Performance Evaluation最新文献

{"title":"Energy-performance tradeoffs in server farms with batch services and setup times","authors":"Thu Le-Anh ,&nbsp;Tuan Phung-Duc","doi":"10.1016/j.peva.2025.102468","DOIUrl":"10.1016/j.peva.2025.102468","url":null,"abstract":"<div><div>Data centers consume a large amount of energy, much of which is wasted due to idle servers. Turning off idle servers might be an effective power-saving solution; however, there is a trade-off between energy savings and system performance. Hence, we propose a setup queueing model with a batching policy that allows servers to process a set of jobs simultaneously to minimize power consumption while maintaining acceptable performance. We consider an M/M/<span><math><mrow><mi>c</mi><mo>/</mo></mrow></math></span>SET–BATCH queue, a multi-server batch service queue with a fixed batch size and setup times, and some variants, including systems in which idle servers delay before turning off or systems in which the batch size is dynamic. We analyze the steady-state probabilities and system performance of the M/M/<span><math><mrow><mi>c</mi><mo>/</mo></mrow></math></span>SET–BATCH system and its variants. Our analysis of the M/M/<span><math><mrow><mi>c</mi><mo>/</mo></mrow></math></span>SET–BATCH system with lower computational complexity is made possible by utilizing the special structure of the model. In addition, we use simulations to compare the M/M/<span><math><mrow><mi>c</mi><mo>/</mo></mrow></math></span>SET–BATCH model with some other variants with different setup time distributions. The results suggest that the model performs better when the setup time has a larger coefficient of variation. Our results indicate that the batching policy enhances the system performance, especially when we allow servers to be idle before turning them off.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102468"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Controller synthesis in timed Büchi automata: Robustness and punctual guards","authors":"Benoît Barbot ,&nbsp;Damien Busatto-Gaston ,&nbsp;Catalin Dima ,&nbsp;Youssouf Oualhadj","doi":"10.1016/j.peva.2025.102483","DOIUrl":"10.1016/j.peva.2025.102483","url":null,"abstract":"<div><div>We consider the synthesis problem on timed automata with Büchi objectives, where delay choices made by a controller are subjected to small perturbations. Usually, the controller needs to avoid punctual guards, such as testing the equality of a clock to a constant. In this work, we generalize to a robustness setting that allows for punctual transitions in the automaton to be taken by controller with no perturbation. In order to characterize cycles that resist perturbations in our setting, we introduce a new structural requirement on the reachability relation along an accepting cycle of the automaton. This property is formulated on the region abstraction, and generalizes the existing characterization of winning cycles in the absence of punctual guards. We show that the problem remains within <span><math><mi>PSPACE</mi></math></span> despite the presence of punctual guards.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102483"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalized result for the discrete-time two-queue randomly alternating service system","authors":"Herwig Bruneel,&nbsp;Arnaud Devos,&nbsp;Joris Walraevens","doi":"10.1016/j.peva.2025.102484","DOIUrl":"10.1016/j.peva.2025.102484","url":null,"abstract":"<div><div>In this paper, we revisit the discrete-time two-queue <em>randomly alternating service</em> system, where one common server is shared by two queues by allocating the server, independently from slot to slot, with fixed probabilities to either queue. Arrivals of new customers into the two-queue system occur independently from slot to slot, but may be mutually dependent within a slot. They are characterized by the joint probability generating function (<em>pgf</em>) <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> of the numbers of arrivals in both queues during one time slot. The service times of all customers are equal to exactly one time slot.</div><div>We extend various existing results with respect to the queueing behavior of this system. Specifically, we show that the <em>exact</em> solutions that were previously found 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 system contents in both queues for the scenarios of <em>independent Bernoulli</em> arrivals, <em>identical Bernoulli</em> arrivals, <em>global geometric</em> arrivals, <em>global geometric group</em> arrivals, and the superposition of <em>identical Bernoulli</em> arrivals and <em>global geometric (group)</em> arrivals, are all special cases of a more general result, which is valid for a whole class of 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> that (among others) encompasses the aforementioned specific arrival scenarios. However, the defined class is much broader than this, and our new result allows the solution for entirely new arrival pgfs as well. We illustrate this abundantly with a large number of detailed examples. The proof of the general result is a mainly <em>algebraic</em> one and, unlike earlier studies, does not require intricate techniques from complex-function analysis.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102484"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Editorial: Special issue on timed and stochastic approaches to system evaluation: Selected papers from QESTFORMATS 2024","authors":"","doi":"10.1016/j.peva.2025.102485","DOIUrl":"10.1016/j.peva.2025.102485","url":null,"abstract":"","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102485"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Multiserver Job Queuing Model with big and small jobs: Stability in the case of infinite servers","authors":"Adityo Anggraito ,&nbsp;Diletta Olliaro ,&nbsp;Marco Ajmone Marsan ,&nbsp;Andrea Marin","doi":"10.1016/j.peva.2025.102477","DOIUrl":"10.1016/j.peva.2025.102477","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102477"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statistical properties of a class of randomized binary search algorithms","authors":"Ye Xia","doi":"10.1016/j.peva.2025.102478","DOIUrl":"10.1016/j.peva.2025.102478","url":null,"abstract":"<div><div>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 <span><math><mi>m</mi></math></span> servers, numbered 1, 2, …, <span><math><mi>m</mi></math></span>, out of which the first <span><math><mi>k</mi></math></span> servers are marked as special, where <span><math><mi>k</mi></math></span> is unknown. These <span><math><mi>k</mi></math></span> 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 <span><math><mi>y</mi></math></span> uniformly at random from <span><math><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>x</mi></mrow></math></span>, where <span><math><mi>x</mi></math></span> is the number chosen in the previous step, initially set to <span><math><mi>m</mi></math></span> in the first step. A query is then sent to server <span><math><mi>y</mi></math></span> asking whether <span><math><mi>y</mi></math></span> is marked. If the answer is yes, the algorithm returns <span><math><mi>y</mi></math></span>; otherwise, the process is repeated with <span><math><mrow><mi>x</mi><mo>←</mo><mi>y</mi></mrow></math></span>. 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.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102478"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computational algorithms and arrival theorem for non-conventional product-form solutions","authors":"Diletta Olliaro ,&nbsp;Gianfranco Balbo ,&nbsp;Andrea Marin ,&nbsp;Matteo Sereno","doi":"10.1016/j.peva.2025.102469","DOIUrl":"10.1016/j.peva.2025.102469","url":null,"abstract":"<div><div>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 <em>skip-over</em> 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.</div><div>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 <em>Arrival Theorem</em> for this class of product-form models is still lacking and relies on certain conjectures.</div><div>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.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102469"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation of cumulative distribution functions by Bernstein phase-type distributions","authors":"András Horváth ,&nbsp;Illés Horváth ,&nbsp;Marco Paolieri ,&nbsp;Miklós Telek ,&nbsp;Enrico Vicario","doi":"10.1016/j.peva.2025.102480","DOIUrl":"10.1016/j.peva.2025.102480","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102480"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimizing parallel I/O performance in NVMe SSDs by Dynamic cache partitioning","authors":"Zecheng Li ,&nbsp;Shu Yin ,&nbsp;Xiaojun Ruan","doi":"10.1016/j.peva.2025.102479","DOIUrl":"10.1016/j.peva.2025.102479","url":null,"abstract":"<div><div>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%.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102479"},"PeriodicalIF":1.0,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symbolic state-space exploration meets statistical model checking","authors":"Mathis Niehage,&nbsp;Anne Remke","doi":"10.1016/j.peva.2024.102449","DOIUrl":"10.1016/j.peva.2024.102449","url":null,"abstract":"<div><div>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 <em>state-based</em> and <em>path-based</em> 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.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"167 ","pages":"Article 102449"},"PeriodicalIF":1.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}