A note on the effect of preemptive policies on the stability of a priority queue

We study the stability condition of an M/G/1 priority queue with two classes of jobs. Class 1 jobs have preemptive priority over class 2 jobs. We consider three different types of preemptions and the effects of possible work loss (due to preemption) on the stability condition for the queueing system.     

A finite capacity dynamic priority queuing model

A single server queueing model with two types of arrivals is discussed under the assumptions of Poisson arrivals, (possibly different) general services and finite waiting room for each type of customer. Under a dynamic non-preemptive priority service rule, the steady state analysis of the model is performed. A number of interesting and intuitive results are obtained. In the case when the services are of phase type, implementable algorithms are developed for computing various system performance measures. The recursive computational schemes can be used interactively in the design of such queuing systems. A number of numerical examples are discussed.     

Three priority queue applications revisited

Results indicate that the two recently introduced self-adjusting heaps are the most competitive choices for the applications considered. Further, the results indicate that only some heap structures support lazymerge/lazydelete operations well, partially confirming that algorithms based on top-down skew heap compare more favorably than those based on binomial queues, that there are strong grounds for believing the conjectured amortized time bounds for pairing heap operations, and that pairing heaps are a competitive alternative to Fibonacci heaps.     

Three priority queue applications revisited

Results indicate that the two recently introduced self-adjusting heaps are the most competitive choices for the applications considered. Further, the results indicate that only some heap structures support lazymerge/lazydelete operations well, partially confirming that algorithms based on top-down skew heap compare more favorably than those based on binomial queues, that there are strong grounds for believing the conjectured amortized time bounds for pairing heap operations, and that pairing heaps are a competitive alternative to Fibonacci heaps.This work was carried out during the author's final graduate year (1987) at Rensselaer Polytechnic Institute. Though the author is currently with Thomson Financial Networks, this is an unaffiliated paper.     

Dream chip 1: a timed priority queue

Real-time programs often need a time-tagged priority queue that must be updated on the tick of a clock. A prime example of such a queue is a list of filter coefficients that must be changed on a given sample clock. A single chip that manages a time-tagged priority queue is proposed. The queue connects either to a static random access memory (SRAM) or directly to a digital signal processor (DSP) microprocessor. The SRAM would be part of the address space of a DSP microprocessor executing digital filter code     

Cost analysis of a finite capacity queue with server breakdowns and threshold-based recovery policy

This paper analyzes a repairable M/M/1/N queueing system under a threshold-based recovery policy. The threshold-based recovery policy means that the server breaks down only if there is at least one customer in the system, and the recovery can be performed when q (1 ≤ q ≤ N) or more customers are present. For this queueing system, a recursive method is applied to obtain steady-state solutions in neat closed-form expressions. We then develop some important system characteristics, such as the number of customers in the system, the probability that the server is busy, the effective arrival rate and the expected waiting time in the system, etc. A cost model is constructed to determine the optimal threshold value, the optimal system capacity and the optimal service rate at a minimum cost. In order to solve this optimization problem, the direct search method and Newton's method are employed. Sensitivity analysis is also conducted with various system parameters. Finally, we present some managerial insights through an application example.     

Analysis of a nonpreemptive priority queue with SPP arrivals of high class

This paper considers a nonpreemptive priority queueing system with two priority classes of customers, where high priority customers arrive to the system in accordance with a switched Poisson process (SPP) and low priority customers in accordance with a Poisson process. Using the supplementary variable technique, we derive the joint probability generating function of the stationary queue length distributions and the Laplace-Stieltjes transforms of the stationary waiting time distributions of high and low priority customers. We also present some numerical results in order to show the computational feasibility of the analytical results.     

Interdeparture times from a queuing system with preemptive resume priority

We derive the Laplace-Stieltjes transform of the limiting interdeparture times distribution for each class of customers of a queuing system with preemptive resume priority, Poisson inputs and general service times. Numerical results and an application to queuing networks are also given.     

Waiting time distribution in a two-class two-server heterogeneous priority queue

Our aim is to analyze a Markovian two-class two-server queue with non-preemptive heterogeneous priority structures. We use matrix-geometric methods and derive the stationary distribution of queue lengths. To obtain the distribution of waiting times, we develop a dedicated algorithm by extending the approach of Ramaswami and Lucantoni.     

Semaphore queue priority assignment for real-time multiprocessorsynchronization

Prior work on real time scheduling with global shared resources in multiprocessor systems assigns as much blocking as possible to the lowest priority tasks. We show that better schedulability can be achieved if global blocking is distributed according to the blocking tolerance of tasks rather than their execution priorities. We describe an algorithm that assigns global semaphore queue priorities according to blocking tolerance, and we present simulation results demonstrating the advantages of this approach with rate monotonic scheduling. Our simulations also show that a simple FIFO usually provides better real time schedulability with global semaphores than priority queues that use task execution priorities     

中心队列二次门限服务的轮询系统分析

采用嵌入Markov链和概率母函数的方法对门限服务优先级排队系统进行分析,提出普通队列和高优先级队列分别采用基本门限和二级门限的服务机制,得出了平均排队队长和平均查询周期的解析式。     

Analysis of a finite buffer queue with different scheduling and push-out schemes

A queueing system M₁, M₂/G₁, G₂/1/N with different scheduling and push-out scheme is analyzed in this paper. This work is motivated by the study of the performance of an output link of ATM switches with traffic of two classes with different priorities. However, the queueing model developed in this paper is more general than that of the output link of ATM switches with two-class priority traffic. General service time distributions are allowed for classes 1 and 2 and a general service discipline function, ₁(i, j), is introduced where ₁(i, j) is the probability that a class 1 packet will be served, given that there are i class 1 and j class 2 packets waiting for service. An exact solution is obtained for the loss probabilities for classes 1 and 2, the queue length distribution and the mean waiting time for class 1. The queue length distribution and the mean waiting time for class 2 are calculated approximately. It is shown that the approximation is an upper bound and the error due to the approximation is very small when the loss probability of class 2 is small (e.g., less than 0.01).     

Design and implementation of an efficient priority queue

We present a data structure, based upon a hierarchically decomposed tree, which enables us to manipulate on-line a priority queue whose priorities are selected from the interval 1,,n with a worst case processing time of (log logn) per instruction. The structure can be used to obtain a mergeable heap whose time requirements are about as good. Full details are explained based upon an implementation of the structure in a PASCAL program contained in the paper.Work supported by grant CR 62-50. Netherlands Organization for the Advancement of Pure Research (Z.W.O.).     

优先级队列的缓存管理机制的性能分析

为了解决好计算机网络中的多媒体通信以及对服务质量的要求,提出了一种基于优先级队列的缓存管理机制。详细研究了该机制的实现原理和方法,并给出了相关的性能分析,并建立端对端多媒体通信系统环境,进行了实验,证明了该缓存管理机制能很好地解决多媒体通信的拥塞控制,满足多媒体通信服务质量的要求。     

Analysis of a multi-server queue with two priority classes and (M, N)-threshold service schedule I: non-preemptive priority

In this paper, we propose an ( M , N )-threshold non-preemptive priority service schedule for a queueing system consisting of two-parallel queues and a multi-server. The arrival process for each queue is Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.     

关于RTOS抢占式调度及优先级反转的几点探讨

抢占式调度是RTOS的一个重要的调度策略,它保证了嵌入式系统的实时性.合理地分配任务的优先级和使用系统资源将会大大提高系统的性能.而解决优先级反转问题将保证系统共享资源的合理使用和多任务的正常运行.在对RTOS抢占式调度策略的研究的基础上,指出了什么是优先级反转,以及问题发生的原因,并给出了优先级继承和优先级封顶的解决方法.     

Parallel heap: An optimal parallel priority queue

We describe a new parallel data structure, namely parallel heap, for exclusive-read exclusive-write parallel random access machines. To our knowledge, it is the first such data structure to efficiently implement a truly parallel priority queue based on a heap structure. Employing p processors, the parallel heap allows deletions of (p) highest priority items and insertions of (p) new items, each in O(log n) time, where n is the size of the parallel heap. Furthermore, it can efficiently utilize processors in the range 1 through n.This work was supported by U.S. Army's PM-TRADE contract N61339-88-g-0002, Florida High Technology and Industry grant 11-28-716, and Georgia State University's internal research support during spring and summer quarters, 1991.     

Smart priority queue algorithms for self-optimizing event storage

Low run-time overhead, self-adapting storage policies for priority queues called smart priority queue (SPQ) techniques are developed and evaluated. The proposed SPQ policies employ a low-complexity linear queue for near-head activities and a rapid-indexing variable bin-width calendar queue for distant events. The SPQ configuration is determined by monitoring queue access behavior using cost-scoring factors and then applying heuristics to adjust the organization of the underlying data structures. To illustrate and evaluate the method, an SPQ-based scheduler for discrete event simulation has been implemented and was used to assess the resulting efficiency, components of access time, and queue usage distributions of the existing and proposed algorithms. Results indicate that optimizing storage to the spatial distribution of queue access can decrease HOLD operation cost between 25% and 250% over existing algorithms such as calendar queues.     

A priority queue with interruptions of service permitted after a time quantum

Summary The queueing theory is applied to analyse a model of a multiprogramming operating system in which preemptive priorities are used for scheduling the service of concurrent streams of requests. Preemptions are permitted at the end of each service quantum. Mean waiting times and higher statistical moments in the M/G/1 system analysed are computed.     

The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity

We propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using discretization, this system is approximately described by a multi-regime Markov fluid queue for which numerical algorithms are available. The computational complexity of the proposed method is linear in the number of regimes used for discretization. We provide numerical examples to validate the proposed approach.