General Resource Allocation Problem Research Articles

Resource Allocation for OFDM-Based Status Update Systems: A Timeliness Perspective

Increasingly more time-sensitive applications emerge in Internet of things (IoT), requiring fresh status updates. Efficient resource allocation is critical for improving the timeliness of information. This paper investigates how to allocate bandwidth and configure the transmission in an orthogonal frequency division multiplexing (OFDM)-based IoT systems for timely status updating. Specifically, a general resource allocation problem is formulated using age of information (AoI) as the timeliness metric. We first consider a static channel case where we propose a fixed time slot length policy, a fixed blocklength policy, an iterative optimization algorithm, and an approximate optimal policy to address the optimal resource allocation and transmission configuration. Then, we extend the study to quasi-static fading channel cases. In particular, sticking to the transmission rate and spectral efficiency, the four policies designated for static channel case are tailored for the quasi-static fading channel case. We show that the iterative algorithms can improve the timeliness of the system significantly. Besides, the approximate optimal policy achieves an AoI performance competitive with the iterative algorithm, while reduces the computation complexity in both channel cases.

Simple and fast algorithm for binary integer and online linear programming

In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and is free of matrix inversion. It can be viewed as both an approximate algorithm for solving binary integer LPs and a fast algorithm for solving online LP problems. The algorithm is inspired by an equivalent form of the dual problem of the relaxed LP and it essentially performs (one-pass) projected stochastic subgradient descent in the dual space. We analyze the algorithm in two different models, stochastic input and random permutation, with minimal technical assumptions on the input data. The algorithm achieves \(O\left( m \sqrt{n}\right) \) expected regret under the stochastic input model and \(O\left( (m+\log n)\sqrt{n}\right) \) expected regret under the random permutation model, and it achieves \(O(m \sqrt{n})\) expected constraint violation under both models, where n is the number of decision variables and m is the number of constraints. The algorithm enjoys the same performance guarantee when generalized to a multi-dimensional LP setting which covers a wider range of applications. In addition, we employ the notion of the permutational Rademacher complexity and derive regret bounds for two earlier online LP algorithms for comparison. Both algorithms improve the regret bound by a factor of \(\sqrt{m}\) by paying more computational cost. Furthermore, we demonstrate how to convert the possibly infeasible solution to a feasible one through a randomized procedure. Numerical experiments illustrate the general applicability and effectiveness of the algorithms.

Resource Allocation via Model-Free Deep Learning in Free Space Optical Communications

This paper investigates the general problem of resource allocation for mitigating channel fading effects in Free Space Optical (FSO) communications. The resource allocation problem is modeled as the constrained stochastic optimization framework, which covers a variety of FSO scenarios involving power adaptation, relay selection and their joint allocation. Under this framework, we propose two algorithms that solve FSO resource allocation problems. We first present the Stochastic Dual Gradient (SDG) algorithm that is shown to solve the problem exactly by exploiting the strong duality but whose implementation necessarily requires explicit and accurate system models. As an alternative we present the Primal-Dual Deep Learning (PDDL) algorithm based on the SDG algorithm, which parameterizes the resource allocation policy with Deep Neural Networks (DNNs) and optimizes the latter via a primal-dual method. The parameterized resource allocation problem incurs only a small loss of optimality due to the strong representational power of DNNs, and can be moreover implemented without knowledge of system models. A wide set of numerical experiments are performed to corroborate the proposed algorithms in FSO resource allocation problems. We demonstrate their superior performance and computational efficiency compared to the baseline methods in both continuous power allocation and binary relay selection settings.

Constrained Reinforcement Learning for Resource Allocation in Network Slicing

In network slicing, dynamic resource allocation is the key to network performance optimization. Deep reinforcement learning (DRL) is a promising method to exploit the dynamic features of network slicing by interacting with the environment. However, the existing DRL-based resource allocation solutions can only handle a discrete action space. In this letter, we tackle a general DRL-based resource allocation problem which considers a mixed action space including both discrete channel allocation and continuous energy harvesting time division, with the constraints of energy consumption and queue package length. We propose a novel DRL algorithm referred to as constrained discrete-continuous soft actor-critic (CDC-SAC) by redesigning the network architecture and policy learning process. Simulation results show that the proposed algorithm can achieve a significant performance improvement in terms of the total throughput with the strict constraints guarantee.

Distributed resource allocation: an indirect dual ascent method with an exponential convergence rate

In this paper, an indirect dual ascent method with an exponential convergence rate is proposed for a general resource allocation problem with convex objectives and weighted constraints. By introducing the indirect dual variables, the dual dynamics can be executed in a decentralized manner by all nodes over the network. In contrast to the conventional methods, consensus on all the dual variables is not required. This further leads to the fast convergence, reduced communication burden and better privacy preserving. Moreover, the exponential convergence rate of the proposed algorithm is established through the Lyapunov method and the singular perturbation theory. Application of the dynamic power dispatch problem in smart grid verifies the effectiveness and performance of the proposed algorithm.

Optimal Posted Prices for Online Resource Allocation with Supply Costs

We study a general online resource allocation problem, where a provider sells multiple types of capacity-limited resources to heterogeneous customers that arrive in a sequential and arbitrary manner. The provider charges payment from customers who purchase a bundle of resources but must pay an increasing supply cost with respect to the total resource allocated. The goal is to maximize the social welfare, namely, the total valuation of customers for their purchased bundles, minus the total supply cost of the provider for all the resources that have been allocated. We adopt the competitive analysis framework and provide an optimal posted-pricing mechanism (PPM). Our PPM is optimal in the sense that no other online algorithms can achieve a better competitive ratio.

Smart Markets for Real-Time Allocation of Multi-Product Resources: The Case of Shared Electric Vehicles

Motivated by the deep transformation of the transportation sector toward electric and shared mobility, this research develops a decision support tool that enables real-time allocation of shared electric vehicles (SEVs) to either the rental market, or - aggregated as a virtual power plant (VPP) - to the electricity market. This multi-purposing of SEVs beyond the traditional scope of mobility services can boost utilization and profitability for fleet operators while also facilitating the integration of variable rate renewable energy sources. We abstract this setting to the general problem of real-time multi-product resource allocation via smart markets. Due to a lack of suitable techniques in the literature, we develop our own general approach that leverages highly digitized real-time markets and intelligent agents to enable dynamic multi-product resource allocation. Agents continuously evaluate which markets are most attractive and strategically and iteratively place bids in the respective markets on the resource owner's behalf until all resources have been committed for a specific period. We contribute a general framework that provides a blueprint for similar multi-product resource allocation settings and demonstrate its efficacy in the domain of SEV fleets by developing tailored analytics and machine learning based solution approaches along the dimensions of this framework.

Optimizing Resource Allocation in the Short Blocklength Regime for Ultra-Reliable and Low-Latency Communications

In this paper, we aim to find the global optimal resource allocation for ultra-reliable and low-latency communications (URLLC), where the blocklength of channel codes is short. The achievable rate in the short blocklength regime is neither convex nor concave in bandwidth and transmit power. Thus, a non-convex constraint is inevitable in optimizing resource allocation for URLLC. We first consider a general resource allocation problem with constraints on the transmission delay and decoding error probability, and prove that a global optimal solution can be found in a convex subset of the original feasible region. Then, we illustrate how to find the global optimal solution for an example problem, where the energy efficiency (EE) is maximized by optimizing antenna configuration, bandwidth allocation, and power control under the latency and reliability constraints. To improve the battery life of devices and EE of communication systems, both uplink and downlink resources are optimized. The simulation and numerical results validate the analysis and show that the circuit power is dominated by the total power consumption when the average inter-arrival time between packets is much larger than the required delay bound. Therefore, optimizing antenna configuration and bandwidth allocation without power control leads to minor EE loss.

Competitive online algorithms for resource allocation over the positive semidefinite cone

We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint. The problem data arrives online, and the algorithm needs to make an irrevocable decision at each step. Of particular interest are classic experiment design problems in the online setting, with the algorithm deciding whether to allocate budget to each experiment as new experiments become available sequentially. We analyze two greedy primal-dual algorithms and provide bounds on their competitive ratios. Our analysis relies on a smooth surrogate of the objective function that needs to satisfy a new diminishing returns (PSD-DR) property (that its gradient is order-reversing with respect to the PSD cone). Using the representation for monotone maps on the PSD cone given by L\"owner's theorem, we obtain a convex parametrization of the family of functions satisfying PSD-DR. We then formulate a convex optimization problem to directly optimize our competitive ratio bound over this set. This design problem can be solved offline before the data start arriving. The online algorithm that uses the designed smoothing is tailored to the given cost function, and enjoys a competitive ratio at least as good as our optimized bound. We provide examples of computing the smooth surrogate for D-optimal and A-optimal experiment design, and demonstrate the performance of the custom-designed algorithm.

Joint spectrum allocation and energy harvesting optimization in green powered heterogeneous cognitive radio networks

We aim at maximizing the sum rate of secondary users (SUs) in OFDM-based Heterogeneous Cognitive Radio (CR) Networks using RF energy harvesting. Assuming SUs operate in a time switching fashion, each time slot is partitioned into three non-overlapping parts devoted for energy harvesting, spectrum sensing and data transmission. The general problem of joint resource allocation and structure optimization is formulated as a Mixed Integer Nonlinear Programming task which is NP-hard and intractable. Thus, we propose to tackle it by decomposing it into two subproblems. We first propose a sub-channel allocation scheme to approximately satisfy SUs’ rate requirements and remove the integer constraints. For the second step, we prove that the general optimization problem is reduced to a convex optimization task. Considering the trade-off among fractions of each time slot, we focus on optimizing the time slot structures of SUs that maximize the total throughput while guaranteeing the rate requirements of both real-time and non-real-time SUs. Since the reduced optimization problem does not have a simple closed-form solution, we thus propose a near optimal closed-form solution by utilizing Lambert-W function. We also exploit iterative gradient method based on Lagrangian dual decomposition to achieve near optimal solutions. Simulation results are presented to validate the optimality of the proposed schemes.

Network Resource Allocation via Stochastic Subgradient Descent: Convergence Rate

This paper considers a general stochastic resource allocation problem that arises widely in wireless networks, cognitive radio, networks, smart-grid communications, and cross-layer design. The problem formulation involves expectations with respect to a collection of random variables with unknown distributions, representing exogenous quantities such as channel gain, user density, or spectrum occupancy. We consider the constant step-size stochastic dual subgradient descent (SDSD) method that has been widely used for online resource allocation in networks. The problem is solved in dual domain, which results in a primal resource allocation subproblem at each time instant. The goal here is to characterize the non-asymptotic behavior of such stochastic resource allocations in an almost sure sense. It is well known that with a step size of $\epsilon $ , SDSD converges to an $\mathcal {O}(\epsilon)$ -sized neighborhood of the optimum. In practice, however, there exists a trade-off between the rate of convergence and the choice of $\epsilon $ . This paper establishes a convergence rate result for the SDSD algorithm that precisely characterizes this trade-off. Toward this end, a novel stochastic bound on the gap between the objective function and the optimum is developed. The asymptotic behavior of the stochastic term is characterized in an almost sure sense, thereby generalizing the existing results for the stochastic subgradient methods. For the stochastic resource allocation problem at hand, the result explicates the rate with which the allocated resources become near-optimal. As an application, the power and user-allocation problem in device-to-device networks is formulated and solved using the SDSD algorithm. Further intuition on the rate results is obtained from the verification of the regularity conditions and accompanying simulation results.

Dynamic resource allocation for uplink non‐orthogonal multiple access systems

This study investigates a problem of resource allocation for an uplink multi-carrier non-orthogonal multiple access (NOMA) system. To provide a general resource allocation problem, the order of successive interference cancellation (SIC), subcarrier assignment and power allocation are all considered as the optimisation variables of interest, with the objective of maximising the weighted sum rate under the transmit power constraint of each user equipment (UE). Firstly, a novel optimal SIC order is proposed based on the inherent structure of the uplink NOMA system. Then, with the optimal SIC order, the Lagrange dual method is employed to solve the joint subcarrier assignment and power allocation problem in an asymptotically optimal manner. In addition, an optimal solution of power allocation with a fixed subcarrier assignment is presented. In light of the optimal power allocation, a tight upper bound of the uplink NOMA system is developed by relaxing the number of multiplexed UEs on each subcarrier. Simulation results show that the proposed algorithm outperforms conventional orthogonal multiple access schemes and other static NOMA schemes, and as a benchmark, the upper bound reveals that multiplexing at most two UEs on each subcarrier is sufficient for the performance improvement.

Models of resource allocation optimization when solving the control problems in organizational systems

The mathematical model of optimizing the allocation of resources to reduce the time for management decisions and algorithms to solve the general problem of resource allocation. The optimization problem of choice of resources in organizational systems in order to reduce the total execution time of a job is solved. This problem is a complex three-level combinatorial problem, for the solving of which it is necessary to implement the solution to several specific problems: to estimate the duration of performing each action, depending on the number of performers within the group that performs this action; to estimate the total execution time of all actions depending on the quantitative composition of groups of performers; to find such a distribution of the existing resource of performers in groups to minimize the total execution time of all actions. In addition, algorithms to solve the general problem of resource allocation are proposed.

Optimal Tradeoff Between Sum-Rate Efficiency and Jain's Fairness Index in Resource Allocation

The focus of this paper is on studying the tradeoff between the sum efficiency and Jain's fairness index in general resource allocation problems. Such problems are frequently encountered in wireless communication systems with M users. Among the commonly-used methods to approach these problems is the one based on the α-fair policy. Analyzing this policy, it is shown that it does not necessarily achieve the optimal Efficiency-Jain tradeoff (EJT) except for the case of M=2 users. When the number of users M>2, it is shown that the gap between the efficiency achieved by the α-fair policy and that achieved by the optimal EJT policy for the same Jain's index can be unbounded. Finding the optimal EJT corresponds to solving a family of potentially difficult non-convex optimization problems. To alleviate this difficulty, we derive sufficient conditions which are shown to be sharp and naturally satisfied in various radio resource allocation problems. These conditions provide us with a means for identifying cases in which finding the optimal EJT and the rate vectors that achieve it can be reformulated as convex optimization problems. The new formulations are used to devise computationally-efficient resource schedulers that enable the optimal EJT to be achieved for both quasi-static and ergodic time-varying communication scenarios. Analytical findings are confirmed by numerical examples.

The technology of interactive resource allocation in accordance with the customizable system of rules

The article deals with the general linear problem of resource allocation. Statement of the problem is designed to complement and combine well-known methods for solving linear problems of resource allocation. The formulation of the problem is represented by the system of mandatory and orienting rules. The technology of search for solution is designed for expert working in the interactive mode of computational experiment.

Applying Bargaining Solutions to Resource Allocation in Multiuser MIMO-OFDMA Broadcast Systems

Multiuser multi-input multi-output orthogonal frequency division multiple access (MIMO-OFDMA) is regarded as an important technology for increasing the flexibility and efficiency of wireless communication systems. A well-behaved resource allocation strategy is crucial for the performance of such systems. In this paper, we systematically study the allocation problem from a game theory perspective for the multiuser downlink broadcast channel. First, we investigate the application of the Nash and Kalai-Smorodinsky bargaining games to a general resource allocation problem and propose algorithms to find the corresponding solutions. Then we apply the general solutions to the special case where spatial block diagonalization is combined with time-sharing to multiplex a subset of the users on every subcarrier. To reduce the computational complexity, a framework for simplifying the resulting algorithms is also given. Numerical results and analysis are provided to compare the performance of the different resource allocation methods.

Protocol suite for exploiting spectrum resourcesin Dynamic Spectrum Access Networks

The success and wide proliferation of wireless and mobile services places extreme pressure on the limited available wireless bandwidth. As this pressure continues to increase with smartphones, new services and users, the available bandwidth will not be able to sustain it, severely limiting the promise of computing on the move. Dynamic Spectrum Access networks (DSANs or sometimes known as Cognitive Radio Networks) offer the potential of alleviating this problem. Unlike traditional wireless networks, DSANs are not restricted to operate over a fixed bandwidth in license-free frequency spectrum. DSANs dynamically utilize the unused bandwidth in licensed bands, such as the bandwidth allocated to cellular networks, without harming the primary licensed users. While DSANs are capable of reusing an otherwise wasted bandwidth, translating the large bandwidth into application requirements, such as higher capacity and lower delays, is a complex problem. The networking protocols have to understand application requirements, monitor the unused spectrum, and dynamically adapt to schedule and route the traffic without affecting the primary licensed users. In this paper, we propose a suite of measurement-based models and protocols that enable applications to realize the lower-layer resources in a DSAN. First, we propose a centralized network-monitoring engine. It dynamically computes the network topology graph and spectrum usage statistics. Based on this information, a stochastic model predicts the available capacity and delay estimates, and exposes them to the applications using simple Application Programming Interfaces (APIs). Second, we propose a routing protocol that uses the API to construct high-capacity or low-delay routes. We have deployed the system in a test bed with software-defined radios at Carnegie Mellon University, Qatar. The proposed framework enables the design of practical and efficient higher-layer protocols. However, the more general problem of optimal resource allocation in DSAN requires solving other complex tasks, such as optimal spectrum assignment and scheduling. In the future, we plan to model and demonstrate practical solutions for these problems. We also plan to pursue distributed heuristics that adapt to mobility.

A tutorial on cross-layer optimization in wireless networks

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.

On Hochbaum's Proximity-Scaling Algorithm for the General Resource Allocation Problem

It is pointed out that the polynomial-time scaling algorithm by Hochbaum does not work correctly for the general resource allocation problem. Hochbaum's algorithm increases a variable by one unit if the variable cannot feasibly be increased by the scaling unit. We modify the algorithm to increase such a variable by the largest possible amount and show that with this modification the algorithm works correctly. The effect is to modify the factor F in the running time of Hochbaum's algorithm for finding whether a certain solution is feasible by the factor F̃ of finding the maximum feasible increment (also called the saturation capacity). Therefore, the corrected algorithm runs in O(n(log n + F̃) log(B/n)) time.

Resource Allocation with Wobbly Functions

We consider resource allocation with separable objective functions defined over subranges of the integers. While it is well known that (the maximisation version of) this problem can be solved efficiently if the objective functions are concave, the general problem of resource allocation with functions that are not necessarily concave is difficult. In this article, we focus on a large class of problem instances, with objective functions that are close to a concave function or some other smooth function, but with small irregularities in their shape. It is described that these properties are important in many practical situations. The irregularities make it hard or impossible to use known, efficient resource allocation techniques. We show that, for this class of functions the optimal solution can be computed efficiently. We support our claims by experimental evidence. Our experiments show that our algorithm in hard and practically relevant cases runs up to 40–60 times faster than the standard method.