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Delay Reduction via Lagrange Multipliers in Stochastic Network Optimization
, 2009
"... In this paper, we consider the problem of reducing network delay in stochastic network utility optimization problems. We start by studying the recently proposed quadratic Lyapunov function based algorithms (QLA). We show that for every stochastic problem, there is a corresponding deterministic prob ..."
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Cited by 33 (15 self)
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In this paper, we consider the problem of reducing network delay in stochastic network utility optimization problems. We start by studying the recently proposed quadratic Lyapunov function based algorithms (QLA). We show that for every stochastic problem, there is a corresponding deterministic problem, whose dual optimal solution “exponentially attracts” the network backlog process under QLA. In particular, the probability that the backlog vector under QLA deviates from the attractor is exponentially decreasing in their Euclidean distance. This not only helps to explain how QLA achieves the desired performance but also suggests that one can roughly “subtract out ” a Lagrange multiplier from the system induced by QLA. We thus develop a family of Fast Quadratic Lyapunov based Algorithms (FQLA) that achieve an [O(1/V), O(log 2 (V))] performance-delay tradeoff for problems with a discrete set of action options, and achieve a square-root tradeoff for continuous problems. This is similar to the optimal performance-delay tradeoffs achieved in prior work by Neely (2007) via drift-steering methods, and shows that QLA algorithms can also be used to approach such performance. These results highlight the “network gravity ” role of Lagrange Multipliers in network scheduling. This role can be viewed as the counterpart of the “shadow price” role of Lagrange Multipliers in flow regulation for classic flow-based network problems.
Delay analysis for cognitive radio networks with random access: A fluid queue view
- In Proc. IEEE INFOCOM
, 2010
"... Abstract—We consider a cognitive radio network where multiple secondary users (SUs) contend for spectrum usage, using random access, over available primary user (PU) channels. Our focus is on SUs ’ queueing delay performance, for which a systematic understanding is lacking. We take a fluid queue app ..."
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Cited by 32 (8 self)
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Abstract—We consider a cognitive radio network where multiple secondary users (SUs) contend for spectrum usage, using random access, over available primary user (PU) channels. Our focus is on SUs ’ queueing delay performance, for which a systematic understanding is lacking. We take a fluid queue approximation approach to study the steady-state delay performance of SUs, for cases with a single PU channel and multiple PU channels. Using stochastic fluid models, we represent the queue dynamics as Poisson driven stochastic differential equations, and characterize the moments of the SUs ’ queue lengths accordingly. Since in practical systems, a secondary user would have no knowledge of other users ’ activities, its contention probability has to be set based on local information. With this observation, we develop adaptive algorithms to find the optimal contention probability that minimizes the mean queue lengths. Moreover, we study the impact of multiple channels and multiple interfaces, on SUs’ delay performance. As expected, the use of multiple channels and/or multiple interfaces leads to significant delay reduction. I.
Efficient Resource Allocation with Flexible Channel Cooperation in OFDMA Cognitive Radio Networks
"... Abstract—Recently, a cooperative paradigm for single-channel cognitive radio networks has been advocated, where primary users can leverage secondary users to relay their traffic. However, it is not clear how such cooperation can be exploited in multi-channel networks effectively. Conventional cooper ..."
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Cited by 22 (1 self)
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Abstract—Recently, a cooperative paradigm for single-channel cognitive radio networks has been advocated, where primary users can leverage secondary users to relay their traffic. However, it is not clear how such cooperation can be exploited in multi-channel networks effectively. Conventional cooperation entails that data on one channel has to be relayed on exactly the same channel, which is inefficient in multi-channel networks with channel and user diversity. Moreover, the selfishness of users complicates the critical resource allocation problem, as both parties target at maximizing their own utility. This work represents the first attempt to address these challenges. We propose FLEC, a novel design of flexible channel cooperation. It allows secondary users to freely optimize the use of channels for transmitting primary data along with their own data, in order to maximize performance. Further, we formulate a unifying optimization framework based on Nash Bargaining Solutions to fairly and efficiently address resource allocation between primary and secondary networks, in both decentralized and centralized settings. We present an optimal distributed algorithm and sub-optimal centralized heuristics, and verify their effectiveness via realistic simulations.
Opportunistic cooperation in cognitive femtocell networks
- the IEEE Journal on Selected Areas in Communications
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 15 (2 self)
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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
LIFO-Backpressure Achieves Near Optimal Utility-Delay Tradeoff
, 2011
"... There has been considerable work developing a stochastic network utility maximization framework using Backpressure algorithms, also known as MaxWeight. A key open problem has been the development of utility-optimal algorithms that are also delay efficient. In this paper, we show that the Backpressu ..."
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Cited by 14 (7 self)
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There has been considerable work developing a stochastic network utility maximization framework using Backpressure algorithms, also known as MaxWeight. A key open problem has been the development of utility-optimal algorithms that are also delay efficient. In this paper, we show that the Backpressure algorithm, when combined with the LIFO queueing discipline (called LIFO-Backpressure), is able to achieve a utility that is within O(1/V) of the optimal value, for any scalar V ≥ 1, while maintaining an average delay of O([log(V)] 2) for all but a tiny fraction of the network traffic. This result holds for a general class of problems with Markovian dynamics. Remarkably, the performance of LIFO-Backpressure can be achieved by simply changing the queueing discipline; it requires no other modifications of the original Backpressure algorithm. We validate the results through empirical measurements from a sensor network testbed, which show a good match between theory and practice. Because some packets may stay in the queues for a very long time under LIFO-Backpressure, we further develop the LIFO p-Backpressure algorithm, which generalizes LIFO-Backpressure by allowing interleaving between FIFO and LIFO. We show that LIFO p-Backpressure also achieves the same O(1/V) close-tooptimal utility performance, and guarantees an average delay of O([log(V)] 2) for the packets that are served during the LIFO period.
Utility Optimal Scheduling in Processing Networks
"... We consider the problem of utility optimal scheduling in general processing networks with random arrivals and network conditions. These are generalizations of traditional data networks where commodities in one or more queues can be combined to produce new commodities that are delivered to other part ..."
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Cited by 13 (6 self)
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We consider the problem of utility optimal scheduling in general processing networks with random arrivals and network conditions. These are generalizations of traditional data networks where commodities in one or more queues can be combined to produce new commodities that are delivered to other parts of the network, and can be used to model problems such as in-network data fusion, stream processing, MapReduce scheduling, and grid computing. Scheduling actions are complicated by the underflow problem that arises when some queues with required components go empty. In this paper, we develop a novel methodology for constructing and analyzing online algorithms for such processing networks. Specifically, we develop the Perturbed Max-Weight algorithm (PMW) to achieve optimal utility. The idea of PMW is to perturb the weights used by the usual Max-Weight algorithm to “push ” queue levels towards non-zero values (avoiding underflows). We then show, using a novel combination of Lyapunov drift analysis and duality theory, that when the perturbations are carefully chosen, PMW is able to achieve a utility that is within O(1/V) of the optimal value for any V ≥ 1, while ensuring an average network backlog of O(V). The methodology developed here is very general and can also be applied to other problems that involve such underflow constraints. 1
Socially optimal queuing control in cognitive radio networks subject to service interruptions: to queue or not to queue
- IEEE Transaction on Wireless Communications
, 2011
"... Abstract—The main challenge to cognitive radio is the emer-gence of primary users, which can be considered as the service interruptions in a queuing system. The service interruption can incur significant delays for secondary users ’ data packets which are considered as secondary customers. Therefore ..."
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Cited by 13 (5 self)
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Abstract—The main challenge to cognitive radio is the emer-gence of primary users, which can be considered as the service interruptions in a queuing system. The service interruption can incur significant delays for secondary users ’ data packets which are considered as secondary customers. Therefore, a secondary customer needs to decide whether to join the queue or leave for other means of transmission. It is shown that the individually optimal strategy for joining the queue is characterized by a threshold of queue length. When the current queue length is above this threshold, the secondary customer should leave; otherwise it should join the queue. The socially optimal threshold of queue length is also obtained and is numerically shown to be smaller than the individually optimal one, which implies that the individually optimal strategy does not yield the socially optimal one. To bridge the gap between the individually and socially optimal strategies, a pricing mechanism is proposed to toll the service of each secondary customer, thus equalizing the two optimal strategies. When the channel statistics are unknown, an online learning procedure, based on the Kiefer-Wolfowitz algorithm, is proposed. The proposed algorithms are then demonstrated using numerical simulations. Index Terms—Cognitive radio, queuing control, service inter-ruption. I.
Opportunism, backpressure, and stochastic optimization with the wireless broadcast advantage
- Asilomar Conference on Signals, Systems, and Computers
, 2008
"... Abstract — This paper provides a tutorial treatment of recent stochastic network optimization techniques, including Lyapunov network optimization, backpressure, and max-weight decision making. A new technique of place holder bits that improves delay for networking problems with general costs is also ..."
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Cited by 12 (7 self)
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Abstract — This paper provides a tutorial treatment of recent stochastic network optimization techniques, including Lyapunov network optimization, backpressure, and max-weight decision making. A new technique of place holder bits that improves delay for networking problems with general costs is also presented. An example application is given for the problem of energy-aware scheduling and routing in a wireless mobile network with channel errors and multi-receiver diversity. The Diversity Backpressure
Streaming Scalable Videos over Multi-Hop Cognitive Radio Networks
- IEEE Trans. Wireless Communications, Vol 9
"... Abstract—We investigate the problem of streaming mul-tiple videos over multi-hop cognitive radio (CR) networks. Fine-Granularity-Scalability (FGS) and Medium-Grain-Scalable (MGS) videos are adopted to accommodate the heterogeneity among channel availabilities and dynamic network conditions. We obtai ..."
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Cited by 10 (7 self)
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Abstract—We investigate the problem of streaming mul-tiple videos over multi-hop cognitive radio (CR) networks. Fine-Granularity-Scalability (FGS) and Medium-Grain-Scalable (MGS) videos are adopted to accommodate the heterogeneity among channel availabilities and dynamic network conditions. We obtain a mixed integer nonlinear programming (MINLP) problem formulation, with objectives to maximize the overall received video quality and to achieve fairness among the video sessions, while bounding the collision rate with primary users under the presence of spectrum sensing errors. We first solve the MINLP problem using a centralized sequential fixing algorithm, and derive upper and lower bounds for the objective value. We then apply dual decomposition to develop a distributed algorithm and prove its optimality and convergence conditions. The proposed algorithms are evaluated with simulations and are shown to be effective in supporting concurrent scalable video sessions in multi-hop CR networks. Index Terms—Cross-layer optimization, dynamic spectrum access, distributed algorithm, multi-hop cognitive radio networks, video streaming. I.