysis can be used to obtain an analytical model for the finite arrival rate case. This finite load model captures very well the qualitative behavior of the system, and also provides a good approximation to the packet discard probability, and the throughput. For the default parameters, the finite load throughput is found to first increase and then decrease with increasing load. We find that for typical performance objectives (mean delay and packet discard) the packet discard probability would constrain the system capacity. Finally, we show how to derive a node lifetime analysis using various rates and probabilities obtained from our performance analysis model.

Spatial SINR Games Combining Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

A coalitional game model for spectrum pooling in wireless data access networks

We consider a setting in which several operators offer downlink wireless data access services in a certain geographical region. Each operator deploys several base stations or access points, and registers some subscribers. In such a situation, if operators pool their infrastructure, and permit the possibility of subscribers being served by any of the cooperating operators, then there can be overall better user satisfaction, and increased operator revenue. We use coalitional game theory to investigate such resource pooling and cooperation between operators.We use utility functions to model user satisfaction, and show that the resulting coalitional game has the property that if all operators cooperate (i.e., form a grand coalition) then there is an operating point that maximizes the sum utility over the operators while providing the operators revenues such that no subset of operators has an incentive to break away from the coalition. We investigate whether such operating points can result in utility unfairness between users of the various operators. We also study other revenue sharing concepts, namely, the nucleolus and the Shapely value. Such investigations throw light on criteria for operators to accept or reject subscribers, based on the service level agreements proposed by them. We also investigate the situation in which only certain subsets of operators may be willing to cooperate.

The wireless multicast coalition game and the non-cooperative association problem

We study in this paper the problem of sharing the cost of a multicast service in a wireless network. In a wireless network, multiple users can decode the same signal of the base station provided the received power exceeds a certain minimum threshold. In this work, the cost for broadcasting is taken to be the transmission power. We begin by proposing various schemes to share the cost, and study their properties. We then study the association problem where an user has options of either joining the multicast group or opting for a unicast connection at a given cost. Next, we extend the association problem to the scenarios with partial information - a user knows his own power requirement, but has to make decision without knowledge of the number of other users in the network and their requirements. The unicast alternative that each mobile has, results in limitations on the coverage (area covered by the multicast service) and the capacity (number of users connected to the multicast service). We derive the expected capacity and coverage as a function of the cost sharing mechanism. We finally extend the model to the case where users have the option of joining any one from a given set of multicast service providers. A users power requirement depends on its association, but its cost share depends on the association profile of all the users. We study the joint problem of the cost allocation and the equilibrium association.

Spatial SINR games of base station placement and mobile association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

Uplink power control and base station association in multichannel cellular networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

Optimal forwarding in delay tolerant networks with multiple destinations

We study the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain and derive the optimal closed loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ODE (i.e., fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed loop policy.

Random Block-Coordinate Gradient Projection Algorithms

In this paper, we study gradient projection algorithms based on random partial updates of decision variables. These algorithms generalize random coordinate descent methods. We analyze these algorithms with and without assuming strong convexity of the objective functions. We also present an accelerated version of the algorithm based on Nesterovs two-step gradient method [1]. In each case, we prove convergence and provide a bound on the rate of convergence. We see that the randomized algorithms exhibit similar rates of convergence as their full gradient based deterministic counterparts.

A coalitional game framework for cooperative secondary spectrum access

We consider a framework in which several service providers offer downlink wireless data access service in a certain area. Each provider serves its end-users through opportunistic secondary spectrum access of licensed spectrum, and needs to pay primary license holders of the spectrum usage based and membership based charges for such secondary spectrum access. In these circumstances, if providers pool their resources and allow end-users to be served by any of the cooperating providers, the total user satisfaction as well as the aggregate revenue earned by providers may increase. We use coalitional game theory to investigate such cooperation among providers, and show that the optimal cooperation schemes can be obtained as solutions of convex optimizations. We next show that under usage based charging scheme, if all providers cooperate, there always exists an operating point that maximizes the aggregate revenue of providers, while presenting each provider a share of the revenue such that no subset of providers has an incentive to leave the coalition. Furthermore, such an operating point can be computed in polynomial time. Finally, we show that when the charging scheme involves membership based charges, the above result holds in important special cases.

Analysis of a Proportionally Fair and Locally Adaptive spatial Aloha in Poisson Networks

The proportionally fair sharing of the capacity of a Poisson network using Spatial-Aloha leads to closed-form performance expressions in two extreme cases: (1) the case without topology information, where the analysis boils down to a parametric optimization problem leveraging stochastic geometry; (2) the case with full network topology information, which was recently solved using shot-noise techniques. We show that there exists a continuum of adaptive controls between these two extremes, based on local stopping sets, which can also be analyzed in closed form. We also show that these control schemes are implementable, in contrast to the full information case which is not. As local information increases, the performance levels of these schemes are shown to get arbitrarily close to those of the full information scheme. The analytical results are combined with discrete event simulation to provide a detailed evaluation of the performance of this class of medium access controls.