Kumar, P. R.
Overview
Works:  76 works in 115 publications in 2 languages and 1,175 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA402, 003 
Publication Timeline
.
Most widely held works by
P. R Kumar
Stochastic systems : estimation, identification, and adaptive control by
P. R Kumar(
Book
)
8 editions published in 1986 in English and held by 315 WorldCat member libraries worldwide
8 editions published in 1986 in English and held by 315 WorldCat member libraries worldwide
Adaptive control, filtering, and signal processing by
Karl J Åström(
Book
)
9 editions published in 1995 in English and held by 178 WorldCat member libraries worldwide
The area of adaptive systems, which encompasses recursive identification, adaptive control, filtering, and signal processing, has been one of the most active areas of the past decade. Since adaptive controllers are fundamentally nonlinear controllers which are applied to nominally linear, possibly stochastic and timevarying systems, their theoretical analysis is usually very difficult. Nevertheless, over the past decade much fundamental progress has been made on some key questions concerning their stability, convergence, performance, and robustness. Moreover, adaptive controllers have been successfully employed in numerous practical applications, and have even entered the marketplace
9 editions published in 1995 in English and held by 178 WorldCat member libraries worldwide
The area of adaptive systems, which encompasses recursive identification, adaptive control, filtering, and signal processing, has been one of the most active areas of the past decade. Since adaptive controllers are fundamentally nonlinear controllers which are applied to nominally linear, possibly stochastic and timevarying systems, their theoretical analysis is usually very difficult. Nevertheless, over the past decade much fundamental progress has been made on some key questions concerning their stability, convergence, performance, and robustness. Moreover, adaptive controllers have been successfully employed in numerous practical applications, and have even entered the marketplace
Discrete event systems, manufacturing systems, and communication networks by
P. R Kumar(
Book
)
7 editions published in 1995 in English and held by 151 WorldCat member libraries worldwide
The study of discrete event dynamical systems (DEDS) has become rapidly popular among researchers in systems and control, in communication networks, in manufacturing, and in distributed computing. This development has created problems for researchers and potential "consumers" of the research. The first problem is the veritable Babel of languages, formalisms, and approaches, which makes it very difficult to determine the commonalities and distinctions among the competing schools of approaches. The second, related problem arises from the different traditions, paradigms, values, and experiences that scholars bring to their study of DEDS, depending on whether they come from control, communication, computer science, or mathematical logic. As a result, intellectual exchange among scholars becomes compromised by unexplicated assumptions
7 editions published in 1995 in English and held by 151 WorldCat member libraries worldwide
The study of discrete event dynamical systems (DEDS) has become rapidly popular among researchers in systems and control, in communication networks, in manufacturing, and in distributed computing. This development has created problems for researchers and potential "consumers" of the research. The first problem is the veritable Babel of languages, formalisms, and approaches, which makes it very difficult to determine the commonalities and distinctions among the competing schools of approaches. The second, related problem arises from the different traditions, paradigms, values, and experiences that scholars bring to their study of DEDS, depending on whether they come from control, communication, computer science, or mathematical logic. As a result, intellectual exchange among scholars becomes compromised by unexplicated assumptions
Scaling laws for ad hoc wireless networks : an information theoretic approach by Feng Xue(
Book
)
6 editions published in 2006 in English and held by 17 WorldCat member libraries worldwide
In recent years there has been significant and increasing interest in ad hoc wireless networks. The design, analysis and deployment of such wireless networks necessitate a fundamental understanding of how much information transfer they can support, as well as what the appropriate architectures and protocols are for operating them. This monograph addresses these questions by presenting various models and results that quantify the information transport capability of wireless networks, as well as shed light on architecture design from a high level point of view. The models take into consideration important features such as the spatial distribution of nodes, strategies for sharing the wireless medium, the attenuation of signals with distance, and how information is to be transferred, whether it be by encoding, decoding, choice of power level, spatiotemporal scheduling of transmissions, choice of multihop routes, or other modalities of cooperation between nodes. An important aspect of the approach is to characterize how the information hauling capacity scales with the number of nodes in the network. The monograph begins by studying models of wireless networks based on current technology, which schedules concurrent transmissions to take account of interference, and then routes packets from their sources to destinations in a multihop fashion. An index of performance, called transport capacity, which is measured by the bit meters per second the network can convey in aggregate, is studied. For arbitrary networks, including those allowing for optimization of node locations, the scaling law for the transport capacity in terms of the number of nodes in the network is identified. For random networks, where nodes are randomly distributed, and sourcedestination pairs are randomly chosen, the scaling law for the maximum common throughput capacity that can be supported for all the sourcedestination pairs is characterized. The constructive procedure for obtaining the sharp lower bound gives insight into an order optimal architecture for wireless networks operating under a multihop strategy. To determine the ultimate limits on how much information wireless networks can carry requires an information theoretic treatment, and this is the subject of the second half of the monograph. Since wireless communication takes place over a shared medium, it allows more advanced operations in addition to multihop. To understand the limitations as well as possibilities for such information transfer, wireless networks are studied from a Shannon informationtheoretic point of view, allowing any causal operation. Models that characterize how signals attenuate with distance, as well as multipath fading, are introduced. Fundamental bounds on the transport capacity are established for both high and low attenuation regimes. The results show that the multihop transport scheme achieves the same order of scaling, though with a different preconstant, as the information theoretically best possible, in the high attenuation regime. However, in the low attenuation regime, superlinear scaling may be possible through recourse to more advanced modes of cooperation between nodes. Techniques used in analyzing multiantenna systems are also studied to characterize the scaling behavior of large wireless networks
6 editions published in 2006 in English and held by 17 WorldCat member libraries worldwide
In recent years there has been significant and increasing interest in ad hoc wireless networks. The design, analysis and deployment of such wireless networks necessitate a fundamental understanding of how much information transfer they can support, as well as what the appropriate architectures and protocols are for operating them. This monograph addresses these questions by presenting various models and results that quantify the information transport capability of wireless networks, as well as shed light on architecture design from a high level point of view. The models take into consideration important features such as the spatial distribution of nodes, strategies for sharing the wireless medium, the attenuation of signals with distance, and how information is to be transferred, whether it be by encoding, decoding, choice of power level, spatiotemporal scheduling of transmissions, choice of multihop routes, or other modalities of cooperation between nodes. An important aspect of the approach is to characterize how the information hauling capacity scales with the number of nodes in the network. The monograph begins by studying models of wireless networks based on current technology, which schedules concurrent transmissions to take account of interference, and then routes packets from their sources to destinations in a multihop fashion. An index of performance, called transport capacity, which is measured by the bit meters per second the network can convey in aggregate, is studied. For arbitrary networks, including those allowing for optimization of node locations, the scaling law for the transport capacity in terms of the number of nodes in the network is identified. For random networks, where nodes are randomly distributed, and sourcedestination pairs are randomly chosen, the scaling law for the maximum common throughput capacity that can be supported for all the sourcedestination pairs is characterized. The constructive procedure for obtaining the sharp lower bound gives insight into an order optimal architecture for wireless networks operating under a multihop strategy. To determine the ultimate limits on how much information wireless networks can carry requires an information theoretic treatment, and this is the subject of the second half of the monograph. Since wireless communication takes place over a shared medium, it allows more advanced operations in addition to multihop. To understand the limitations as well as possibilities for such information transfer, wireless networks are studied from a Shannon informationtheoretic point of view, allowing any causal operation. Models that characterize how signals attenuate with distance, as well as multipath fading, are introduced. Fundamental bounds on the transport capacity are established for both high and low attenuation regimes. The results show that the multihop transport scheme achieves the same order of scaling, though with a different preconstant, as the information theoretically best possible, in the high attenuation regime. However, in the low attenuation regime, superlinear scaling may be possible through recourse to more advanced modes of cooperation between nodes. Techniques used in analyzing multiantenna systems are also studied to characterize the scaling behavior of large wireless networks
Packets with deadlines : a framework for realtime wireless networks by
IHong Hou(
Book
)
6 editions published in 2013 in English and held by 16 WorldCat member libraries worldwide
"With the explosive increase in the number of mobile devices and applications, it is anticipated that wireless traffic will increase exponentially in the coming years. Moreover, future wireless networks all carry a wide variety of flows, such as video streaming, online gaming, and VoIP, which have various quality of service (QoS) requirements. Therefore, a new mechanism that can provide satisfactory performance to the complete variety of all kinds of flows, in a coherent and unified framework, is needed. In this book, we introduce a framework for realtime wireless networks. This consists of a model that jointly addresses several practical concerns for realtime wireless networks, including perpacket delay bounds, throughput requirements, and heterogeneity of wireless channels. We detail how this framework can be employed to address a wide range of problems, including admission control, packet scheduling, and utility maximization."Page [vi]
6 editions published in 2013 in English and held by 16 WorldCat member libraries worldwide
"With the explosive increase in the number of mobile devices and applications, it is anticipated that wireless traffic will increase exponentially in the coming years. Moreover, future wireless networks all carry a wide variety of flows, such as video streaming, online gaming, and VoIP, which have various quality of service (QoS) requirements. Therefore, a new mechanism that can provide satisfactory performance to the complete variety of all kinds of flows, in a coherent and unified framework, is needed. In this book, we introduce a framework for realtime wireless networks. This consists of a model that jointly addresses several practical concerns for realtime wireless networks, including perpacket delay bounds, throughput requirements, and heterogeneity of wireless channels. We detail how this framework can be employed to address a wide range of problems, including admission control, packet scheduling, and utility maximization."Page [vi]
Research on rapeseed & mustard : proceedings of an IndoSwedish Symposium, September 46, 1989(
Book
)
4 editions published in 1990 in English and held by 10 WorldCat member libraries worldwide
4 editions published in 1990 in English and held by 10 WorldCat member libraries worldwide
Proceedings, twentyfifth annual Allerton Conference on Communication, Control, and Computing : conference held September
30October 2, 1987, Allerton House, Monticello, Illinois by
Control, and Computing Allerton Conference on Communication(
Book
)
3 editions published in 1987 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 1987 in English and held by 8 WorldCat member libraries worldwide
Lecture series in mobile telecommunications and networks : transcripts of the third series of three lectures, March 2008 
February 2009 by
P. R Kumar(
Book
)
1 edition published in 2009 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 6 WorldCat member libraries worldwide
Stochastic optimal control and stochastic differential games by
P. R Kumar(
Book
)
4 editions published between 1977 and 1979 in English and held by 4 WorldCat member libraries worldwide
4 editions published between 1977 and 1979 in English and held by 4 WorldCat member libraries worldwide
Brassica Oliseeds : breeding and management(
Book
)
1 edition published in 2015 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 3 WorldCat member libraries worldwide
Closedloop analysis and feedback design in the presence of limited information by Dapeng Li(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Recent progress in communication technologies and their use in feedback control systems motivate to look deeper into the interplay of control and communication in the closedloop feedback architecture. Among several research directions on this topic, a great deal of attention has been given to the fundamental limitations in the presence communication constraints. Entropy rate inequalities corresponding to the information flux in a typical causal closed loop have been derived towards obtaining a Bodelike integral formula. This work extends the discretetime result to continuoustime systems. The main challenge in this extension is that Kolmogorov's entropy rate equality, which is fundamental to the derivation of the result in discretetime case, does not hold for continuoustime systems. Mutual information rate instead of entropy rate is used to represent the information flow in the closedloop, and a limiting relationship due to Pinsker towards obtaining the mutual information rate between two continuous time processes from their discretized sequence is used to derive the Bodelike formula. The results are further extended to switched systems and a Bode integral formula is obtained under the assumption that the switching sequence is an ergodic Markov chain. To enable simplified calculation of the resulting lower bound, some Lie algebraic conditions are developed. Besides analysis results, this dissertation also includes joint control/communication design for closedloop stability of performance. We consider the stabilization problem within Linear Quadratic Regulator framework, where a control gain is chosen to minimize a linear quadratic cost functional while subject to the input power constraint imposed by an additive Gaussian channel which closes the loop. Also focused on Gaussian channel, the channel noise attenuation problem is addressed, by using Hinfinity/H2 methodology. Similar feedback optimal estimation problem is solved by using Kalman filtering theory
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Recent progress in communication technologies and their use in feedback control systems motivate to look deeper into the interplay of control and communication in the closedloop feedback architecture. Among several research directions on this topic, a great deal of attention has been given to the fundamental limitations in the presence communication constraints. Entropy rate inequalities corresponding to the information flux in a typical causal closed loop have been derived towards obtaining a Bodelike integral formula. This work extends the discretetime result to continuoustime systems. The main challenge in this extension is that Kolmogorov's entropy rate equality, which is fundamental to the derivation of the result in discretetime case, does not hold for continuoustime systems. Mutual information rate instead of entropy rate is used to represent the information flow in the closedloop, and a limiting relationship due to Pinsker towards obtaining the mutual information rate between two continuous time processes from their discretized sequence is used to derive the Bodelike formula. The results are further extended to switched systems and a Bode integral formula is obtained under the assumption that the switching sequence is an ergodic Markov chain. To enable simplified calculation of the resulting lower bound, some Lie algebraic conditions are developed. Besides analysis results, this dissertation also includes joint control/communication design for closedloop stability of performance. We consider the stabilization problem within Linear Quadratic Regulator framework, where a control gain is chosen to minimize a linear quadratic cost functional while subject to the input power constraint imposed by an additive Gaussian channel which closes the loop. Also focused on Gaussian channel, the channel noise attenuation problem is addressed, by using Hinfinity/H2 methodology. Similar feedback optimal estimation problem is solved by using Kalman filtering theory
Mode identification using stochastic hybrid models with applications to conflict detection and resolution by Asal Naseri Kouzehgarani(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
Most models of aircraft trajectories are nonlinear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multiaircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizonthereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finitestate Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the nondeterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers.We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
Most models of aircraft trajectories are nonlinear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multiaircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizonthereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finitestate Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the nondeterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers.We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs
A digital interface for wireless networks by Anand Muralidhar(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
This dissertation addresses the problem of determining the capacity of wireless networks and how to operate them. Within this context we present results on Gaussian relay, interference, and multicast networks. Two new models for wireless networks are introduced here: the discrete network and the superposition network. As with a Gaussian network, one can construct either a discrete network or a superposition network. The discrete network is obtained by simply quantizing the received signals in the Gaussian model and by restricting the transmit signals to a finite alphabet. The superposition network, inspired by the Gaussian model, is a noiseless deterministic network, the inputs and outputs of the channels are discrete, and channel gains are signed integers. The capacity of a class of Gaussian relay networks and its corresponding discrete or superposition network is always within a bounded gap, where the gap is independent of channel gains or signaltonoise ratio (SNR), and depends only on the number $M$ of nodes in the network. More importantly, a nearoptimal coding strategy for either the discrete or the superposition network can be converted into a nearoptimal coding strategy for the original Gaussian network. Hence, both these networks serve as nearoptimal digital interfaces for operating the Gaussian network. The discrete network is obtained from a Gaussian network by simply quantizing the received signals and restricting transmitted signals to a certain finite precision. Since its signals are obtained from those of a Gaussian network and its transmissions are transmittable asis on a Gaussian network, the discrete network provides a particularly simple quantizationbased digital interface for operating layered Gaussian relay networks. These are relay networks in which the nodes are grouped into layers, and only nodes of one layer can transmit to the nodes of the next layer. The cutset upper bounds on the capacities of the Gaussian and the discrete network are within an SNRindependent bounded gap of $O(M log M)$ bits. Moreover, a simple linear network code is a nearoptimal coding strategy for the discrete relay network, achieving all rates within $O(M^2)$ bits of its cutset bound, where the bound is independent of channel gains or SNR. The linear code can be used asis on the Gaussian network after quantizing its received signals. It achieves all rates within $O(M^2)$ bits of the capacity for Gaussian relay networks. The linear network code improves on existing approximatelyoptimal coding schemes for the relay network by virtue of its simplicity and robustness, and it explicitly connects wireline network coding with codes for Gaussian networks. The approximation of Gaussian networks by other previously proposed deterministic networks is also studied in this dissertation, and two main results are presented, one positive and the other negative. The gap between the capacity of a Gaussian relay network and a corresponding linear deterministic network can be unbounded. The key reasons are that the linear deterministic model fails to capture the phase of received signals, and there is a loss in signal strength in the reduction to a linear deterministic network. On the positive side, Gaussian relay networks with a single sourcedestination pair are indeed well approximated by the superposition network. The difference between the capacity of a Gaussian relay network and the corresponding superposition network is bounded by $O(M log M)$ bits, where the gap is again independent of channel gains or SNR. As a corollary, multipleinput multipleoutput (MIMO) channels cannot be approximated by the linear deterministic model but can be by the superposition model. A code for a Gaussian relay network can be designed from {em any} code for the corresponding superposition network simply by pruning it, suffering no more than a rate loss of $O(M log M)$ bits that is independent of SNR. Similar results hold for the $K times K$ Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
This dissertation addresses the problem of determining the capacity of wireless networks and how to operate them. Within this context we present results on Gaussian relay, interference, and multicast networks. Two new models for wireless networks are introduced here: the discrete network and the superposition network. As with a Gaussian network, one can construct either a discrete network or a superposition network. The discrete network is obtained by simply quantizing the received signals in the Gaussian model and by restricting the transmit signals to a finite alphabet. The superposition network, inspired by the Gaussian model, is a noiseless deterministic network, the inputs and outputs of the channels are discrete, and channel gains are signed integers. The capacity of a class of Gaussian relay networks and its corresponding discrete or superposition network is always within a bounded gap, where the gap is independent of channel gains or signaltonoise ratio (SNR), and depends only on the number $M$ of nodes in the network. More importantly, a nearoptimal coding strategy for either the discrete or the superposition network can be converted into a nearoptimal coding strategy for the original Gaussian network. Hence, both these networks serve as nearoptimal digital interfaces for operating the Gaussian network. The discrete network is obtained from a Gaussian network by simply quantizing the received signals and restricting transmitted signals to a certain finite precision. Since its signals are obtained from those of a Gaussian network and its transmissions are transmittable asis on a Gaussian network, the discrete network provides a particularly simple quantizationbased digital interface for operating layered Gaussian relay networks. These are relay networks in which the nodes are grouped into layers, and only nodes of one layer can transmit to the nodes of the next layer. The cutset upper bounds on the capacities of the Gaussian and the discrete network are within an SNRindependent bounded gap of $O(M log M)$ bits. Moreover, a simple linear network code is a nearoptimal coding strategy for the discrete relay network, achieving all rates within $O(M^2)$ bits of its cutset bound, where the bound is independent of channel gains or SNR. The linear code can be used asis on the Gaussian network after quantizing its received signals. It achieves all rates within $O(M^2)$ bits of the capacity for Gaussian relay networks. The linear network code improves on existing approximatelyoptimal coding schemes for the relay network by virtue of its simplicity and robustness, and it explicitly connects wireline network coding with codes for Gaussian networks. The approximation of Gaussian networks by other previously proposed deterministic networks is also studied in this dissertation, and two main results are presented, one positive and the other negative. The gap between the capacity of a Gaussian relay network and a corresponding linear deterministic network can be unbounded. The key reasons are that the linear deterministic model fails to capture the phase of received signals, and there is a loss in signal strength in the reduction to a linear deterministic network. On the positive side, Gaussian relay networks with a single sourcedestination pair are indeed well approximated by the superposition network. The difference between the capacity of a Gaussian relay network and the corresponding superposition network is bounded by $O(M log M)$ bits, where the gap is again independent of channel gains or SNR. As a corollary, multipleinput multipleoutput (MIMO) channels cannot be approximated by the linear deterministic model but can be by the superposition model. A code for a Gaussian relay network can be designed from {em any} code for the corresponding superposition network simply by pruning it, suffering no more than a rate loss of $O(M log M)$ bits that is independent of SNR. Similar results hold for the $K times K$ Gaussian interference network, MIMO Gaussian interference networks, MIMO Gaussian relay networks, and multicast networks, with the constant gap depending additionally on the number of antennas in case of MIMO networks
Enforcing cooperation and providing quality of service in wireless networks by Juan J Jaramillo Jimenez(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
The purpose of this dissertation is to design algorithms that provide quality of service and enforce cooperation in wireless ad hoc networks. Using a simple network model, we first study the performance of some previously proposed cooperationenforcing strategies and then present a new mechanism. We prove that our mechanism is robust to imperfect measurements, is collusionresistant, and can achieve full cooperation among nodes. Assuming cooperation is being enforced, we then study the problem of optimal routing and admission control for flows which require a prespecified bandwidth from the network. We develop an algorithm whose performance is close to that of an omniscient offline algorithm that has complete a priori knowledge of the entire sequence of flow arrivals and their bandwidth requests, including the future. We then study the problem of congestion control and scheduling in wireless ad hoc networks that have to support a mixture of besteffort and realtime traffic. We propose a model for incorporating the requirements of packets with deadlines in an optimization framework. The solution to the problem results in a joint congestion control and scheduling algorithm which fairly allocates resources to meet the fairness objectives of both elastic and inelastic flows, and the perpacket delay requirements of inelastic flows
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
The purpose of this dissertation is to design algorithms that provide quality of service and enforce cooperation in wireless ad hoc networks. Using a simple network model, we first study the performance of some previously proposed cooperationenforcing strategies and then present a new mechanism. We prove that our mechanism is robust to imperfect measurements, is collusionresistant, and can achieve full cooperation among nodes. Assuming cooperation is being enforced, we then study the problem of optimal routing and admission control for flows which require a prespecified bandwidth from the network. We develop an algorithm whose performance is close to that of an omniscient offline algorithm that has complete a priori knowledge of the entire sequence of flow arrivals and their bandwidth requests, including the future. We then study the problem of congestion control and scheduling in wireless ad hoc networks that have to support a mixture of besteffort and realtime traffic. We propose a model for incorporating the requirements of packets with deadlines in an optimization framework. The solution to the problem results in a joint congestion control and scheduling algorithm which fairly allocates resources to meet the fairness objectives of both elastic and inelastic flows, and the perpacket delay requirements of inelastic flows
Ramana pahavanum thirukkoiyilkalum by
P. R Kumar(
Book
)
1 edition published in 2010 in Tamil and held by 2 WorldCat member libraries worldwide
Temples in South India
1 edition published in 2010 in Tamil and held by 2 WorldCat member libraries worldwide
Temples in South India
Verification and Enforcement of StateBased Notions of Opacity in Discrete Event Systems by Anooshiravan Saboori(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Motivated by security and privacy considerations in applications of discrete event systems, we describe and analyze the complexity of verifying various statebased notions of opacity in systems that are modeled as (possibly nondeterministic) finite automata with partial observation on their transitions. Assuming that the intruder observes system activity through some projection map and has complete knowledge of the system model, we define three notions of opacity with respect to a set of secret states: (i) initialstate opacity is a notion that requires the membership of the system true initial state to the set of secret states remain opaque (i.e., uncertain) to the intruder; (ii) Kstep opacity is a notion that requires that at any specific point in time within the last K observations, the entrance of the system state to the given set of secret states remain opaque to the intruder; (iii) infinitestep opacity is a notion that requires the entrance of the system state at any particular instant to the set of secret states remain opaque, for the length of the system operation, to the intruder. As illustrated via examples in the thesis, the above statebased notions of opacity can be used to characterize the security requirements in many applications, including encryption using pseudorandom generators, coverage properties in sensor networks, and anonymity requirements in protocols for web transactions. In order to model the intruder capabilities regarding initialstate opacity, we address the initialstate estimation problem in a nondeterministic finite automaton under partial observations on its transitions via the construction of an initialstate estimator. We analyze the properties and complexity of the initialstate estimator, and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant (i.e., it does not change over time). We also establish that the verification of initialstate opacity is a PSPACEcomplete problem. In order to verify Kstep opacity, we introduce the Kdelay state estimator which constructs the estimate of the state of the system K observations ago (Kdelayed state estimates) for a given nondeterministic finite automaton under partial observation on its transitions. We provide two methods for constructing Kdelay state estimators, and hence two methods for verifying Kstep opacity, and analyze the computational complexity of both. In the process, we also establish that the verification of $K$step opacity is an NPhard problem. We also investigate the role of the delay K in Kstep opacity and show that there exists a delay K* such that Kstep opacity implies K'step opacity for any K and K' such that K'>K>= K*. This is not true for arbitrary K'>K though the converse holds trivially. Infinitestep opacity can be verified via the construction of a currentstate estimator and a bank of appropriate initialstate estimators. The verification of infinitestep opacity is also shown to be a PSPACEhard problem. Finally, we tackle the problem of constructing a minimally restrictive opacityenforcing supervisor (MOES) which limits the system's behavior within some prespecified legal behavior while enforcing opacity requirements. We characterize the solution to MOES, under some mild assumptions, in terms of the supremal element of certain controllable, normal, and opaque languages. We also show that this supremal element always exists and that it can be implemented using state estimators. The result is a supervisor that achieves conformance to the prespecified legal behavior while enforcing opacity by disabling, at any given time, a subset of the controllable system events, in a way that minimally restricts the range of allowable system behavior
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
Motivated by security and privacy considerations in applications of discrete event systems, we describe and analyze the complexity of verifying various statebased notions of opacity in systems that are modeled as (possibly nondeterministic) finite automata with partial observation on their transitions. Assuming that the intruder observes system activity through some projection map and has complete knowledge of the system model, we define three notions of opacity with respect to a set of secret states: (i) initialstate opacity is a notion that requires the membership of the system true initial state to the set of secret states remain opaque (i.e., uncertain) to the intruder; (ii) Kstep opacity is a notion that requires that at any specific point in time within the last K observations, the entrance of the system state to the given set of secret states remain opaque to the intruder; (iii) infinitestep opacity is a notion that requires the entrance of the system state at any particular instant to the set of secret states remain opaque, for the length of the system operation, to the intruder. As illustrated via examples in the thesis, the above statebased notions of opacity can be used to characterize the security requirements in many applications, including encryption using pseudorandom generators, coverage properties in sensor networks, and anonymity requirements in protocols for web transactions. In order to model the intruder capabilities regarding initialstate opacity, we address the initialstate estimation problem in a nondeterministic finite automaton under partial observations on its transitions via the construction of an initialstate estimator. We analyze the properties and complexity of the initialstate estimator, and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant (i.e., it does not change over time). We also establish that the verification of initialstate opacity is a PSPACEcomplete problem. In order to verify Kstep opacity, we introduce the Kdelay state estimator which constructs the estimate of the state of the system K observations ago (Kdelayed state estimates) for a given nondeterministic finite automaton under partial observation on its transitions. We provide two methods for constructing Kdelay state estimators, and hence two methods for verifying Kstep opacity, and analyze the computational complexity of both. In the process, we also establish that the verification of $K$step opacity is an NPhard problem. We also investigate the role of the delay K in Kstep opacity and show that there exists a delay K* such that Kstep opacity implies K'step opacity for any K and K' such that K'>K>= K*. This is not true for arbitrary K'>K though the converse holds trivially. Infinitestep opacity can be verified via the construction of a currentstate estimator and a bank of appropriate initialstate estimators. The verification of infinitestep opacity is also shown to be a PSPACEhard problem. Finally, we tackle the problem of constructing a minimally restrictive opacityenforcing supervisor (MOES) which limits the system's behavior within some prespecified legal behavior while enforcing opacity requirements. We characterize the solution to MOES, under some mild assumptions, in terms of the supremal element of certain controllable, normal, and opaque languages. We also show that this supremal element always exists and that it can be implemented using state estimators. The result is a supervisor that achieves conformance to the prespecified legal behavior while enforcing opacity by disabling, at any given time, a subset of the controllable system events, in a way that minimally restricts the range of allowable system behavior
Generalized Nash games with shared constraints: Existence, efficiency, refinement and equilibrium constraints by Ankur A Kulkarni(
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
The thesis pertains to some fundamental questions in the theory of games. Our focus is on a class of noncooperative N player games, called generalized Nash games with shared constraints, or simply, sharedconstraint games. In such a game, every strategytuple is constrained to lie in a subset C of the product space of strategies. Thus strategies available to a player are only those which when taken jointly with the strategies of all other players, form a tuple that lies in C. The set C is called the shared constraint. Despite their relevance in realworld settings, there are many theoretical properties of these games that are not well understood. What interests us in this thesis is the theoretical character of the equilibria of these games. Sharedconstraint games admit two kinds of equilibria: generalized Nash equilibria (GNE) that are illposed and often intractable and a smaller subset of them (called variational equilibria or VE) satisfying an exogenous regularity condition that are wellposed and surprisingly tractable. We seek to clarify the nature of these equilibria, study their economic implications and exploit their properties to advance the analytical theory for conventional and somewhat unconventional sharedconstraint games. The unconventional sharedconstraint games are in fact a class of dynamic games, called multileader multifollower games, which we view through the lens of shared constraints. Four questions are addressed in this thesis with the central theme as sharedconstraint games. In the first part of the thesis we present a refinement of the GNE. A refinement of an equilibrium is a subset of the set of equilibria which is nonempty whenever the original set of equilibria is nonempty. Refined equilibria are representative of the set of equilibria and have additional properties that make them more attractive as solution concepts than the original equilibria. The contribution of this work is a theory that gives sufficient conditions for a game to admit the VE as a refinement of the GNE. These conditions are expressed in terms of the Brouwer degree, which is seen to relate the GNE and the VE in a profound manner. Importantly, for certain classes of games, these conditions are also seen to be necessary. The degree theoretic relationship holds in both, primal and primaldual space. Our work unifies some previously known results and provides mathematical justification for ideas that were known to be intuitive appealing but were hitherto unsubstantiated formally. The second part of this thesis is about multileader multifollower games. These games are highly nonconvex and irregular and no reliable theory is available for claiming the existence of equilibria of these games. We develop such a theory for multileader multifollower games with shared constraints. The application of standard fixed point arguments to the reaction map of general multileader multifollower games is hindered by the lack of suitable continuity properties, amongst other requirements, in this map. We observe that these games bear a close resemblance to sharedconstraint games and present modifications of the canonical multileader multifollower game that result in sharedconstraint games, with far more favorable properties. Specifically, a global equilibrium of this game exists when a suitably defined modified reaction map admits a fixed point. Sufficient conditions for the existence of these fixed points are obtained via topological fixed point theory. Finally, the paradigm developed is applied to a class of LCPconstrained leader problems where conditions for the contractibility of the domain are derived via the theory of retracts. The third part of thesis concerns the use of variational inequalities for claiming the existence of an equilibrium to sharedconstraint games. The equilibrium conditions of a generalized Nash game can be compactly stated as a quasivariational inequality (QVI), an extension of the variational inequality (VI). Harker showed that under certain conditions on the maps defining the QVI, a solution to a related VI solves the QVI. But the application of Harker⁰́₉s result to the QVI associated with sharedconstraint games proves difficult because its hypotheses can fail to hold even for simple sharedconstraint games. We show these hypotheses are in fact impossible to satisfy in most settings. But we show that for a modified QVI, whose solution set equals that of the original QVI, the hypothesis of Harker⁰́₉s result always hold. This paves the way for applying this result to sharedconstraint games, albeit in an indirect manner. This avenue allows us to recover as a special case, a result proved by Facchinei et al., in which it is shown that a suitably defined variational inequality provides a solution to the QVI of a sharedconstraint game. In the fourth part we take a systemlevel view of sharedconstraint games that result from resource allocation. We clarify the relation between this mode of allocating resources and the other conventional modes via either perfect competition or through the use of a mechanism. We find that for perfectly competitive settings the VE is the same as the competitive equilibrium. We then compare the performance of GNE and VE of the sharedconstraint game with respect to the systemlevel objective of maximization of social welfare or aggregate utility. We are specifically interested in the efficiency of an equilibrium, which is the ratio of the aggregate utility for this equilibrium to the optimal aggregate utility, and in the lowest value this efficiency can take for a class of utility functions. We show that for a certain class of utility functions the VEs are fully efficient. We characterize this class and show that departures from this setting can lead to arbitrarily low efficiency in the worst case. Specifically, in this class, even while the VEs are efficient, GNEs can be arbitrarily inefficient, and VEs of games not belonging to the ⁰́₈efficient⁰́₉ class can have arbitrarily low efficiency in the worst case. Finally we suggest ways to remedy the low efficiency of equilibria in these cases. We find that a more restricted class of utility functions, in which the gradient map of every member utility function is bounded away from zero and from above uniformly over the domain, gives a more favorable worst case efficiency. We then consider a game where players incur costs that, from the system point of view are not additive, whereby the system problem is not merely the sum of the objectives of all players. We characterize utility functions for which the VE is efficient under this notion of efficiency. Finally we consider the imposition of a reserve price on players. The reserve price has the effect of eliminating players with low interest in the resource. The GNE is more indicative of the system optimal. We find that under certain conditions, efficiency as high as unity is obtainable by the imposition of an appropriate reserve price
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
The thesis pertains to some fundamental questions in the theory of games. Our focus is on a class of noncooperative N player games, called generalized Nash games with shared constraints, or simply, sharedconstraint games. In such a game, every strategytuple is constrained to lie in a subset C of the product space of strategies. Thus strategies available to a player are only those which when taken jointly with the strategies of all other players, form a tuple that lies in C. The set C is called the shared constraint. Despite their relevance in realworld settings, there are many theoretical properties of these games that are not well understood. What interests us in this thesis is the theoretical character of the equilibria of these games. Sharedconstraint games admit two kinds of equilibria: generalized Nash equilibria (GNE) that are illposed and often intractable and a smaller subset of them (called variational equilibria or VE) satisfying an exogenous regularity condition that are wellposed and surprisingly tractable. We seek to clarify the nature of these equilibria, study their economic implications and exploit their properties to advance the analytical theory for conventional and somewhat unconventional sharedconstraint games. The unconventional sharedconstraint games are in fact a class of dynamic games, called multileader multifollower games, which we view through the lens of shared constraints. Four questions are addressed in this thesis with the central theme as sharedconstraint games. In the first part of the thesis we present a refinement of the GNE. A refinement of an equilibrium is a subset of the set of equilibria which is nonempty whenever the original set of equilibria is nonempty. Refined equilibria are representative of the set of equilibria and have additional properties that make them more attractive as solution concepts than the original equilibria. The contribution of this work is a theory that gives sufficient conditions for a game to admit the VE as a refinement of the GNE. These conditions are expressed in terms of the Brouwer degree, which is seen to relate the GNE and the VE in a profound manner. Importantly, for certain classes of games, these conditions are also seen to be necessary. The degree theoretic relationship holds in both, primal and primaldual space. Our work unifies some previously known results and provides mathematical justification for ideas that were known to be intuitive appealing but were hitherto unsubstantiated formally. The second part of this thesis is about multileader multifollower games. These games are highly nonconvex and irregular and no reliable theory is available for claiming the existence of equilibria of these games. We develop such a theory for multileader multifollower games with shared constraints. The application of standard fixed point arguments to the reaction map of general multileader multifollower games is hindered by the lack of suitable continuity properties, amongst other requirements, in this map. We observe that these games bear a close resemblance to sharedconstraint games and present modifications of the canonical multileader multifollower game that result in sharedconstraint games, with far more favorable properties. Specifically, a global equilibrium of this game exists when a suitably defined modified reaction map admits a fixed point. Sufficient conditions for the existence of these fixed points are obtained via topological fixed point theory. Finally, the paradigm developed is applied to a class of LCPconstrained leader problems where conditions for the contractibility of the domain are derived via the theory of retracts. The third part of thesis concerns the use of variational inequalities for claiming the existence of an equilibrium to sharedconstraint games. The equilibrium conditions of a generalized Nash game can be compactly stated as a quasivariational inequality (QVI), an extension of the variational inequality (VI). Harker showed that under certain conditions on the maps defining the QVI, a solution to a related VI solves the QVI. But the application of Harker⁰́₉s result to the QVI associated with sharedconstraint games proves difficult because its hypotheses can fail to hold even for simple sharedconstraint games. We show these hypotheses are in fact impossible to satisfy in most settings. But we show that for a modified QVI, whose solution set equals that of the original QVI, the hypothesis of Harker⁰́₉s result always hold. This paves the way for applying this result to sharedconstraint games, albeit in an indirect manner. This avenue allows us to recover as a special case, a result proved by Facchinei et al., in which it is shown that a suitably defined variational inequality provides a solution to the QVI of a sharedconstraint game. In the fourth part we take a systemlevel view of sharedconstraint games that result from resource allocation. We clarify the relation between this mode of allocating resources and the other conventional modes via either perfect competition or through the use of a mechanism. We find that for perfectly competitive settings the VE is the same as the competitive equilibrium. We then compare the performance of GNE and VE of the sharedconstraint game with respect to the systemlevel objective of maximization of social welfare or aggregate utility. We are specifically interested in the efficiency of an equilibrium, which is the ratio of the aggregate utility for this equilibrium to the optimal aggregate utility, and in the lowest value this efficiency can take for a class of utility functions. We show that for a certain class of utility functions the VEs are fully efficient. We characterize this class and show that departures from this setting can lead to arbitrarily low efficiency in the worst case. Specifically, in this class, even while the VEs are efficient, GNEs can be arbitrarily inefficient, and VEs of games not belonging to the ⁰́₈efficient⁰́₉ class can have arbitrarily low efficiency in the worst case. Finally we suggest ways to remedy the low efficiency of equilibria in these cases. We find that a more restricted class of utility functions, in which the gradient map of every member utility function is bounded away from zero and from above uniformly over the domain, gives a more favorable worst case efficiency. We then consider a game where players incur costs that, from the system point of view are not additive, whereby the system problem is not merely the sum of the objectives of all players. We characterize utility functions for which the VE is efficient under this notion of efficiency. Finally we consider the imposition of a reserve price on players. The reserve price has the effect of eliminating players with low interest in the resource. The GNE is more indicative of the system optimal. We find that under certain conditions, efficiency as high as unity is obtainable by the imposition of an appropriate reserve price
Proceedings of the ACM/IEEE 4th International Conference on CyberPhysical Systems by IEEE/ACM International Conference on CyberPhysical Systems(
)
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
Mathematical foundations of complex networked information systems : Politecnico di Torino, Verrès, Italy 2009 by Mathematical foundations of complex networked information systems (Summer School)(
)
1 edition published in 2015 in English and held by 0 WorldCat member libraries worldwide
Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is selfcontained, and requires only an undergraduate mathematical background
1 edition published in 2015 in English and held by 0 WorldCat member libraries worldwide
Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is selfcontained, and requires only an undergraduate mathematical background
ANC'13 : proceedings of the 2013 Workshop on Airborne Networks and Communications : July 29, 2013, Bangalore, India by ACM MobiHoc Workshop on Airborne Networks and Communications(
)
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 0 WorldCat member libraries worldwide
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