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Discounted-rate utility maximization (DRUM): A framework for delay-sensitive fair resource allocation
... Thus, the allocations of all applications are coupled. Our contributions can be summarized as follows: 1) We apply the DRUM framework, proposed in [19], in the context of allocating rates to different cellular users to exploit temporal diversity, to the problem of application rate allocation over different RATs. We demonstrate that using the DRUM framework with a discount tied to application delay sensitivity results in a fair allocation with desirable characteristics in terms of balancing the per-application tradeoff between throughput, delay, and cost. ...
... Finally, we assume that all queues carrying different flows are infinitely backlogged, i.e., we assume that the flows are elastic. B. Flow Utility: We use the Discounted Rate Utility framework introduced in [19] to capture the utility of flow i ...
... where D = min U (yc) − pcyc yc , U (yc + cmax) − pcyc yc + cmax (19) Before proving the theorem, we discuss the implications of this result. First, it is clear that the bound improves with increased prediction window w. ...
... However, if the utility functions are unknown, these methods are useful only once the utilities are learned. Many of the NUM variants with full knowledge of utilities aim to find an optimal policy that meets several constraints like stability, fairness, and resource (Neely, 2010;Eryilmaz and Koprulu, 2017;Sinha and Modiano, 2018). In this work, we only focus on resource constraint due to limited divisible resource (bandwidth, power, rate). ...
This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem, where one can not infer the loss incurred for selecting an action from observed feedback. We also introduce a new setup named Censored Semi Bandits, where the loss incurred for selecting an action can be observed under certain conditions. Finally, we study the channel selection problem in the communication networks, where the reward for an action is only observed when no other player selects that action to play in the round. These problems find applications in many fields like healthcare, crowd-sourcing, security, adaptive resource allocation, among many others. This thesis aims to address the above-described sequential decision problems by exploiting specific structures these problems exhibit. We develop provably optimal algorithms for each of these setups with weak feedback and validate their empirical performance on different problem instances derived from synthetic and real datasets.
... However, if the utility functions are unknown, these methods are useful only once the utilities are learned. Many of the NUM variants with full knowledge of utilities aim to find an optimal policy that meets several constraints like stability, fairness, and resource [3], [4], [5]. In this work, we only focus on resource constraint due to limited divisible resource (bandwidth, power, rate). ...
In this paper, we study a novel Stochastic Network Utility Maximization (NUM) problem where the utilities of agents are unknown. The utility of each agent depends on the amount of resource it receives from a network operator/controller. The operator desires to do a resource allocation that maximizes the expected total utility of the network. We consider threshold type utility functions where each agent gets non-zero utility if the amount of resource it receives is higher than a certain threshold. Otherwise, its utility is zero (hard real-time). We pose this NUM setup with unknown utilities as a regret minimization problem. Our goal is to identify a policy that performs as `good' as an oracle policy that knows the utilities of agents. We model this problem setting as a bandit setting where feedback obtained in each round depends on the resource allocated to the agents. We propose algorithms for this novel setting using ideas from Multiple-Play Multi-Armed Bandits and Combinatorial Semi-Bandits. We show that the proposed algorithm is optimal when all agents have the same utility. We validate the performance guarantees of our proposed algorithms through numerical experiments.
... However, there are notable differences between our work and traditional NUM research. Existing studies have explored various scenarios including time varying channel with delay constraints [6], delay sensitive fairness [19], multiple flow classes [20], multiple protocols [21] and so on, while assuming a static sourcedestination pair per user (flow). In contrast, in our work, a user could obtain its desired content from in-network caches as well as the content producer. ...
Wireless edge networks are promising to provide better video streaming services to mobile users by provisioning computing and storage resources at the edge of wireless network. However, due to the diversity of user interests, user devices, video versions or resolutions, cache sizes, network conditions, etc., it is challenging to decide where to place the video contents, and which cache and video version a mobile user device should select. In this paper, we study the joint optimization of cache-version selection and content placement for adaptive video streaming in wireless edge networks. We propose a set of practical distributed algorithms that operate at each user device and each network cache to maximize the overall network utility. In addition to proving that our algorithms indeed achieve the optimal performance, we implement our algorithms as well as several baseline algorithms on ndnSIM, an ns-3 based Named Data Networking simulator. Simulation evaluations demonstrate that our algorithms significantly outperform conventional heuristic solutions for adaptive video streaming.
... However, since future system events are unknown in general, [11] uses the optimum answer to this problem as a benchmark to evaluate a non-anticipating algorithm. Following this perspective [9] proposed a mobility-aware resource allocation in the Discounted Rate Utility Maximization (DRUM) framework [12]. This algorithm requires the knowledge of time-varying capacities of all radio interfaces and is applicable if the wireless channel is predictable for some specific duration. ...
Visible light communication (VLC) uses huge license-free spectral bandwidth of visible light for high-speed wireless communication. Since each VLC access point covers a small area, handovers of mobile users are inevitable. In order to deal with these handovers, developing fast and effective resource allocation algorithms is a challenge. This paper introduces the problem of mobility-aware optimization of resources in VLC networks using the T-step look-ahead policy and employing the notion of handover efficiency. It is shown that the handover efficiency can correlate the overall performance of the network with future actions based on the mobility of users. Due to the stationary nature of indoor optical wireless channels, future channel state information (CSI) can be predicted by anticipating the future locations of users. A resource allocation algorithm is thus proposed, which uses CSI to dynamically allocate network resources to users. To solve this mathematically intractable problem, a novel relaxation method is proposed, which proves to be a useful tool to develop efficient algorithms for network optimization problems with a proportional fairness utility function. The resulting algorithm is extremely faster than the previous method and awareness of mobility enhances the overall performance of the network in terms of rate and fairness utility function.
... [5]- [7]. It has been shown to provide a stochastic approximation of the optimal solution of the Network Utility Maximization problem [1], [5], [6], while it can also provide good short-term fairness performance by using discounting factors when averaging [2], [8]. For these reasons, and also for its great simplicity, GBS has become the de facto scheduling policy in 3G base stations [9]. ...
Imposing fairness in resource allocation incurs a loss of system throughput, known as the Price of Fairness (PoF). In wireless scheduling, PoF increases when serving users with very poor channel quality because the scheduler wastes resources trying to be fair. This paper proposes a novel resource allocation framework to rigorously address this issue. We introduce selective fairness: being fair only to selected users, and improving PoF by momentarily blocking the rest. We study the associated admission control problem of finding the user selection that minimizes PoF subject to selective fairness, and show that this combinatorial problem can be solved efficiently if the feasibility set satisfies a condition; in our model it suffices that the wireless channels are stochastically dominated. Exploiting selective fairness, we design a stochastic framework where we minimize PoF subject to an SLA, which ensures that an ergodic subscriber is served frequently enough. In this context, we propose an online policy that combines the drift-plus-penalty technique with Gradient-Based Scheduling experts, and we prove it achieves the optimal PoF. Simulations show that our intelligent blocking outperforms by 40 in throughput previous approaches which satisfy the SLA by blocking low-SNR users.
Visible light communication (VLC) uses huge license-free spectral bandwidth of visible light for high-speed wireless communication. Since each VLC access point covers a small area, handovers of mobile users are inevitable. In order to deal with these handovers, developing fast and effective resource allocation algorithms is a challenge. This paper introduces the problem of mobility-aware optimization of resources in VLC networks using the T-step look-ahead policy and employing the notion of handover efficiency. It is shown that the handover efficiency can correlate the overall performance of the network with future actions based on the mobility of users. Due to the stationary nature of indoor optical wireless channels, future channel state information (CSI) can be predicted by anticipating the future locations of users. A resource allocation algorithm is thus proposed, which uses CSI to dynamically allocate network resources to users. To solve this mathematically intractable problem, a novel relaxation method is proposed, which proves to be a useful tool to develop efficient algorithms for network optimization problems with a proportional fairness utility function. The resulting algorithm is extremely faster than the previous method and awareness of mobility enhances the overall performance of the network in terms of rate and fairness utility function.
The rapidly changing network topologies bring some challenges to optimize congestion control, routing and power control in delay-constrained flying ad hoc networks (FANETs). Traditional methods designed for mobile ad hoc networks (MANETs) underperform due to their poor adaptability to the changing network topologies. In this work, we propose an optimization framework with end-to-end (E2E) delay constraint, and formulate the problems as a utility maximization problem with respect to link capacity, E2E delay and flow conservation by coupling data flows and decomposing the E2E delay constraint. Further, to optimize such a non-linear maximization problem, we employ primal–dual decomposition and the delay scale factors to cast the maximization problem into several sub-problems with lower complexity. Subsequently, we propose a delay-constrained path selection algorithm and an asynchronous distributed optimization method which requires only the local channel information and outdated messages to optimize different parameters. Finally, to highlight the advantages of the proposed method, we further give the related analysis from the viewpoint of the different solutions of the maximization problem. Simulation results demonstrate that the proposed framework obtains significant network performance in terms of energy efficiency and packet timeout rate, compared with traditional methods.
In this paper, we consider the problem of rate and power allocation in a multiple-access channel (MAC). Our objective is to obtain rate and power allocation policies that maximize a general concave utility function of average transmission rates on the information-theoretic capacity region of the MAC without using queue-length information. First, we address the utility maximization problem in a nonfading channel and present a gradient projection algorithm with approximate projections. By exploiting the polymatroid structure of the capacity region, we show that the approximate projection can be implemented in time polynomial in the number of users. Second, we present optimal rate and power allocation policies in a fading channel where channel statistics are known. For the case that channel statistics are unknown and the transmission power is fixed, we propose a greedy rate allocation policy and characterize the performance difference of this policy and the optimal policy in terms of channel variations and structure of the utility function. The numerical results demonstrate superior convergence rate performance for the greedy policy compared to queue-length-based policies. In order to reduce the computational complexity of the greedy policy, we present approximate rate allocation policies which track the greedy policy within a certain neighborhood.
Abstrucl- We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many com- peting flows, where each flow is intended for a different receiver, The channel conditions may be time-varying and different for dif- ferent receivers. It is well-known that appropriately chosen queue- length based poticies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination ofqueue-length- based scheduling at the base station and congestion control imple- mented either at the base station or at the end users can lead to fair resource allocation and queue-length stability.
We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision “produces” a certain vector of “commodities”; it also has associated “traditional” queueing control effect, i.e., it determines traffic (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to find a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable.
We introduce a dynamic control algorithm, which we call Greedy Primal-Dual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traffic sources and network processing nodes may be randomly time-varying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traffic rate constraints.
We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropriately chosen queue-length based policies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queue-length-based scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queue-length stability.
We present an “opportunistic” transmission scheduling
policy that exploits time-varying channel conditions and maximizes the
system performance stochastically under a certain resource allocation
constraint. We establish the optimality of the scheduling scheme and
also that every user experiences a performance improvement over any
nonopportunistic scheduling policy when users have independent
performance values. We demonstrate via simulation results that the
scheme is robust to estimation errors and also works well for
nonstationary scenarios, resulting in performance improvements of
20%-150% compared with a scheduling scheme that does not take into
account channel conditions. Last, we discuss an extension of our
opportunistic scheduling scheme to improve “short-term”
performance
Opportunistic beamforming was discussed using dumb antennas. The focus was on the downlink of a cellular system. Multiple antennas were used at the base-station to transmit the same signals from each antenna modulated by a gain whose phase and magnitude is changing in time in a controlled but pseudo random fashion. The scheme can be interpreted as performing opportunistic beamforming: the transmit powers and phases are randomized and transmission is scheduled to the user which is close to being in the beamforming configuration.
Preface Introduction Resource Allocation Congestion Control: A Decentralized Solution Relationship to Current Internet Protocols Linear Analysis with Delay: The Single Link Case Linear Analysis with Delay: The Network Case Global Stability for a Single Link and Single Flow Stochastic Models and Their Deterministic Limits Connection-level Models Real-Time Sources and Distributed Admission Control Conclusions References Index
This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: • Queue stability theory • Backpressure, max-weight, and virtual queue methods • Primal-dual methods for non-convex stochastic utility maximization • Universal scheduling theory for arbitrary sample paths • Approximate and randomized scheduling theory • Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts.
Consider N parallel queues competing for the attention of a single server. At each time slot each queue may be connected to the server or not depending on the value of a binary random variable, the connectivity variable. Allocation at each slot; is based on the connectivity information and on the lengths of the connected queues only. At the end of each slot, service may be completed with a given fixed probability. Such a queueing model is appropriate for some communication networks with changing topology. In the case of infinite buffers, necessary and sufficient conditions are obtained for stabilizability of the system in terms of the different system parameters. The allocation policy that serves the longest connected queue stabilizes the system when the stabilizability conditions hold. The same policy minimizes the delay for the special case of symmetric queues. In a system with a single buffer per queue, an allocation policy is obtained that maximizes the throughput and minimizes the delay when the arrival and service statistics of different queues are identical.<
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We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capacity. The strategy is decoupled into separate algorithms for flow control, routing, and resource allocation, and allows each user to make decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimal operating point achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network. Analysis is performed at the packet level and considers the full effects of queueing.
In this paper, we demonstrate the existence of fair end-to-end window-based congestion control protocols for packet-switched networks with first come-first served routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of max-min fairness. The protocols use only information that is available to end hosts and are designed to converge reasonably fast. Our study is based on a multiclass fluid model of the network. The convergence of the protocols is proved using a Lyapunov function. The technical challenge is in the practical implementation of the protocols
We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using a gradient projection algorithm. In this system, sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial, and time varying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment. We discuss its fairness property.
A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable
This tutorial paper overviews recent developments in optimization-based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a clean-slate optimization-based approach to the multihop resource allocation problem naturally results in a "loosely coupled" cross-layer solution. That is, the algorithms obtained map to different layers [transport, network, and medium access control/physical (MAC/PHY)] of the protocol stack, and are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex, and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the cross-layer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems
Technical report-DRUM: A Framework for Delay-Sensitive Fair Resource Allocation
- A Eryilmaz
- I Koprulu
Rate control for communication networks: shadow prices, proportional fairness and stability
- F Kelly
- A Maulloo
- D Tan