Preemptive Priority Queue Research Articles

Multi‐layer task scheduling and resource allocation schemes considering idle resource and task priority in IoT networks

AbstractWith more and more interconnected smart devices (ISDs) accessing the Internet of Things (IoT), massive and diverse tasks need to be transformed and computed. Mobile edge computing enables the offloading of tasks to nearby servers to enhance processing efficiency, which makes ISDs idle, causing resource waste and failing to satisfy the high real‐time requirements of tasks. Besides, when tasks with different priorities are processed in the order they are generated, it will be difficult for IoT to guarantee a timely response to high‐priority tasks. To address the aforementioned issues, we establish an edge‐terminal‐local architecture by software‐defined networking to centrally manage idle ISD resource (2ISDR). Then the proposed two‐step scheduling mechanism with preemptive priority queue ensures the real‐time responses to high‐priority tasks, and the minimum resource allocation coefficients make offloading effective. Finally, we also propose a modified NSGA‐III algorithm named MNSGA‐III, which is designed to make decisions about offloading and solve resource allocation for tasks, and we correct infeasible solutions by a two‐step correction function to ensure the feasibility of MNSGA‐III. Experimental results show that the method can ensure a timely response to high‐priority tasks and optimize processing time, energy consumption, and economic cost through the utilization of 2ISDR.

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.

Reinforcement Learning-Based Joint Reliability and Performance Optimization for Hybrid-Cache Computing Servers

Computing servers play a key role in the development and process of emerging compute-intensive applications in recent years. However, they need to operate efficiently from an energy perspective viewpoint, while maximizing the performance and lifetime of the hottest server components (i.e., cores and cache). Previous methods focused on either improving energy efficiency by adopting new hybrid-cache architectures including the resistive random-access memory (RRAM) and static random-access memory (SRAM) at the hardware level, or exploring tradeoffs between lifetime limitation and performance of multicore processors under stable workloads conditions. Therefore, no work has so far proposed a co-optimization method with hybrid-cache-based server architectures for real-life dynamic scenarios taking into account scalability, performance, lifetime reliability, and energy efficiency at the same time. In this article, we first formulate a reliability model for the hybrid-cache architecture to enable precise lifetime reliability management and energy efficiency optimization. We also include the performance and energy overheads of cache switching, and optimize the benefits of hybrid-cache usage for better energy efficiency and performance. Then, we propose a runtime <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -learning-based reliability management and performance optimization approach for multicore microprocessors with the hybrid-cache architecture, jointly incorporated with a dynamic preemptive priority queue management method to improve the overall tasks’ performance by targeting to respect their end time limits. Experimental results show that our proposed method achieves up to 44% average performance (i.e., tasks execution time) improvement, while maintaining the whole system design lifetime longer than five years, when compared to the latest state-of-the-art energy efficiency optimization and reliability management methods for computing servers.

Analysis of a single server serving three queues m[x 1 ] /g1/1, m[x 2 ] /g2/1 , m[x 3 ] /g3/1 with priority services, working breakdown, modified bernoulli vacation

In this paper considers M[X1]/G1/1, M[X2]/G2/1 , M[X3]/G3/1 general queueing system with priority services . Three types of customers from different classes arrive at the system in different independent Poisson process. The server follows the non preemptive priority rule subject to working breakdown, and modified Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there is no high priority customers present in the system. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained. Also the average number of customer in the priority and non priority, preemptive priority queue and the average waiting time are derived.

Analysis and assessment of software reliability modeling with preemptive priority queueing policy

Due to the growing complexity and size of software systems in modern society, the quality requirements for computer software have become ever more stringent. In the past, many software reliability growth models (SRGMs) have been proposed to evaluate and assess the reliability and quality of software systems. Some studies have demonstrated that both infinite server queueing (ISQ) and finite server queueing (FSQ) models can be applied to describe the fault detection process (FDP) and fault correction process (FCP) of software systems. However, it has also been noted that most ISQ and FSQ models assumed and obeyed the first come first served (FCFS) rule when removing the detected faults in FDP. In practice, the detected faults generally are classified into different levels of priority and those with higher priority should be fixed earlier. That is, high-priority faults have to be removed quickly to minimize their impact on software systems. Consequently, this assumption should be properly modified or adjusted. In this paper, we proposed a preemptive priority queueing (PPQ) model that considers both a finite number of debuggers and different priority levels. In our proposed PPQ model, faults assigned higher priority would be able to preemptively acquire resources already occupied by lower priority faults. Some numerical examples based on real failure data from different open-source and closed-source software are analyzed and discussed in detail. Experimental results show that the proposed PPQ model can provide more accurate estimation capability for software reliability, compared to traditional SRGMs.

Mathematical modeling on minimizing the waiting time in (i,j) preemptive priority queueing system

In this paper, we analyze the waiting time in two stage preemptive priority queueing system. The service time considered here is k-phase Erlang distribution. We have assign the priority server to the emergency customer without affecting the regular priority unit. It is possible only if the servers are independent. In this case, we derive the steady state probability of the waiting time customers in ordinary and priority unit. A numerical example is included.

M/G/1 Preemptive Priority Queues With Finite and Infinite Buffers

Recently, M/G/1 priority queues with a finite buffer for high-priority customers and an infinite buffer for low-priority customers have applied to the analysis of communication systems with two heterogeneous traffics : delay-sensitive traffic and loss-sensitive traffic. However, these studies are limited to M/G/1 priority queues with finite and infinite buffers under a work-conserving priority discipline such as the nonpreemptive or preemptive resume priority discipline. In many situations, if a service is preempted, then the preempted service should be completely repeated when the server is available for it. This study extends the previous studies to M/G/1 priority queues with finite and infinite buffers under the preemptive repeat-different and preemptive repeat-identical priority disciplines. We derive the loss probability of high-priority customers and the waiting time distributions of high- and low-priority customers. In order to do this, we utilize the delay cycle analysis of finite-buffer M/G/1/K queues, which has been recently developed for the analysis of M/G/1 priority queues with finite and infinite buffers, and combine it with the analysis of the service time structure of a low-priority customer for the preemptive-repeat and preemptive-identical priority disciplines. We also present numerical examples to explore the impact of the size of the finite buffer and the arrival rates and service distributions of both classes on the system performance for various preemptive priority disciplines.

Performance analysis and optimization research of multi-channel cognitive radio networks with a dynamic channel vacation scheme

&lt;p style='text-indent:20px;'&gt;In order to resolve the issues of channel scarcity and low channel utilization rates in cognitive radio networks (CRNs), some researchers have proposed the idea of "secondary utilization" for licensed channels. In "secondary utilization", secondary users (SUs) opportunistically take advantage of unused licensed channels, thus guaranteeing the transmission performance and quality of service (QoS) of the system. Based on the channel vacation scheme, we analyze a preemptive priority queueing system with multiple synchronization working vacations. Under this discipline, we build a three-dimensional Markov process for this queueing model. Through the analysis of performance measures, we obtain the average queueing length for the two types of users, the mean busy period and the channel utility. By analyzing several numerical experiments, we demonstrate the effect of the parameters on the performance measures. Finally, in order to optimize the system individually and socially, we establish utility functions and provide some optimization results for PUs and SUs.&lt;/p&gt;

Optimal Pricing Strategies in Cognitive Radio Networks With Multiple Spectrums

A vast body of literature usually has treated cognitive radio (CR) networks as single-band queues with preemptive priority for mathematical tractability, although, in practice, they are multiple-spectrum CR systems. In this article, we overcome these restrictions and employ a two-server preemptive priority queue to study CR systems with multiple spectrums. We obtain a joint optimal pricing strategy to maximize profit for the service provider (SP), as well as an optimal pricing strategy to maximize social welfare from the social administrator's viewpoint. We find that the socially optimal pricing strategy is to provide free service for all PUs, whereas the joint optimal pricing strategy for SP's maximum is equivalent to the pricing strategy that maximizes the two servers' own expected net benefit.

Social welfare and price of anarchy in preemptive priority queues

Consider an unobservable M|G|1 queue with preemptive-resume scheduling and two priority classes. Customers are strategic and may join the premium class for a fee. We analyze the resulting equilibrium outcomes, equilibrium stability, and social welfare. We find that for service distributions with coefficient of variation greater than 1, there exists a unique and stable mixed equilibrium at low loads. We also establish a tight bound on the price of anarchy, which is 4∕3.

Scalability analysis of request scheduling in cloud computing

Rapid advancement of distributed computing systems enables complex services in remote computing clusters. Massive applications with large-scale and disparate characteristics also create high requirements for computing systems. Cloud computing provides a series of novel approaches to meet new trends and demands. However, some scalability issues have to be addressed in the request scheduling process and few studies have been conducted to solve these problems. Thus, this study investigates the scalability of the request scheduling process in cloud computing. We provide a theoretical definition of the scalability of this process. By modeling the scheduling server as a stochastic preemptive priority queue, we conduct a comprehensive theoretical and numerical analysis of the scalability metric under different structures and various environment configurations. The comparison and conclusion are expected to shed light on the future design and deployment of the request scheduling process in cloud computing.

Performance Simulation of Finite-Source Cognitive Radio Networks with Servers Subjects to Breakdowns and Repairs

The present paper deals with the performance evaluation of a cognitive radio network with the help of a queueing model. The queueing system contains two interconnected, not independent sub-systems. The first part is for the requests of the Primary Units (PU). The number of sources is finite, and each source generates high priority requests after a exponentially distributed time. The requests are sent to a single server unit or Primary Channel Service (PCS) with a preemptive priority queue. The service times are assumed to be exponentially distributed. The second sub-system is for the requests of the Secondary Units (SU), which is finite sources system too; the inter-request times and service times of the single server unit or Secondary system Channel Service (SCS) are assumed to be exponentially distributed, respectively. A generated high priority packet goes to the primary service unit. If the unit is idle, the service of the packet begins immediately. If the server is busy with a high priority request, the packet joins the preemptive priority queue. When the unit is engaged with a request from SUs, the service is interrupted and the interrupted low priority task is sent back to the SCS. Depending on the state of the secondary channel, the interrupted job is directed to either the server or the orbit. In case the requests from SUs find the SCS idle, the service starts, and if the SCS is busy, the packet looks for the PCS. In the case of an idle PCS, the service of the low-priority packet begins at the high-priority channel (PCS). If the PCS is busy, the packet goes to the orbit. From the orbit it retries to be served after an exponentially distributed time. The novelty of our investigation is that each server is subject to random breakdowns, in which case the interrupted request is sent to the queue or orbit, respectively. The operating and repair times of the servers are assumed to be generally distributed. Finally, all the random times included in the model construction are assumed to be independent of each other. The main aim of the paper is to analyze the effect of the nonreliability of the servers on the mean and variance of the response time for the SUs by using simulation.

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Abstract We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

English

English

Optimal Service Rate in Cognitive Radio Networks With Different Queue Length Information

Cognitive radio (CR) technology effectively overcomes spectrum inefficiency by providing the capability that unlicensed users can share the radio frequency spectrum with licensed users. In this paper, we consider a CR system with heterogeneous users. A single primary user (PU) randomly generates service requests and a licensed band processes these requests. This PU band also can be flexibly accessed by secondary users (SUs) if available. The CR system is regarded as a preemptive priority queueing system. Under different information levels, we investigate the equilibrium strategic behaviors of PU and SUs. Based on users’ strategies, we study SU’s sojourn time (i.e., the period beginning from the time an SU request enters the system and ending from the time the SU request is completed), and obtain the analytical solutions of SU’s mean sojourn time. By theoretical and numerical analysis, the SU’s mean sojourn time is found not decreasing with the service rate of PU. This phenomenon is counterintuitive, and it implies the increase of the service rate of PU does not necessarily reduce the mean sojourn time of SU. In this sense, we investigate and find optimal service rates of PU in different information levels to meet the PU’s QoS requirement and simultaneously to maximize SU’s throughput from the viewpoint of the service providers.

(N, n)-Preemptive Repeat-Different Priority Queues

(N, n)-Preemptive Repeat-Different Priority Queues

Multi-server preemptive priority queue with general arrivals and service times

We present a simple approximate solution for preemptive-resume queues with multiple servers, general (phase-type) service and general (phase-type) interarrival time distributions. In our solution, priority levels are solved one at a time in the order of decreasing priorities. Each priority level is solved approximately using a reduced state description. The complexity of our approximate solution in terms of the number of equations solved grows linearly with the number of servers and priority levels.We studied a large number of numerical examples with a range of values for mean service times and offered loads across priority levels, varying the number of servers from 8 to 48. Discrete-event simulation was used to assess the accuracy of our approximate solution. Overall, in the case of Poisson and quasi-Poisson arrivals, expected relative error for the mean number of customers in the system was below 2% while the corresponding median relative error was below 0.25%. The good accuracy of our approximation appears to extend to the case of phase-type times between arrivals, with expected relative errors for the mean number in system below 5% even for a Pareto-like distribution of interarrival times with a large coefficient of variation. Our numerical results indicate that the proposed approximation provides a relatively simple and generally accurate approach to preemptive-resume queues with larger numbers of servers and general distributions of service and interarrival times.

Heavy-traffic asymptotics of a priority polling system with threshold service policy

In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system with three queues under threshold policy. It turns out that the scaled queue-length of the critically loaded queue is exponentially distributed, independent of that of the stable queues, which possess the same distributions as a two-class priority queue with N-policy vacation. Further, we provide an approximation of the tail queue-length distribution of the stable queues, which shows that it has the same prefactors and decay rates as the classical two-class preemptive priority queue. Stochastic simulations are taken to support the results.

Exact tail asymptotics for a discrete-time preemptive priority queue

In this paper, we consider a discrete-time preemptive priority queue with different service completion probabilities for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated than the continuous-time model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the low-priority queue, as well as along the direction of the high-priority queue.

A preemptive priority queue with preemptions penalty

Preemption is one of the important features in scheduling problems. When preemption is allowed, a customer can immediately receive the service on the arrival time whenever the server is idle or the preemption is justified. While a customer receives a service, one or more preemptions may occur. The primary objective of this paper is to minimize the average waiting time that all customers spend on the system. We consider some thresholds for the maximum allowed number of preemptions and their times to prevent from having a very long waited customer. A heuristic algorithm is presented for the problem, and the implementation of the proposed approach is demonstrated using some numerical examples. In addition, the performance of the proposed algorithm is compared with another existing algorithm.