Veeraruna Kavitha

Generalized Analysis of a Distributed Energy Efficient Algorithm for Change Detection

We propose an energy efficient distributed cooperative Change Detection scheme called DualCUSUM based on Pages CUSUM algorithm. In the algorithm, each sensor runs a CUSUM and transmits only when the CUSUM is above some threshold. The transmissions from the sensors are fused at the physical layer. The channel is modeled as a Multiple Access Channel (MAC) corrupted with noise. The fusion center performs another CUSUM to detect the change. The algorithm performs better than several existing schemes when energy is at a premium. We generalize the algorithm to also include nonparametric CUSUM and provide a unified analysis. Our results show that while the false alarm probability is smaller for observation distribution with a lighter tail, the detection delay is asymptotically the same for any distribution. Consequently, we provide a new viewpoint on why parametric CUSUM performs better than nonparametric CUSUM. In the process, we also develop new results on a reflected random walk which can be of independent interest.

Energy efficient change detection over a MAC using physical layer fusion

We propose a simple and energy efficient distributed change detection scheme for sensor networks based on Pages parametric CUSUM algorithm. The sensor observations are IID over time and across the sensors conditioned on the change variable. Each sensor runs CUSUM and transmits only when the CUSUM is above some threshold. The transmissions from the sensors are fused at the physical layer. The channel is modeled as a multiple access channel (MAC) corrupted with IID noise. The fusion center which is the global decision maker, performs another CUSUM to detect the change. We provide the analysis and simulation results for our scheme and compare the performance with an existing scheme which ensures energy efficiency via optimal power selection.

Impact of mobility on call block, call drops and optimal cell size in small cell networks

We consider small cell networks and study the impact of user mobility. Assuming Poisson call arrivals at random positions with random velocities, we discuss the characterization of handovers at the boundaries. We derive explicit expressions for call block and call drop probabilities using tools from spatial queuing theory. We also derive expressions for the average virtual server held up time. These expressions are used to derive optimal cell sizes for various profile of velocities in small cell networks via some numerical examples. We further discuss the performance of the optimal system.

Fair scheduling in cellular systems in the presence of noncooperative mobiles

We consider the problem of “fair” scheduling the resources to one of the many mobile stations by a centrally controlled base station (BS). The BS is the only entity taking decisions in this framework based on truthful information from the mobiles on their radio channel. We study the well-known family of parametric α-fair scheduling problems from a game-theoretic perspective in which some of the mobiles may be noncooperative. We first show that if the BS is unaware of the noncooperative behavior from the mobiles, the noncooperative mobiles become successful in snatching the resources from the other cooperative mobiles, resulting in unfair allocations. If the BS is aware of the noncooperative mobiles, a new game arises with BS as an additional player. It can then do better by neglecting the signals from the noncooperative mobiles. The BS, however, becomes successful in eliciting the truthful signals from the mobiles only when it uses additional information (signal statistics). This new policy along with the truthful signals from mobiles forms a Nash equilibrium (NE) that we call a Truth Revealing Equilibrium. Finally, we propose new iterative algorithms to implement fair scheduling policies that robustify the otherwise nonrobust (in presence of noncooperation) α-fair scheduling algorithms.

Load dependent optimal ON-OFF policies in cellular heterogeneous networks

The use of small cells has been proposed to increase system capacity by installation of base stations close to user location. Proximity of the base station with the user equipment also implies lesser power requirement for transmitting the same information. Thus one may expect improvement in energy efficiency. But installing a large number of base stations can also lead to an increase in the total energy consumption of the system. To combat this, mechanisms have been proposed to switch OFF these base stations at times of low load. In this paper, we consider the problem of finding the fraction of base stations that can be switched OFF while maintaining quality of service (measured in terms of the average waiting time of users), for given load conditions. We also obtain the optimal switch OFF pattern. We do this in two steps. First, we determine the optimal ON-OFF pattern of base stations and user-base station association policy for a fixed fraction of base stations to be switched OFF. Then, we find the maximum fraction of base stations that can be switched OFF for given load conditions.

Open loop optimal control of base station activation for green networks

In recent years there has been an increasing awareness that the deployment as well as utilization of new information technology may have some negative ecological impact. This includes awareness to energy consumption which could have negative consequences on the environment. In recent years, it was suggested to increase energy saving by deactivating base stations during periods in which the traffic is expected to be low. In this paper we study the optimal deactivation policies, using recent tools from Multimodularity (which is the analog concept of convexity in optimization over integers). We consider two scenarios: In the first case, a central control derives the optimal open loop policies so as to maximize the expected throughput of the system given that at least a certain percentage of Base stations are deactivated (switched OFF). In the second case, we derive optimal open loop polices, which each base station can employ in a decentralized manner to minimize the average buffer occupancy cost when the fraction of time for which the BS station is deactivated (idle mode) is lower bounded. In both the cases, we show that the cost structure is Multimodular and characterize the structure of optimal policies.

Spatial queueing for analysis, design and dimensioning of Picocell networks with mobile users

In this work, we characterize the performance of Picocell networks in the presence of moving users. We model various traffic types between base-stations and mobiles as different types of queues. We derive explicit expressions for expected waiting time, service time and drop/block probabilities for both fixed as well as random velocity of mobiles. We obtain (approximate) closed form expressions for optimal cell size when the velocity variations of the mobiles is small for both non-elastic as well as elastic traffic. We conclude from the study that, if the expected call duration is long enough, the optimal cell size depends mainly on the velocity profile of the mobiles, its mean and variance. It is independent of the traffic type or duration of the calls. Further, for any fixed power of transmission, there exists a maximum velocity beyond which successful communication is not possible. This maximum possible velocity increases with the power of transmission. Also, for any given power, the optimal cell size increases when either the mean or the variance of the mobile velocity increases.

Risk sensitive optimal control framework applied to delay tolerant networks

Epidemics dynamics can describe the dissemination of information in delay tolerant networks, in peer to peer networks and in content delivery networks. The control of such dynamics has thus gained a central role in all of these areas. However, a major difficulty in this context is that the objective functions to be optimized are often not additive in time but are rather multiplicative. The classical objective function in DTNs, i.e., the successful delivery probability of a message within a given deadline, falls precisely in this category, because it takes often the form of the expectation of the exponent of some integral cost. So far, models involving such costs have been solved by interchanging the order of expectation and the exponential function. While reducing the problem to a standard optimal control problem, this interchange is only tight in the mean field limit obtained as the population tends to infinity. In this paper we identify a general framework from optimal control in finance, known as risk sensitive control, which let us handle the original (multiplicative) cost and obtain solutions to several novel control problems in DTNs. In particular, we can derive the structure of state-dependent controls that optimize transmission power at the source node. Further, we can account for the propagation loss factor of the wireless medium while obtaining these controls, and, finally, we address power control at the destination node, resulting in a novel threshold optimal activation policy. Combined optimal power control at source and destination nodes is also obtained.

Mixed polling with rerouting and applications

Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a continuum are called continuous polling systems. Often one encounters a combination of the two systems: the users can either arrive in a continuum or wait in a finite set (i.e. wait at a finite number of queues). We call these systems mixed polling systems. Also, in some applications, customers are rerouted to a new location (for another service) after their service is completed. In this work, we study mixed polling systems with rerouting. We obtain their steady state performance by discretization using the known pseudo conservation laws of discrete polling systems. Their stationary expected workload is obtained as a limit of the stationary expected workload of a discrete system. The main tools for our analysis are: (a) the fixed point analysis of infinite dimensional operators and; (b) the convergence of Riemann sums to an integral. We analyze two applications using our results on mixed polling systems and discuss the optimal system design. We consider a local area network, in which a moving ferry facilitates communication (data transfer) using a wireless link. We also consider a distributed waste collection system and derive the optimal collection point. In both examples, the service requests can arrive anywhere in a subset of the two dimensional plane. Namely, some users arrive in a continuous set while others wait for their service in a finite set. The only polling systems that can model these applications are mixed systems with rerouting as introduced in this manuscript.

Satisfying demands in a multicellular network: A universal power allocation algorithm

Power allocation to satisfy user demands in the presence of large number of interferers in a multicellular network is a challenging task. Further, the power to be allocated depends upon the system architecture, for example upon components like coding, modulation, transmit precoder, rate allocation algorithms, available knowledge of the interfering channels, etc. This calls for an algorithm via which each base station in the network can simultaneously allocate power to their respective users so as to meet their demands (when they are within the achievable limits), using whatever information is available of the other users. The goal of our research is to propose one such algorithm which in fact is universal: the proposed algorithm works from a fully co-operative setting to almost no co-operation and or for any configuration of modulation, rate allocation, etc. schemes. The algorithm asymptotically satisfies the user demands, running simultaneously and independently within a given total power budget at each base station. Further, it requires minimal information to achieve this: every base station needs to know its own users demands, its total power constraint and the transmission rates allocated to its users in every time slot. We formulate the power allocation problem in a system specific game theoretic setting, define system specific capacity region and analyze the proposed algorithm using ordinary differential equation (ODE) framework. Simulations confirm the effectiveness of the proposed algorithm.