Queue Stability Research Articles

Shannonian Maximum Entropy Balking Threshold Mechanism (BTM) for a Stable M/G/1 Queue with Significant Applications of M/G/1 Queue Theory to Augmented Reality (AR)

An exposition is undertaken to analytically derive validate the Shannonian Maximum Entropy BTM for the underlying stable queue. Most importantly, the analytic derivation of the upper and lower bounds 0f the absolute difference between Shannonian Cumulative service time distribution functions (CDFs) with and without balking. Typical numerical experiments are provided. Additionally, some applications of M/G/1 queue theory to AR are given. Some challenging open problems are addressed combined with closing remarks and future research directions.

Maximizing Computation Rate for Sustainable Wireless-Powered MEC Network: An Efficient Dynamic Task Offloading Algorithm with User Assistance

In the Internet of Things (IoT) era, Mobile Edge Computing (MEC) significantly enhances the efficiency of smart devices but is limited by battery life issues. Wireless Power Transfer (WPT) addresses this issue by providing a stable energy supply. However, effectively managing overall energy consumption remains a critical and under-addressed aspect for ensuring the network’s sustainable operation and growth. In this paper, we consider a WPT-MEC network with user cooperation to migrate the double near–far effect for the mobile node (MD) far from the base station. We formulate the problem of maximizing long-term computation rates under a power consumption constraint as a multi-stage stochastic optimization (MSSO) problem. This approach is tailored for a sustainable WPT-MEC network, considering the dynamic and varying MEC network environment, including randomness in task arrivals and fluctuating channels. We introduce a virtual queue to transform the time-average energy constraint into a queue stability problem. Using the Lyapunov optimization technique, we decouple the stochastic optimization problem into a deterministic problem for each time slot, which can be further transformed into a convex problem and solved efficiently. Our proposed algorithm works efficiently online without requiring further system information. Extensive simulation results demonstrate that our proposed algorithm outperforms baseline schemes, achieving approximately 4% enhancement while maintain the queues stability. Rigorous mathematical analysis and experimental results show that our algorithm achieves O(1/V),O(V) trade-off between computation rate and queue stability.

Task-Importance-Oriented Task Selection and Allocation Scheme for Mobile Crowdsensing

In Mobile Crowdsensing (MCS), sensing tasks have different impacts and contributions to the whole system or specific targets, so the importance of the tasks is different. Since resources for performing tasks are usually limited, prioritizing the allocation of resources to more important tasks can ensure that key data or information can be collected promptly and accurately, thus improving overall efficiency and performance. Therefore, it is very important to consider the importance of tasks in the task selection and allocation of MCS. In this paper, a task queue is established, the importance of tasks, the ability of participants to perform tasks, and the stability of the task queue are considered, and a novel task selection and allocation scheme (TSAS) in the MCS system is designed. This scheme introduces the Lyapunov optimization method, which can be used to dynamically keep the task queue stable, balance the execution ability of participants and the system load, and perform more important tasks in different system states, even when the participants are limited. In addition, the Double Deep Q-Network (DDQN) method is introduced to improve on the traditional solution of the Lyapunov optimization problem, so this scheme has a certain predictive ability and foresight on the impact of future system states. This paper also proposes action-masking and iterative training methods for the MCS system, which can accelerate the training process of the neural network in the DDQN and improve the training effect. Experiments show that the TSAS based on the Lyapunov optimization method and DDQN performs better than other algorithms, considering the long-term stability of the queue, the number and importance of tasks to be executed, and the congestion degree of tasks.

Energy‐efficient adaptive dependent task scheduling in cooperative vehicle‐infrastructure system

AbstractIn the cooperative vehicle‐infrastructure system (CVIS), due to its computation limitation, vehicles are difficult to handle computing‐intensive delay‐sensitive tasks, so offload tasks to roadside unit (RSU) become popular. Due to the complexity of vehicles’ tasks and tasks generated by different vehicles have different delay constraints, minimize energy consumption of RSUs under task dependence and delay constraints is challenging. This paper defines the task priority queuing criterion for the task priority division problem, proposes a task scheduling strategy for energy‐packet queue length tradeoff (TSET) in CVIS under RSUs distributed task scheduling problem and establishes the vehicle speed state model, task model, data queue model, task computing model and energy consumption model. After Lyapunov optimization theory transformed the optimization model, a knapsack problem was described. The simulation results verify that TSET reduces the average energy consumption of roadside units and ensures the stability of the data queue under task dependence and deadline conditions.

Dynamic Scheduling and Power Allocation with Random Arrival Rates in Dense User-Centric Scalable Cell-Free MIMO Networks

In this paper, we address scheduling methods for queue stabilization and appropriate power allocation techniques in downlink dense user-centric scalable cell-free multiple-input multiple-output (CF-MIMO) networks. Scheduling is performed by the central processing unit (CPU) scheduler using Lyapunov optimization for queue stabilization. In this process, the drift-plus-penalty is utilized, and the control parameter V serves as the weighting factor for the penalty term. The control parameter V is fixed to achieve queue stabilization. We introduce the dynamic V method, which adaptively selects the control parameter V considering the current queue backlog, arrival rate, and effective rate. The dynamic V method allows flexible scheduling based on traffic conditions, demonstrating its advantages over fixed V scheduling methods. In cases where UEs scheduled with dynamic V exceed the number of antennas at the access point (AP), the semi-orthogonal user selection (SUS) algorithm is employed to reschedule UEs with favorable channel conditions and orthogonality. Dynamic V shows the best queue stabilization performance across all traffic conditions. It shows a 10% degraded throughput performance compared to V = 10,000. Max-min fairness (MMF), sum SE maximization, and fractional power allocation (FPA) are widely considered power allocation methods. However, the power allocation method proposed in this paper, combining FPA and queue-based FPA, achieves up to 60% better queue stabilization performance compared to MMF. It is suitable for systems requiring low latency.

Resource management for computational offload in MEC networks with energy harvesting and relay assistance

In mobile edge computing (MEC) networks, the integrated application of energy harvesting (EH) and relay cooperation is a promising technology, which ensures the real-time performance of the system and computing power supply. Relay and EH cooperation also expand communication range and extend the battery life of energy-constrained devices. However, in wireless powered and relay-assisted MEC networks, it is challenging to jointly dispatch energy, and computing resources to coordinate heterogeneous performance requirements. To fill this gap, this paper examines the fundamental compromise between utility energy efficiency (UEE) and stable queue length in wireless powered and relay-assisted MEC network systems, and the amount of data transferred for each unit of energy is called UEE. The data queue and energy queue models are introduced and the constraints of stability of two queues in long term are included in the formulated problem. To tackle the fractional and nonconvex optimization problems, the Dinkelsbach method is utilized. Since optimization problems change from time to time and the long-term averaging queue stability is considered, the Lyapunov optimization theory is introduced to convert the non-convex problems into the solvable one. An online resource offloading allocation algorithm is proposed to determine the solution. In addition, the algorithm implements the control parameter V to achieve the compromise between UEE and stable queue length, while the impact of various parameters are also revealed on system performance.

Queue stability and dynamic throughput maximization in multi-agent heterogeneous wireless networks

Queue stability and dynamic throughput maximization in multi-agent heterogeneous wireless networks

Lyapunov Drift-Plus-Penalty-Based Cooperative Uplink Scheduling in Dense Wi-Fi Networks.

In high-density network environments with multiple access points (APs) and stations, individual uplink scheduling by each AP can severely interfere with the uplink transmissions of neighboring APs and their associated stations. In congested areas where concurrent uplink transmissions may lead to significant interference, it would be beneficial to deploy a cooperative scheduler or a central coordinating entity responsible for orchestrating cooperative uplink scheduling by assigning several neighboring APs to support the uplink transmission of a single station within a proximate service area to alleviate the excessive interference. Cooperative uplink scheduling facilitated by cooperative information sharing and management is poised to improve the likelihood of successful uplink transmissions in areas with a high concentration of APs and stations. Nonetheless, it is crucial to account for the queue stability of the stations and the potential delays arising from information exchange and the decision-making process in uplink scheduling to maintain the overall effectiveness of the cooperative approach. In this paper, we propose a Lyapunov drift-plus-penalty framework-based cooperative uplink scheduling method for densely populated Wi-Fi networks. The cooperative scheduler aggregates information, such as signal-to-interference-plus-noise ratio (SINR) and queue status. During the aggregation procedure, propagation delays are also estimated and utilized as a value of expected cooperation delays in scheduling decisions. Upon aggregating the information, the cooperative scheduler calculates the Lyapunov drift-plus-penalty value, incorporating a predefined model parameter to adjust the system accordingly. Among the possible scheduling candidates, the proposed method proceeds to make uplink decisions that aim to reduce the upper bound of the Lyapunov drift-plus-penalty value, thereby improving the network performance and stability without a severe increase in cooperation delay in highly congested areas. Through comprehensive performance evaluations, the proposed method effectively enhances network performance with an appropriate model parameter. The performance improvement is particularly notable in highly congested areas and is achieved without a severe increase in cooperation delays.

Stable QoE-Aware Multi-SFCs Cooperative Routing Mechanism Based on Deep Reinforcement Learning

The explosive development of the Internet of Things (IOT) has stimulated the sudden and dynamic demand pattern of potential Service Function Chain (SFC) traffic. The virtual network built based on the requirements of Multiple SFCs (Multi-SFCs), sharing the resource, should provide better Quality of Experience (QoE) for Multi-SFCs according to the real-time network status. However, simultaneous Multi-SFCs in the routing process compete for the VNF resources of the same node and preempt the same link. The instability of QoE caused by node invalidation and link faults is highlighted. Therefore, to provide a more efficient and stable service to Multi-SFCs, quantitative QoE utility and stability models and cooperative Multi-SFCs path allocation are needed. Considering the limited resources, this paper designs a stable QoE-aware Multi-SFCs Cooperative Routing Mechanism (CRM) based on Deep Reinforcement Learning (DRL). Firstly, we model the problem of Multi-SFCs cooperative routing aiming at optimizing diverse QoEs of utility, stability and delay, and formulate it as a multi-objective optimization problem. Moreover, the QoE stable queueing model based on node and link availability is formulated by Lyapunov drift, which can potentially mitigate the QoE fluctuations. Then we associate triple Dueling Deep Q-Networks (DDQNs) and propose a cooperative computing multi-task DRL to obtain the optimal path allocation policy. Experiments are conducted to verify the effectiveness and the results show that our method outperforms its peers on QoE, delay, throughput and stability.

Cost-aware defense for parallel server systems against reliability and security failures

Parallel server systems in transportation, manufacturing, and computing heavily rely on dynamic routing using connected cyber components for computation and communication. Yet, these components remain vulnerable to random malfunctions and malicious attacks, motivating the need for resilient dynamic routing that is both traffic-stabilizing and cost-efficient. In this paper, we consider a parallel server system with dynamic routing subject to reliability and stability failures. For the reliability setting, we consider an infinite-horizon Markov decision process where the system operator strategically activates a protection mechanism upon each job arrival based on traffic state observations. We prove that an optimal deterministic threshold protecting policy exists based on the dynamic programming recursion of the Hamilton–Jacobi–Bellman equation. For the security setting, we extend the model to an infinite-horizon stochastic game where the attacker strategically manipulates routing assignments. We show that both players follow a threshold strategy at every Markov perfect equilibrium. For both failure settings, we also analyze the stability of the traffic queues. Finally, we develop approximate dynamic programming algorithms to compute the optimal/equilibrium policies and present numerical examples/experiments for validation and illustration.

Energy-Efficient and Low-Complexity Transmission Control With SWIPT-NOMA for Green Cellular Networks

In this study, we consider an energy-efficient and low-complexity transmission control in a SWIPT-NOMA-based green cellular network (GCN) that consists of a green base station (GBS) and green users (GUEs). First, we formulate a non-convex problem that minimizes transmit power consumption while supporting minimum downlink user service rate, downlink data queue stability, and user battery availability. Then, we transform the problem into a Lyapunov-drift-penalty minimization problem, which can determine a new resource allocation scheme that balances transmit power consumption and queue stability. Second, the Lyapunov-drift-penalty problem is decomposed into subchannel assignment, power allocation, and power splitting (PS) ratio control problems. The subchannel assignment problem is solved using a matching theory-based low-complexity algorithm. The power allocation and PS ratio control problems are solved using the alternating optimization (AO) approach and bisection method. This decomposed subproblem-based control also enables distributed control between the GBS and GUEs. Third, we prove the convergence, optimality, and polynomial computation complexity of the proposed algorithm. Lastly, we demonstrate that the proposed control outperforms the benchmark controls regarding transmit power consumption and the achievable rate. Owing to the optimality and low complexity, the proposed control can be efficiently applied to large-scale and distributed GCNs in sixth-generation environments.

On Flow Control and Optimized Back-Off in Non-Saturated CSMA

Medium Access Control (MAC) main functions encompass contention for channel access, packet scheduling, error control, and data integrity. Channel contention is a collective function involving all stations in the network, while data integrity pertains to data flows of each individual station. We propose a design where contention related functions are separated from other data management functions. The hinge connecting contention and other data management functions is a flow control algorithm, aiming at guaranteeing stability of contention queues and load on the MAC channel. With reference to Carrier-Sense Multiple Access (CSMA), we define an analytical model of contention queues under non saturated traffic. An asymptotic analysis of the model for large number of stations yields a closed form of the optimal flow control rate. The insight gained from the model is used to design an adaptive flow control algorithm that guarantees throughput optimality for all values of the number of stations.

Age-Optimal Downlink NOMA Resource Allocation for Satellite-Based IoT Network

The upcoming satellite-based Internet of Things (S-IoT) has the capability to provide timely status updates to massive terrestrial user equipments (UEs) via non-orthogonal multiple access (NOMA), due to the worldwide coverage inherited from satellite. Considering the constrained power and storage resources while keeping the information freshness in S-IoT, we first propose three constraint conditions including average/peak power constraints, network stability and minimum requirement. Then, we formulate a long-term age of information (AoI) minimization problem under the three constraint conditions. To solve this complex long-term problem, we transform the above mentioned constraints into three queue stability problems via the Lyapunov optimization framework, thus converting our long-term multi-slot stochastic optimization problem into a series of single time slot deterministic optimization problems. Moreover, we leverage the ListNet algorithm to derive the weights of the queue backlog and channel conditions to obtain an optimized power allocation order with linear complexity. Finally, we utilize the particle swarm optimization algorithm to derive the NOMA long-term AoI minimization (AM) power allocation problem within a practical complexity, named NOMA-AM scheme. Simulation results show that the proposed NOMA-AM scheme has the lowest expected weighted sum AoI compared to several benchmark schemes.

Lyapunov optimized energy-efficient dynamic offloading with queue length constraints

With the advent of the Internet of Things (IoT), more computation-intensive applications are migrated to IoT devices. Whereas the battery with limited capacity and the processor with low computing power become the bottlenecks that limit its further development. Mobile edge computing (MEC) provides a promising solution to break through the bottlenecks. Many effective methods are proposed to guide how to offload tasks from IoT devices to MEC to enhance the computing capacity and prolong the battery life of devices. This paper investigates the task offloading problem for a multi-device single-MEC system whose status, such as task arrival rate and channel state, is dynamically changing over time and aims at minimizing the energy consumption of devices and maintaining the system stability in the long term. This problem requires lots of future information about the system, which brings a challenge since it is difficult to obtain future information. Moreover, to improve the system performance with respect to task response time, we define an individual queue length threshold for each IoT device such that the queue length of each device can stabilize around the predefined threshold. To address this problem, we first construct a virtual queue for each device to transform the queue length threshold constraint into the virtual queue stability constraint. Secondly, applying the Lyapunov optimization method, the original problem, which requires future system information, is transformed into a problem that only depends on the information of the current time. Thirdly, a dynamic energy-efficient task offloading algorithm is proposed to optimize the time-average energy consumption while maintaining the queue length constraint. This algorithm generates the offloading decision in real-time without requiring system statistical information. Lastly, simulations are conducted to analyze the effect of different parameters on performance. A group of comparisons are given, showing that the task queue length under the proposed method can be controlled effectively compared with the existing studies.

Robust Energy-Efficient Transmission for Cell-Free Massive MIMO Systems with Imperfect CSI

In this paper, we investigate a long-term power minimization problem of cell-free massive multiple-input multiple-output (MIMO) systems. To address this issue and to ensure the system queue stability, we formulate a dynamic optimization problem aiming to minimize the average total power cost in a time-varying system under imperfect channel conditions. The problem is then converted into a real-time weighted sum rate maximization problem for each time slot using the Lyapunov optimization technique. We employ approximation techniques to design robust sparse beamforming, which enables energy savings of the network and mitigates channel uncertainty. By applying direct fractional programming (DFP) and alternating optimization, we can obtain a locally optimal solution. Our DFP-based algorithm minimizes the average total power consumption of the network while satisfying the quality of service requirements for each user. Simulation results demonstrate the rapid convergence of the proposed algorithm and illustrate the tradeoff between average network power consumption and queue latency.

Semantic Communication-Based Dynamic Resource Allocation in D2D Vehicular Networks

The semantic communication mechanism enables wireless devices in vehicular networks to communicate more effectively with the semantic meaning. However, in high-dynamic vehicular networks, the transmission of semantic information faces challenges in terms of reliability and stability. To address these challenges, a long-term robust resource allocation scheme is proposed under the Device-to-Device (D2D) vehicular (D2D-V) networks, where multiple performance indicators (user satisfaction, queue stability, and communication delay) are considered. Due to the sophisticated probabilistic form with consideration of channel fluctuations, the Bernstein approximation is introduced to acquire the deterministic constraint more efficiently. The robust resource allocation problem is proposed and separated into two independent subproblems by the Lyapunov optimization method, which includes semantic access control in the application layer and power control in the physical layer. After that, the successive convex approximation method and Karush-Kuhn-Tucher conditions are adopted to solve the subproblems, thereby proposing a robust resource allocation algorithm. The simulations reveal the trade-off relationship between user satisfaction, queue stability, and communication delay, which is on the premise of meeting the user SINR requirement. Moreover, the simulations also prove the necessity of considering channel uncertainty in high-speed mobile vehicular communication scenarios.

IRS Assisted NOMA Aided Mobile Edge Computing With Queue Stability: Heterogeneous Multi-Agent Reinforcement Learning

By employing powerful edge servers for data processing, mobile edge computing (MEC) has been recognized as a promising technology to support emerging computation-intensive applications. Besides, non-orthogonal multiple access (NOMA)-aided MEC system can further enhance the spectral-efficiency with massive tasks offloading. However, with more dynamic devices brought online and the uncontrollable stochastic channel environment, it is even desirable to deploy appealing technique, i.e., intelligent reflecting surfaces (IRS), in the MEC system to flexibly tune the communication environment and improve the system energy efficiency. In this paper, we investigate the joint offloading, communication and computation resource allocation for the IRS-assisted NOMA MEC system. We first formulate a mixed integer energy efficiency maximization problem with system queue stability constraint. We then propose the Lyapunov-function-based Mixed Integer Deep Deterministic Policy Gradient (LMIDDPG) algorithm which is based on the centralized reinforcement learning (RL) framework. To be specific, we design the mixed integer action space mapping which contains both continuous mapping and integer mapping. Moreover, the award function is defined as the upper-bound of the Lyapunov drift-plus-penalty function. To enable end devices (EDs) to choose actions independently at the execution stage, we further propose the Heterogeneous Multi-agent LMIDDPG (HMA-LMIDDPG) algorithm based on distributed RL framework with homogeneous EDs and heterogeneous base station (BS) as heterogeneous multi-agent. Numerical results show that our proposed algorithms can achieve superior energy efficiency performance to the benchmark algorithms while maintaining the queue stability. Specially, the distributed structure HMA-LMIDDPG can acquire more energy efficiency gain than the centralized structure LMIDDPG.

Economical revenue maximization in mobile edge caching and blockchain enabled space-air-ground integrated networks

In this paper, we study an edge caching and blockchain enabled space-air-ground integrated networking (SAGIN) network, where a low-earth-orbit (LEO) satellite serves as the content provider, and multiple edge caching enabled unmanned aerial vehicles (UAVs) will cache some contents to provide user equipments (UEs) with satisfactory content access services together with the satellite. Moreover, there’s a blockchain system that is deployed on UAVs, to provide the network with trust mechanism without requiring a centralized authority. From the standpoint of the operator, we intend to maximize the long-term averaged economical revenue by providing UEs with satisfactory and secure content access services. To achieve this purpose, we will jointly optimize the content placement of each UAV, content replacement when each UAV is full, the access control of each UE, and the blockchain deployment strategy about each UAV. the concept of queues in Lyapunov optimization is utilized to represent the backlog of edge equipment, ensuring the stability of virtual queues on UAVs and satellites, while satisfying the caching capacity constraints for content caching and blockchain deployment. Due to the tight coupling of optimization in each time slot and the variables within each time slot, our problem, which involves stochastic optimization and binary integer programming, is challenging to solve. To address this issue, we initially employ Lyapunov optimization theory to transform and decouple the problem into individual time-slot optimization problems. Subsequently, we utilize an effective heuristic algorithm called the fireworks algorithm to solve these individual optimization problems. However, the original fireworks algorithm cannot be directly applied to our problem due to its binary characteristics and inter-coupling constraints. Therefore, we have redesigned the explosion and mutation operations to adapt them to our specific problem. Simulation results demonstrate that our proposed algorithm outperforms other baseline algorithms.

Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates

Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates

Energy-efficient and delay-guaranteed routing algorithm for software-defined wireless sensor networks: A cooperative deep reinforcement learning approach

Wireless sensor networks (WSNs) have undergone rapid development but still suffer from energy shortage issues. Meanwhile, existing energy-efficient routing approaches lack a cross-layer cooperation mechanism and cannot offer intelligent decision-making capabilities for resource-constrained nodes. In this paper, we design an intelligent routing algorithm with adaptive duty cycling for application in software-defined WSNs (SDWSNs) to maximize the network lifetime and data transmission reliability subject to a long-term data queue stability constraint. In particular, we introduce Lyapunov optimization to decouple the multistage routing optimization problem into per-frame deterministic problems with delay guarantee. To optimize the routing algorithm and adaptively adjust the duty-cycling mechanism, we propose a cooperative deep reinforcement learning (CDRL) model. Moreover, we develop a centralized training and distributed execution framework to decouple the model training and inference processes, which provides the capability of intelligent routing decision-making for resource-constrained nodes with low computational complexity. In addition, we design a new hybrid routing metric and a unique feature construction and extraction scheme to capture fine-grained information from our hybrid routing metric. The proposed CDRL algorithm adopts a cooperative and iterative model optimization strategy to achieve highly reliable data transmission and optimal long-term network performance. Simulation results demonstrate the effectiveness of the proposed algorithm in terms of network lifetime, packet delivery ratio, and statistical delay performance under various scenarios compared to the EBR-RL, EA-AGG, and QLRP algorithms.