Efficient scheduling of multi-antenna broadcast systems

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 65-67).In this thesis, we study the problem of efficiently scheduling users in a multi-antenna Gaussian broadcast channel with 1M transmit antennas and K independent receivers each with a single receive antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain., and selects a second user from the next L - 1 largest ones to form the best pair, taking the orientation of channel vectors into account as well. We prove that the expected rate gap converges to 1/(L - 1) nats/symbol when the total number of users K tends to infinity. Allowing L to increase with K, it; may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while dramatically reducing the feedback overhead and operational complexity. Next, we tackle the problem of maximizing a weighted sum rate in a scenario with heterogeneous user characteristics.(cont.) We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at most MC users, where C denotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.by Krishna Prasanna Jagannathan.S.M

Asymptotic performance of queue length based network control policies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 199-204).In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length information to perform effectively, which inevitably adds to the control overheads in a network. Therefore, it is important to understand the role played by queue length information in network control, and its impact on various performance metrics. In this thesis, we study the interplay between the asymptotic behavior of buffer occupancy, queue length information, and traffic statistics in the context of scheduling, flow control, and resource allocation. First, we consider a single-server queue and deal with the question of how often control messages need to be sent in order to effectively control congestion in the queue. Our results show that arbitrarily infrequent queue length information is sufficient to ensure optimal asymptotic decay for the congestion probability, as long as the control information is accurately received. However, if the control messages are subject to errors, the congestion probability can increase drastically, even if the control messages are transmitted often. Next, we consider a system of parallel queues sharing a server, and fed by a statistically homogeneous traffic pattern. We obtain the large deviation exponent of the buffer overflow probability under the well known max-weight scheduling policy. We also show that the queue length based max-weight scheduling outperforms some well known queue-blind policies in terms of the buffer overflow probability. Finally, we study the asymptotic behavior of the queue length distributions when a mix of heavy-tailed and light-tailed traffic flows feeds a system of parallel queues. We obtain an exact asymptotic queue length characterization under generalized max-weight scheduling. In contrast to the statistically homogeneous traffic scenario, we show that max-weight scheduling leads to poor asymptotic behavior for the light-tailed traffic, whereas a queue-blind priority policy gives good asymptotic behavior.by Krishna Prasanna Jagannathan.Ph.D

The Impact of Queue Length Information on Buffer Overflow in Parallel Queues

We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. We first characterize the exponent of the buffer overflow probability and the most likely overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals to each queue, we show that the buffer overflow exponents can be simply expressed in terms of the total system occupancy exponent of $m$ parallel queues, for some m ≤ N. We next turn our attention to the rate of queue length information needed to operate a scheduling policy, and its relationship to the buffer overflow exponents. It is known that queue length blind policies such as processor sharing and random scheduling perform worse than the queue aware LQF policy, when it comes to buffer overflow probability. However, we show that the overflow exponent of the LQF policy can be preserved with arbitrarily infrequent queue length updates.National Science Foundation (U.S.) (Grant CNS-0626781)National Science Foundation (U.S.) (Grant CNS0915988)United States. Army Research Office. Multidisciplinary University Research Initiativ

On the Role of Queue Length Information in Network Control

We study the role played by queue length information in the operation of flow control and server allocation policies. We first consider a simple model of a single server queue with congestion-based flow control. The input rate at any instant is decided by a flow control policy, based on the queue occupancy. We identify a simple “two-threshold” control policy, which achieves the best possible exponential scaling for the queue congestion probability, for any rate of control. We show that when the control channel is reliable, the control rate needed to ensure the optimal decay exponent for the congestion probability can be made arbitrarily small. However, if control channel erasures occur probabilistically, we show the existence of a critical erasure probability threshold beyond which the congestion probability undergoes a drastic increase due to the frequent loss of control packets. We also determine the optimal amount of error protection to apply to the control signals by using a simple bandwidth sharing model. Finally, we show that the queue length based server allocation problem can also be treated using this framework and that the results obtained for the flow control setting can also be applied to the server allocation case

Scheduling of multi-antenna broadcast systems with heterogeneous users

We study the problem of efficiently scheduling users in a Gaussian broadcast channel with M transmit antennas and K independent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the next L - 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of users K tends to infinity. Allowing L to increase with K, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing a weighted sum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at most MC users, where C denotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users

A state action frequency approach to throughput maximization over uncertain wireless channels

We consider scheduling over a wireless system, where the channel state information is not available a priori to the scheduler, but can be inferred from the past. Specifically, the wireless system is modeled as a network of parallel queues. We assume that the channel state of each queue evolves stochastically as an ON/OFF Markov chain. The scheduler, which is aware of the queue lengths but is oblivious of the channel states, has to choose one queue at a time for transmission. The scheduler has no information regarding the current channel states, but can estimate them by using the acknowledgment history. We first characterize the capacity region of the system using tools from Markov Decision Processes (MDP) theory. Specifically, we prove that the capacity region boundary is the uniform limit of a sequence of Linear Programming (LP) solutions. Next, we combine the LP solution with a queue length based scheduling mechanism that operates over long `frames,' to obtain a throughput optimal policy for the system. By incorporating results from MDP theory within the Lyapunov-stability framework, we show that our frame-based policy stabilizes the system for all arrival rates that lie in the interior of the capacity region.National Science Foundation (U.S.) (NSF grants CNS-0626781)National Science Foundation (U.S.) (NSF grant CNS-0915988)United States. Army Research Office (ARO Muri Grant W911NF-08-1-0238)Israel Science Foundation (contract 890015

Non-Cooperative Spectrum Access -- The Dedicated vs. Free Spectrum Choice

We consider a dynamic spectrum access system in which Secondary Users (SUs) choose to either acquire dedicated spectrum or to use spectrum-holes (white spaces) which belong to Primary Users (PUs). The trade-off incorporated in this decision is between immediate yet costly transmission and free but delayed transmission (a consequence of both the possible appearance of PUs and sharing the spectrum holes with multiple SUs). We first consider a system with a single PU band, in which the SU decisions are fixed. Employing queueing-theoretic methods, we obtain explicit expressions for the expected delays associated with using the PU band. Based on that, we then consider self-interested SUs and study the interaction between them as a non-cooperative game. We prove the existence and uniqueness of a symmetric Nash equilibrium, and characterize the equilibrium behavior explicitly. Using our equilibrium results, we show how to maximize revenue from renting dedicated bands to SUs and briefly discuss the extension of our model to multiple PUs. Finally, since spectrum sensing can be resource-consuming, we characterize the gains provided by this capability.National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (Grant CNS-0916263)National Science Foundation (U.S.) (Grant CNS-1054856)National Science Foundation (U.S.). Engineering Research Centers Program (Center for Integrated Access Networks Grant EEC-0812072)United States. Office of Naval Research (Grant N00014-12-1-0064)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Scheduling strategies to mitigate the impact of bursty traffic in wireless networks

Recent work has shown that certain queue-length based scheduling algorithms, such as max-weight, can lead to poor delays in the presence of bursty traffic. To overcome this phenomenon, we consider the problem of designing scheduling policies that are robust to bursty traffic, while also amenable to practical implementation. Specifically, we discuss two mechanisms, one based on adaptive CSMA, and the second based on maximum-weight scheduling with capped queue lengths. We consider a simple queueing network consisting of two conflicting links. The traffic served by the first link is bursty, and is modeled as being heavy-tailed, while traffic at the second link is modeled using a light-tailed arrival process. In this setting, previous work has shown that even the light-tailed traffic would experience heavy-tailed delays under max-weight scheduling. In contrast, we demonstrate a threshold phenomenon in the relationship between the arrival rates and the queue backlog distributions. In particular, we show that with an adaptive CSMA scheme, when the arrival rate of the light-tailed traffic is less than a threshold value, the light-tailed traffic experiences a light-tailed queue backlog at steady state, whereas for arrival rates above the same threshold, the light-tailed traffic experiences a heavy-tailed queue backlog. We also show that a similar threshold behavior for max-weight scheduling with capped queue lengthsNational Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (Grant CNS-1217048)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

Throughput Optimal Scheduling Over Time-Varying Channels in the Presence of Heavy-Tailed Traffic

We study the problem of scheduling over time varying links in a network that serves both heavy-tailed and light tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic (the heavy queue), and the other receives light-tailed traffic (the light queue). The queues are connected to the server through time-varying ON/OFF links, which model fading wireless channels. We first show that the policy that gives complete priority to the light-tailed traffic guarantees the best possible tail behavior of both queue backlog distributions, whenever the queues are stable. However, the priority policy is not throughput maximizing, and can cause undesirable instability effects in the heavy queue. Next, we study the class of throughput optimal max-weight-α scheduling policies. We discover a threshold phenomenon, and show that the steady state light queue backlog distribution is heavy-tailed for arrival rates above a threshold value, and light-tailed otherwise. We also obtain the exact tail coefficient of the light queue backlog distribution under max-weight-α scheduling. Finally, we study a log-max-weight scheduling policy, which is throughput optimal, and ensures that the light queue backlog distribution is light-tailed.National Science Foundation (U.S.) (Grant CNS-1217048)National Science Foundation (U.S.) (Grant CNS-0915988)National Science Foundation (U.S.) (CMMI-1234062)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

The impact of queue length information on buffer overflow in parallel queues

We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. In the first part of the paper, we characterize the buffer overflow exponents and the likeliest overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals to each queue, we show that the buffer overflow exponent can be simply expressed in terms of the total system occupancy exponent of m parallel queues, for some m ≤ N. We next turn our attention to the rate of queue length information needed to operate a scheduling policy, and its relationship to the buffer overflow exponents. It is known that LQF scheduling has superior overflow exponents compared to queue blind policies such as processor sharing (PS) and random scheduling. However, we show that the overflow exponent of the LQF policy can be preserved under arbitrarily infrequent queue length information.National Science Foundation (U.S.) (grant CNS-0626781National Science Foundation (U.S.) (grant CNS- 0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (MURI) (Multidisciplinary University Research Initiative (MURI) (grant W911NF-08-1-0238