Performance Evaluation最新文献_第5页

Editorial: Special issue on timed and stochastic approaches to system evaluation: Selected papers from QESTFORMATS 2024 社论：关于系统评估的定时和随机方法的特刊：来自QESTFORMATS 2024的论文选集

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-06-01 Epub Date: 2025-04-02 DOI: 10.1016/j.peva.2025.102485

引用次数: 0

The Multiserver Job Queuing Model with big and small jobs: Stability in the case of infinite servers 具有大小作业的多服务器作业排队模型：无限服务器情况下的稳定性

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-06-01 Epub Date: 2025-02-27 DOI: 10.1016/j.peva.2025.102477

Adityo Anggraito , Diletta Olliaro , Marco Ajmone Marsan , Andrea Marin

The Multiserver Job Queuing Model (MJQM) is a queuing system that plays a key role in the study of the dynamics of resource allocation in data centers. The MJQM comprises a waiting line with infinite capacity and a large number of servers. In this paper, we look at the limiting case in which the number of servers is infinite. Jobs are termed “multiserver” because each one is characterized by a resource demand in terms of number of simultaneously used servers and by a service duration. Job classes are defined by collecting all jobs that require the same number of servers. Job service times are independent and identically distributed random variables whose distributions depend on the class of the job. We consider the case of only two job classes: “small” jobs use a fixed number of servers, while “big” jobs use all servers in the system. The service discipline is First-In First-Out (FIFO). This means that if the job at the Head-of-Line (HOL) cannot enter service because the number of free servers is not sufficient to meet the job requirement, it blocks all subsequent jobs, even if there are sufficient free servers for them. Despite its importance, only few results exist for the MJQM, whose analysis is challenging, especially because the MJQM is not work-conserving. This implies that even the stability region of the MJQM is known only in special cases. In a previous work, we obtained a closed-form stability condition for MJQM with big and small jobs under the assumption of exponentially distributed service times for small jobs. In this paper, we compute the stability condition of MJQM with an infinite number of servers processing big and small jobs, considering different distributions of the service times of small jobs. Simulations are used to support the analytical results and to investigate the impact of service time distributions on the average job waiting time before saturation.

多服务器作业排队模型（MJQM）是一种排队系统，在数据中心资源分配动态研究中起着关键作用。MJQM由无限容量的等待队列和大量服务器组成。在本文中，我们研究了服务器数量为无穷大的极限情况。作业被称为“多服务器”，因为每个作业都以同时使用的服务器数量和服务持续时间的资源需求为特征。作业类是通过收集需要相同数量服务器的所有作业来定义的。作业服务时间是独立且同分布的随机变量，其分布取决于作业的类别。我们只考虑两个作业类别的情况：“小”作业使用固定数量的服务器，而“大”作业使用系统中的所有服务器。服务原则是先进先出（FIFO）。这意味着，如果由于空闲服务器的数量不足以满足作业需求，位于排队头（HOL）的作业无法进入服务，则它会阻塞所有后续作业，即使有足够的空闲服务器可供它们使用。尽管MJQM很重要，但只有很少的结果存在于MJQM中，其分析具有挑战性，特别是因为MJQM不节省工作。这意味着即使是MJQM的稳定区域也只有在特殊情况下才知道。在前人的工作中，我们在小作业服务时间呈指数分布的假设下，得到了具有大小作业的MJQM的闭型稳定性条件。本文考虑小任务服务时间的不同分布，计算了无限多个服务器处理大小任务时MJQM的稳定性条件。模拟用于支持分析结果，并研究服务时间分布对饱和前平均作业等待时间的影响。

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引用次数: 0

Approximation of cumulative distribution functions by Bernstein phase-type distributions 用Bernstein相型分布逼近累积分布函数

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-06-01 Epub Date: 2025-03-11 DOI: 10.1016/j.peva.2025.102480

András Horváth , Illés Horváth , Marco Paolieri , Miklós Telek , Enrico Vicario

The inclusion of generally distributed random variables in stochastic models is often tackled by choosing a parametric family of distributions and applying fitting algorithms to find appropriate parameters. A recent paper proposed the approximation of probability density functions (PDFs) by Bernstein exponentials, which are obtained from Bernstein polynomials by a change of variable and result in a particular case of acyclic phase-type distributions. In this paper, we show that this approximation can also be applied to cumulative distribution functions (CDFs), which enjoys advantageous properties and achieves similar accuracy; by focusing on CDFs, we propose an approach to obtain stochastically ordered approximations. The use of a scaling parameter in the approximation is also presented, evaluating its effect on approximation accuracy.

在随机模型中包含一般分布的随机变量通常是通过选择一个参数分布族和应用拟合算法来找到合适的参数来解决的。最近的一篇论文提出了用伯恩斯坦指数逼近概率密度函数（pdf）的方法，该方法是由伯恩斯坦多项式通过变量的变化得到的，并导致了非循环相型分布的特殊情况。在本文中，我们证明了这种近似也可以应用于累积分布函数（CDFs），它具有优越的性质并达到类似的精度；通过关注CDFs，我们提出了一种获得随机有序近似的方法。文中还介绍了尺度参数在近似中的应用，并评价了尺度参数对近似精度的影响。

引用次数: 0

Statistical properties of a class of randomized binary search algorithms 一类随机二叉搜索算法的统计性质

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-06-01 Epub Date: 2025-03-05 DOI: 10.1016/j.peva.2025.102478

Ye Xia

In this paper, we analyze the statistical properties of a randomized binary search algorithm and its variants. These algorithms have applications in caching and load balancing in distributed environments such as peer-to-peer networks, cloud storage, data centers, and content distribution networks. The basic discrete version of the problem is as follows. Suppose there are

m

servers, numbered 1, 2, …,

m

, out of which the first

k

servers are marked as special, where

k

is unknown. These

k

servers may contain a particular file or service that clients want. The objective is to select one of the marked servers uniformly at random. Considering the intended applications, we impose the constraint that there is no central controller to facilitate the selection process. We start with a basic algorithm: In each step, the client requesting the service chooses a number

y

uniformly at random from

1, 2, \dots, x

, where

x

is the number chosen in the previous step, initially set to

m

in the first step. A query is then sent to server

y

asking whether

y

is marked. If the answer is yes, the algorithm returns

y

; otherwise, the process is repeated with

x \leftarrow y

. In this paper, we primarily consider two batch versions of this algorithm in which multiple numbers are chosen in each step and multiple queries are made in parallel. We derive the mean and variance (exact and/or asymptotic) for the number of search steps in each version of the algorithm, and when possible, we give its distribution. Additionally, we analyze the access pattern of queries across the entire search space.

本文分析了一种随机化二分搜索算法及其变体的统计性质。这些算法在分布式环境（如点对点网络、云存储、数据中心和内容分发网络）中的缓存和负载平衡中有应用。这个问题的基本离散版本如下。假设有m个服务器，编号为1,2，…，m，其中前k个服务器被标记为特殊服务器，其中k是未知的。这些服务器可能包含客户端需要的特定文件或服务。。目标是均匀随机地选择一个标记的服务器。考虑到预期的应用程序，我们施加了没有中央控制器来促进选择过程的约束。我们从一个基本算法开始：在每一步中，请求服务的客户端从1、2、…、x中均匀随机选择一个数字y，其中x是在前一步中选择的数字，在第一步中初始设置为m。然后向服务器y发送查询，询问y是否被标记。如果答案是肯定的，算法返回y；否则，以x←y重复该过程。在本文中，我们主要考虑该算法的两个批处理版本，其中每一步选择多个数字，并行进行多个查询。我们推导出每个版本算法中搜索步骤数的均值和方差（精确和/或渐近），并在可能的情况下给出其分布。此外，我们还分析了整个搜索空间的查询访问模式。

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引用次数: 0

Computational algorithms and arrival theorem for non-conventional product-form solutions 非常规积型解的计算算法和到达定理

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-06-01 Epub Date: 2025-02-21 DOI: 10.1016/j.peva.2025.102469

Diletta Olliaro , Gianfranco Balbo , Andrea Marin , Matteo Sereno

Queuing networks with finite capacity are widely discussed in performance analysis literature. One approach to address the finite capacity of stations involves the implementation of a skip-over policy. Under this policy, when a customer arrives at a saturated station, service at that station is skipped, and the customer is rerouted based on the predefined network routing protocol.

Skip-over networks have been extensively investigated, and they exhibit a product-form stationary distribution under the exponential assumptions of Jackson networks. However, a comprehensive understanding of the celebrated Arrival Theorem for this class of product-form models is still lacking and relies on certain conjectures.

This paper makes three contributions: (i) it provides an in-depth comprehension of the Arrival Theorem for skip-over networks by offering a proof for the conjectures outlined in existing literature, (ii) it introduces a Mean Value Analysis (MVA) algorithm tailored for this type of queuing networks, and (iii) it explores the implications of these findings on the class of product-form queuing networks with fetching and repetitive service discipline.

有限容量排队网络在性能分析文献中得到了广泛的讨论。解决电台有限容量问题的一个办法是执行跳过政策。在此策略下，当客户到达饱和站点时，跳过该站点的服务，并根据预定义的网络路由协议重新路由客户。跳过网络已被广泛研究，在Jackson网络的指数假设下，它们表现出产品形式的平稳分布。然而，对这类产品形式模型的著名的到达定理的全面理解仍然缺乏，并且依赖于某些猜想。本文做出了三个贡献：(i)通过对现有文献中概述的猜想提供证明，它提供了对跳过网络的到达定理的深入理解，（ii）它引入了为这种类型的排队网络定制的均值分析（MVA）算法，以及（iii）它探索了这些发现对具有获取和重复服务纪律的产品形式排队网络类的影响。

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引用次数: 0

Optimizing parallel I/O performance in NVMe SSDs by Dynamic cache partitioning 通过动态缓存分区优化NVMe ssd的并行I/O性能

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-06-01 Epub Date: 2025-03-10 DOI: 10.1016/j.peva.2025.102479

Zecheng Li , Shu Yin , Xiaojun Ruan

Solid State Drive cache, implemented as on-board shared DRAM memory, can significantly enhance I/O performance by caching frequently accessed data. Although SSD caching strategies for single I/O data flows have been extensively explored, studies on cache partitioning to optimize parallel I/O in an SSD are scarce. In this paper, we present a novel dynamic cache partitioning approach designed to improve overall performance of multi-parallel I/O data flows by minimizing performance degradation of cache pollution and resource contention. By dynamically adjusting cache partition sizes for each data flow by considering cache sensitivity on performance, our strategy seeks to determine the optimal cache partition sizes to maximize overall I/O throughput. We implemented the strategy in the SSD simulator MQSim and evaluated its performance using various synthetic and real-world workloads. Our experimental results indicate that our dynamic cache partitioning strategy achieves an overall throughput increase of up to 33.22% compared to shared cache methods and outperforms static cache partitioning strategies by up to 21.19%.

固态硬盘缓存实现为板载共享DRAM内存，可以通过缓存频繁访问的数据来显著提高I/O性能。尽管针对单个I/O数据流的SSD缓存策略已经得到了广泛的研究，但针对SSD中并行I/O优化的缓存分区研究却很少。在本文中，我们提出了一种新的动态缓存分区方法，旨在通过最小化缓存污染和资源争用的性能降低来提高多并行I/O数据流的整体性能。通过考虑缓存对性能的敏感性，动态调整每个数据流的缓存分区大小，我们的策略旨在确定最佳缓存分区大小，以最大化总体I/O吞吐量。我们在SSD模拟器MQSim中实现了该策略，并使用各种合成工作负载和实际工作负载评估了其性能。我们的实验结果表明，与共享缓存方法相比，我们的动态缓存分区策略的总体吞吐量提高了33.22%，比静态缓存分区策略的吞吐量提高了21.19%。

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引用次数: 0

Symbolic state-space exploration meets statistical model checking 符号状态空间探索与统计模型检查的结合

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-03-01 Epub Date: 2024-11-02 DOI: 10.1016/j.peva.2024.102449

Mathis Niehage, Anne Remke

Efficient reachability analysis, as well as statistical model checking have been proposed for the evaluation of Hybrid Petri nets with general transitions (HPnGs). Both have different (dis-)advantages. The performance of statistical simulation suffers in large models and the number of required simulation runs to achieve a relatively small confidence interval increases considerably. The approach introduced for analytical reachability analysis of HPnGs, however, becomes infeasible for a large number of random variables. To overcome these limitations, this paper applies statistical model checking (SMC) for a stochastic variant of the Signal Temporal Logic (STL) to a pre-computed symbolic state-space representation of HPnGs, i.e., the Parametric Location Tree (PLT), which has previously been used for model checking HPnGs. Furthermore, we define how to reduce the PLT for a given state-based and path-based STL property, by introducing a three-valued interpretation of a given STL property for every location of the PLT. This paper applies learning in the presence of nondeterminism and considers four different scheduler classes. The proposed improvement is especially useful if a large number of training runs is necessary to optimize the probability that a given STL property holds. A case study on a water tank model shows the feasibility of the approach, as well as improved computation times, when applying the above-mentioned reduction for varying time bounds. We validate our results with existing analytical and simulation tools, as applicable for different types of schedulers.

为评估具有一般转换的混合 Petri 网（HPnGs），人们提出了高效的可达性分析和统计模型检查。这两种方法都有不同的优势。在大型模型中，统计模拟的性能会受到影响，而且要达到相对较小的置信区间所需的模拟运行次数也会大大增加。然而，为分析 HPnGs 的可达性而引入的方法对于大量随机变量来说是不可行的。为了克服这些局限性，本文将信号时态逻辑（STL）随机变体的统计模型检查（SMC）应用于 HPnGs 的预计算符号状态空间表示法，即参数位置树（PLT）。此外，通过为 PLT 的每个位置引入对给定 STL 属性的三值解释，我们定义了如何针对给定的基于状态和基于路径的 STL 属性缩小 PLT。本文将学习应用于存在非确定性的情况，并考虑了四种不同的调度器类别。如果需要大量的训练运行来优化给定 STL 属性成立的概率，那么所提出的改进方法就特别有用。一项关于水箱模型的案例研究表明了该方法的可行性，以及在应用上述针对不同时间界限的缩减方法时计算时间的改进。我们利用适用于不同类型调度器的现有分析和仿真工具验证了我们的结果。

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引用次数: 0

Trust your local scaler: A continuous, decentralized approach to autoscaling 信任您的本地扩展器持续、分散的自动扩展方法

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-03-01 Epub Date: 2024-11-08 DOI: 10.1016/j.peva.2024.102452

Martin Straesser , Stefan Geissler , Stanislav Lange , Lukas Kilian Schumann , Tobias Hossfeld , Samuel Kounev

Autoscaling is a critical component of modern cloud computing environments, improving flexibility, efficiency, and cost-effectiveness. Current approaches use centralized autoscalers that make decisions based on averaged monitoring data of managed service instances in fixed intervals. In this scheme, autoscalers are single points of failure, tightly coupled to monitoring systems, and limited in reaction times, making non-optimal scaling decisions costly. This paper presents an approach for continuous decentralized autoscaling, where decisions are made on a service instance level. By distributing scaling decisions of instances over time, autoscaling evolves into a quasi-continuous process, enabling great adaptability to different workload patterns. We analyze our approach on different abstraction levels, including a model-based, simulation-based, and real-world evaluation. Proof-of-concept experiments show that our approach is able to scale different applications deployed in containers and virtual machines in realistic environments, yielding better scaling performance compared to established baseline autoscalers, especially in scenarios with highly dynamic workloads.

自动扩展是现代云计算环境的重要组成部分，可提高灵活性、效率和成本效益。当前的方法使用集中式自动扩展器，根据固定时间间隔内托管服务实例的平均监控数据做出决策。在这种方案中，自动扩展器是单点故障，与监控系统紧密耦合，反应时间有限，使得非最佳扩展决策成本高昂。本文提出了一种持续分散式自动扩展方法，可在服务实例级别上做出决策。通过在一段时间内分散实例的扩展决策，自动扩展演变成了一个准连续过程，从而极大地适应了不同的工作负载模式。我们从不同的抽象层面分析了我们的方法，包括基于模型、基于仿真和基于真实世界的评估。概念验证实验表明，我们的方法能够在现实环境中扩展部署在容器和虚拟机中的不同应用，与已有的基线自动扩展器相比，尤其是在工作负载高度动态的场景中，能产生更好的扩展性能。

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引用次数: 0

Dimensioning leaky buckets in stochastic environments 随机环境下漏桶的量规

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-03-01 Epub Date: 2024-12-04 DOI: 10.1016/j.peva.2024.102461

Peter Buchholz , András Mészáros , Miklós Telek

Leaky buckets are commonly used for access control in networks, where access control stands for traffic regulation at the ingress of the network. In network calculus, which is often applied for performance analysis or dimensioning of networks, leaky buckets are the model behind piecewise linear arrival curves that specify an input bound to a network. In this paper we present the analysis of leaky bucket based access control under stochastic arrivals using fluid queues, when the access control is implemented by possibly more than one leaky buckets. This results in methods to dimension parameters of access control for different stochastic arrival processes including correlated arrivals. The approach is one step to bridge the gap between classical stochastic analysis using queuing networks and deterministic analysis using network calculus. Results are presented for stochastic arrival processes using numerical methods and for measured arrivals using trace driven simulation.

泄漏桶通常用于网络接入控制，其中接入控制代表网络入口处的流量调节。在网络微积分中，泄漏桶是指定网络输入边界的片断线性到达曲线背后的模型，通常用于网络的性能分析或尺寸确定。在本文中，我们利用流体队列分析了随机到达情况下基于漏斗的访问控制，此时访问控制可能由多个漏斗实现。这就产生了针对不同随机到达过程（包括相关到达）的访问控制参数维度的方法。这种方法是弥合使用队列网络的经典随机分析与使用网络微积分的确定性分析之间差距的一步。文中介绍了使用数值方法对随机到达过程进行分析的结果，以及使用轨迹驱动模拟对测量到达过程进行分析的结果。

引用次数: 0

Coupled queues with server interruptions: Some solutions 带有服务器中断的耦合队列：一些解决方案

IF 1 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Performance Evaluation

Pub Date : 2025-03-01 Epub Date: 2024-12-18 DOI: 10.1016/j.peva.2024.102466

Herwig Bruneel, Arnaud Devos

<div><div>We study three different <em>discrete-time</em> queueing systems, which accommodate two types of customers, named type 1 and type 2. New customers arrive independently from slot to slot, but the numbers of arrivals of both types in any slot are possibly mutually dependent; their joint probability generating function (<em>pgf</em>) is <span><math><mrow><mi>A</mi><mrow><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>. The service times of all customers are deterministically equal to one time slot.</div><div>We first consider a scenario (<em>Option</em> <span><math><mi>A</mi></math></span>) with <em>one single server</em> which is to be shared by the two customer types. Here, we assume that type-1 customers have <em>absolute service priority</em> over type-2 customers. Moreover, the server is subject to <em>random server interruptions</em>, which occur independently from slot to slot. We derive a functional equation for the steady-state joint pgf <span><math><mrow><mi>U</mi><mrow><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span> of the numbers of type-1 and type-2 customers in the system. Relying on the application of Rouché’s theorem, we are able to explicitly solve the functional equation for <em>arbitrary</em> arrival pgfs <span><math><mrow><mi>A</mi><mrow><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>, but more elegant results are obtained for some specific choices of <span><math><mrow><mi>A</mi><mrow><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>.</div><div>Next, we focus on two different scenarios (<em>Option</em> <span><math><mi>B</mi></math></span> and <em>Option</em> <span><math><mi>C</mi></math></span>) where both customer types have their <em>own dedicated server</em>. Here, there are no service priorities involved. In Option <span><math><mi>B</mi></math></span>, the two servers experience <em>simultaneous</em> interruptions, whereas in Option <span><math><mi>C</mi></math></span>, <em>only one</em> of the servers is subject to interruptions. Again, we derive functional equations for the pgf <span><math><mrow><mi>U</mi><mrow><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>. Although solving these equations for arbitrary arrival pgfs <span><math><mrow><mi>A</mi><mrow><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></ms

我们研究了三种不同的离散时间排队系统，它们容纳两种类型的顾客，分别命名为类型1和类型2。新用户在不同时段独立到达，但在任何时段两种类型的到达数量可能是相互依赖的；它们的联合概率生成函数是A（z1,z2）。所有客户的服务时间确定等于一个时隙。我们首先考虑一个场景（选项a），其中一个服务器将由两种客户类型共享。这里，我们假设类型1的客户比类型2的客户拥有绝对的服务优先级。此外，服务器还会受到随机服务器中断的影响，这些中断会独立地发生在各个插槽之间。导出了系统中1型和2型客户数量的稳态联合pgf U（z1,z2）的泛函方程。依靠rouch定理的应用，我们可以显式地求解任意到达pgfs A（z1,z2）的泛函方程，但对于A（z1,z2）的某些特定选择，我们得到了更优雅的结果。接下来，我们关注两种不同的场景（选项B和选项C），其中两种客户类型都有自己的专用服务器。这里不涉及服务优先级。在选项B中，两个服务器同时经历中断，而在选项C中，只有一个服务器受到中断的影响。再一次，我们推导出pgf U（z1,z2）的泛函方程。虽然解任意到达的pgfs A（z1,z2）的这些方程似乎是不可行的，但我们成功地找到了A（z1,z2）的特定选择的精确封闭解。值得注意的是，在选项A中获得的单服务器优先级系统的结果可以用于解决选项B的特定实例，其中两种类型的客户在任何时间段的到达部分相同。事实证明，（完全或部分）相同的到达也允许选项C的显式解。此外，我们还提供了选项B和C的函数方程可以显式解的其他示例。

引用次数: 0