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 despite the presence of punctual guards.
{"title":"Controller synthesis in timed Büchi automata: Robustness and punctual guards","authors":"Benoît Barbot , Damien Busatto-Gaston , Catalin Dima , 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":"2025-04-05","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}
Pub Date : 2025-04-03DOI: 10.1016/j.peva.2025.102484
Herwig Bruneel, Arnaud Devos, Joris Walraevens
In this paper, we revisit the discrete-time two-queue randomly alternating service 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 (pgf) 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.
We extend various existing results with respect to the queueing behavior of this system. Specifically, we show that the exact solutions that were previously found for the steady-state joint pgf of the system contents in both queues for the scenarios of independent Bernoulli arrivals, identical Bernoulli arrivals, global geometric arrivals, global geometric group arrivals, and the superposition of identical Bernoulli arrivals and global geometric (group) arrivals, are all special cases of a more general result, which is valid for a whole class of arrival pgfs 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 algebraic one and, unlike earlier studies, does not require intricate techniques from complex-function analysis.
{"title":"A generalized result for the discrete-time two-queue randomly alternating service system","authors":"Herwig Bruneel, Arnaud Devos, 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":"2025-04-03","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}
Pub Date : 2025-04-02DOI: 10.1016/j.peva.2025.102485
{"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":"2025-04-02","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}
Pub Date : 2025-03-24DOI: 10.1016/j.peva.2025.102482
Christel Baier, Calvin Chau, Sascha Klüppelholz
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 multi-objective 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.
{"title":"Certificates and witnesses for multi-objective queries in Markov decision processes","authors":"Christel Baier, Calvin Chau, 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}
Pub Date : 2025-03-13DOI: 10.1016/j.peva.2025.102481
Bao The Phung , Ba Cao Nguyen , Nguyen Van Vinh , Bui Vu Minh , Nguyen Huu Khanh Nhan
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- 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.
{"title":"Optimizing spatial modulation MIMO IoT systems with full-duplex/half-duplex UAVs and enhanced transmit antenna selection","authors":"Bao The Phung , Ba Cao Nguyen , Nguyen Van Vinh , Bui Vu Minh , 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}
Pub Date : 2025-03-11DOI: 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.
{"title":"Approximation of cumulative distribution functions by Bernstein phase-type distributions","authors":"András Horváth , Illés Horváth , Marco Paolieri , Miklós Telek , 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}
Pub Date : 2025-03-10DOI: 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%.
{"title":"Optimizing parallel I/O performance in NVMe SSDs by Dynamic cache partitioning","authors":"Zecheng Li , Shu Yin , 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}
Pub Date : 2025-03-05DOI: 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 servers, numbered 1, 2, …, , out of which the first servers are marked as special, where is unknown. These 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 uniformly at random from , where is the number chosen in the previous step, initially set to in the first step. A query is then sent to server asking whether is marked. If the answer is yes, the algorithm returns ; otherwise, the process is repeated with . 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.
{"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}
Pub Date : 2025-02-27DOI: 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.
{"title":"The Multiserver Job Queuing Model with big and small jobs: Stability in the case of infinite servers","authors":"Adityo Anggraito , Diletta Olliaro , Marco Ajmone Marsan , 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}
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.
{"title":"Computational algorithms and arrival theorem for non-conventional product-form solutions","authors":"Diletta Olliaro , Gianfranco Balbo , Andrea Marin , 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}
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