Performance Evaluation最新文献

{"title":"Certificates and witnesses for multi-objective queries in Markov decision processes","authors":"Christel Baier,&nbsp;Calvin Chau,&nbsp;Sascha Klüppelholz","doi":"10.1016/j.peva.2025.102482","DOIUrl":"10.1016/j.peva.2025.102482","url":null,"abstract":"<div><div>Probabilistic model checking is a technique for formally verifying the correctness of probabilistic systems w.r.t. given specifications. Typically, a model checking procedure outputs whether a specification is satisfied or not, but does not provide additional insights on the correctness of the result, thereby diminishing the trustworthiness and understandability of the verification process. In this work, we consider certifying verification algorithms that also provide an independently checkable certificate and witness in addition to the verification result. The certificate can be used to easily validate the correctness of the result and the witness provides useful diagnostic information, e.g. for debugging purposes. More specifically, we study certificates and witnesses for specifications in the form of <em>multi-objective</em> queries in Markov decision processes. We first consider multi-objective reachability and invariant queries and then extend our techniques to mean-payoff expectation and mean-payoff percentile queries. Thereby, we generalize previous works on certificates and witnesses for single reachability and invariant constraints. In essence, we derive certifying verification algorithms from known linear programming techniques and show that witnesses, both in the form of schedulers and subsystems, can be obtained from the certificates. As a proof-of-concept, we report on an implementation of our certifying verification algorithms and present experimental results, demonstrating the applicability on moderately-sized case studies.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102482"},"PeriodicalIF":1.0,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748192","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 spatial modulation MIMO IoT systems with full-duplex/half-duplex UAVs and enhanced transmit antenna selection","authors":"Bao The Phung ,&nbsp;Ba Cao Nguyen ,&nbsp;Nguyen Van Vinh ,&nbsp;Bui Vu Minh ,&nbsp;Nguyen Huu Khanh Nhan","doi":"10.1016/j.peva.2025.102481","DOIUrl":"10.1016/j.peva.2025.102481","url":null,"abstract":"<div><div>Multiple-input multiple-output (MIMO) systems play a crucial role in elevating the efficiency and reliability of communication networks, especially within Internet of Things (IoT) applications. This article introduces a novel approach involving full-duplex (FD) and half-duplex (HD) relays mounted on unmanned aerial vehicles (UAVs) to enhance MIMO systems. Incorporating spatial modulation (SM) and transmit antenna selection (TAS) techniques aims to optimize system performance while reducing computational complexity to meet IoT requirements. The article mathematically formulates outage probabilities (OPs) and system throughputs (STs) for the proposed MIMO-IoT-UAV systems utilizing SM with FD/HD-UAV, both with and without TAS, over practical Nakagami-<span><math><mi>m</mi></math></span> channels. Numerical illustrations underscore the advantages of employing FD/HD-UAV and TAS in MIMO-IoT-UAV systems. Specifically, OPs with TAS are significantly lower, while STs with TAS are notably higher than their counterparts without TAS. Additionally, TAS with FD-UAV yields greater benefits than HD-UAV, particularly in preventing the error floor associated with residual self-interference (RSI). To mitigate this error floor in MIMO-IoT-UAV systems using FD-UAV, an effective strategy involves increasing the number of transmit/receive antennas. The choice between FD and HD modes hinges on parameters such as transmit power, data rate, and RSI. Depending on these factors, FD-UAV performance may exhibit lower or higher error rates than HD-UAV. Hence, the optimal selection of FD or HD mode, combined with TAS, is essential for enhancing MIMO-IoT-UAV system performance. This optimization process should consider parameters like RSI level, the number of transmit/receive antennas, data rate requirements, and UAV position to ensure efficient and reliable communication across diverse scenarios.</div></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"168 ","pages":"Article 102481"},"PeriodicalIF":1.0,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642833","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":"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":"2025-03-11","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":"2025-03-10","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":"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":"2025-03-05","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":"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":"2025-02-27","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":"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":"2025-02-21","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":"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":"2025-01-30","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":"Foreword - Special Issue - MASCOTS 2023","authors":"Maria Carla Calzarossa ,&nbsp;Anshul Gandhi","doi":"10.1016/j.peva.2025.102467","DOIUrl":"10.1016/j.peva.2025.102467","url":null,"abstract":"","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"167 ","pages":"Article 102467"},"PeriodicalIF":1.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182336","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":"Coupled queues with server interruptions: Some solutions","authors":"Herwig Bruneel,&nbsp;Arnaud Devos","doi":"10.1016/j.peva.2024.102466","DOIUrl":"10.1016/j.peva.2024.102466","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study three different &lt;em&gt;discrete-time&lt;/em&gt; 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 (&lt;em&gt;pgf&lt;/em&gt;) is &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The service times of all customers are deterministically equal to one time slot.&lt;/div&gt;&lt;div&gt;We first consider a scenario (&lt;em&gt;Option&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;) with &lt;em&gt;one single server&lt;/em&gt; which is to be shared by the two customer types. Here, we assume that type-1 customers have &lt;em&gt;absolute service priority&lt;/em&gt; over type-2 customers. Moreover, the server is subject to &lt;em&gt;random server interruptions&lt;/em&gt;, which occur independently from slot to slot. We derive a functional equation for the steady-state joint pgf &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; 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 &lt;em&gt;arbitrary&lt;/em&gt; arrival pgfs &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, but more elegant results are obtained for some specific choices of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;Next, we focus on two different scenarios (&lt;em&gt;Option&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;em&gt;Option&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;) where both customer types have their &lt;em&gt;own dedicated server&lt;/em&gt;. Here, there are no service priorities involved. In Option &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, the two servers experience &lt;em&gt;simultaneous&lt;/em&gt; interruptions, whereas in Option &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;only one&lt;/em&gt; of the servers is subject to interruptions. Again, we derive functional equations for the pgf &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Although solving these equations for arbitrary arrival pgfs &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/ms","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"167 ","pages":"Article 102466"},"PeriodicalIF":1.0,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181845","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}