Pub Date : 2024-12-18DOI: 10.1016/j.orl.2024.107236
Yuanyuan Liu, Zhaozeng Yan
This paper studies a time-limited Markovian polling queueing system with service rate regeneration. When the server moves to a new station, it announces the next station to open based on a given discrete-time Markov chain. We calculate the expected waiting time for customers in each queue, which is shown to be monotonic with respect to their position in the queue. Personal optimal thresholds for the customers are then determined, and an optimal joining strategy is proposed based on these thresholds.
{"title":"Strategic behavior in a time-limited Markovian polling queue with service rate regeneration","authors":"Yuanyuan Liu, Zhaozeng Yan","doi":"10.1016/j.orl.2024.107236","DOIUrl":"10.1016/j.orl.2024.107236","url":null,"abstract":"<div><div>This paper studies a time-limited Markovian polling queueing system with service rate regeneration. When the server moves to a new station, it announces the next station to open based on a given discrete-time Markov chain. We calculate the expected waiting time for customers in each queue, which is shown to be monotonic with respect to their position in the queue. Personal optimal thresholds for the customers are then determined, and an optimal joining strategy is proposed based on these thresholds.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107236"},"PeriodicalIF":0.8,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-13DOI: 10.1016/j.orl.2024.107230
Dan Garber, Atara Kaplan
We consider a class of important semidefinite optimization problems that involve a convex smooth or nonsmooth objective function and linear constraints. Focusing on high-dimensional settings with a low-rank solution that also satisfies a low-rank complementarity condition, we prove that the well-known Extragradient method, when initialized with a “warm-start”, converges with its standard convergence rate guarantees, using only efficient low-rank singular value decompositions to project onto the positive semidefinite cone. Supporting numerical evidence with a dataset of Max-Cut instances is provided.
{"title":"Low-rank extragradient methods for scalable semidefinite optimization","authors":"Dan Garber, Atara Kaplan","doi":"10.1016/j.orl.2024.107230","DOIUrl":"10.1016/j.orl.2024.107230","url":null,"abstract":"<div><div>We consider a class of important semidefinite optimization problems that involve a convex smooth or nonsmooth objective function and linear constraints. Focusing on high-dimensional settings with a low-rank solution that also satisfies a low-rank complementarity condition, we prove that the well-known Extragradient method, when initialized with a “warm-start”, converges with its standard convergence rate guarantees, using only efficient low-rank singular value decompositions to project onto the positive semidefinite cone. Supporting numerical evidence with a dataset of Max-Cut instances is provided.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107230"},"PeriodicalIF":0.8,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143140227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-12DOI: 10.1016/j.orl.2024.107231
Doudou Gong , Wenzhong Li
This paper introduces two values for cooperative games, called the constrained equal individual worth value and the constrained equal marginal contribution value, respectively. We show that the first value is the unique value satisfying the bilateral projection reduced game property and constrained egalitarianism, and the second one is the unique value satisfying the bilateral complement reduced game property and constrained egalitarianism. Replacing constrained egalitarianism by other properties, we provide another axiomatization for each value.
{"title":"Reduced game and constrained egalitarianism","authors":"Doudou Gong , Wenzhong Li","doi":"10.1016/j.orl.2024.107231","DOIUrl":"10.1016/j.orl.2024.107231","url":null,"abstract":"<div><div>This paper introduces two values for cooperative games, called the constrained equal individual worth value and the constrained equal marginal contribution value, respectively. We show that the first value is the unique value satisfying the bilateral projection reduced game property and constrained egalitarianism, and the second one is the unique value satisfying the bilateral complement reduced game property and constrained egalitarianism. Replacing constrained egalitarianism by other properties, we provide another axiomatization for each value.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107231"},"PeriodicalIF":0.8,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-12DOI: 10.1016/j.orl.2024.107222
Bara Kim , Jeongsim Kim
We consider a tollbooth tandem queue with a Poisson arrival process and two heterogeneous servers of exponential service times. We show that performance measures, such as queue length, system size, waiting time and sojourn time, are stochastically larger when a server with a larger service rate is used as the first server. Our results include a rigorous proof of the observation made by He and Chao (2014) and Do (2015) regarding the performance comparison between two alternative server arrangements.
{"title":"Optimal arrangement of servers for a tollbooth tandem queue with two heterogeneous servers","authors":"Bara Kim , Jeongsim Kim","doi":"10.1016/j.orl.2024.107222","DOIUrl":"10.1016/j.orl.2024.107222","url":null,"abstract":"<div><div>We consider a tollbooth tandem queue with a Poisson arrival process and two heterogeneous servers of exponential service times. We show that performance measures, such as queue length, system size, waiting time and sojourn time, are stochastically larger when a server with a larger service rate is used as the first server. Our results include a rigorous proof of the observation made by He and Chao (2014) and Do (2015) regarding the performance comparison between two alternative server arrangements.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107222"},"PeriodicalIF":0.8,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-05DOI: 10.1016/j.orl.2024.107221
Yule Zhang , Jia Wu , Liwei Zhang
An augmented Lagrangian-type stochastic approximation method (ALSAssdp) is proposed to solve the convex stochastic semidefinite optimization problem defined by expectations and regrets of this method are analyzed. Under mild conditions, we show that this method exhibits regret for both objective reduction and constraint violation. Moreover, we show that, with at least probability, the method has no more than for both objective regret and constraint violation regret.
{"title":"An augmented Lagrangian-type stochastic approximation method for convex stochastic semidefinite programming defined by expectations","authors":"Yule Zhang , Jia Wu , Liwei Zhang","doi":"10.1016/j.orl.2024.107221","DOIUrl":"10.1016/j.orl.2024.107221","url":null,"abstract":"<div><div>An augmented Lagrangian-type stochastic approximation method (ALSAssdp) is proposed to solve the convex stochastic semidefinite optimization problem defined by expectations and regrets of this method are analyzed. Under mild conditions, we show that this method exhibits <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> regret for both objective reduction and constraint violation. Moreover, we show that, with at least <span><math><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>T</mi></math></span> probability, the method has no more than <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mo>(</mo><mi>T</mi><mo>)</mo><mo>/</mo><msqrt><mrow><mi>T</mi></mrow></msqrt><mo>)</mo></math></span> for both objective regret and constraint violation regret.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107221"},"PeriodicalIF":0.8,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-04DOI: 10.1016/j.orl.2024.107220
Guergana P. Ilieva, Hayriye Ayhan
We consider a Markovian queueing system with finite buffer space. Arriving customers belong to different classes and have class dependent service rates. At the time of an arrival, if the system is full, one of the existing customers has to be discharged prematurely, incurring a class dependent cost, whereas class dependent rewards are earned upon successful service completions. Our objective is to determine which customer class to discharge prematurely in order to maximize the long-run average profit.
{"title":"Optimal control of queues with demand-driven discharge","authors":"Guergana P. Ilieva, Hayriye Ayhan","doi":"10.1016/j.orl.2024.107220","DOIUrl":"10.1016/j.orl.2024.107220","url":null,"abstract":"<div><div>We consider a Markovian queueing system with finite buffer space. Arriving customers belong to different classes and have class dependent service rates. At the time of an arrival, if the system is full, one of the existing customers has to be discharged prematurely, incurring a class dependent cost, whereas class dependent rewards are earned upon successful service completions. Our objective is to determine which customer class to discharge prematurely in order to maximize the long-run average profit.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107220"},"PeriodicalIF":0.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-03DOI: 10.1016/j.orl.2024.107217
Adrian Calinescu , Gruia Călinescu
Let be a polymatroid (an integer-valued non-decreasing submodular set function with ). A k-polymatroid satisfies that for all . We call independent if and for all . Such a set was also called a matching. Finding a maximum-size independent set in a 2-polymatroid has been studied and polynomial-time algorithms are known for linear polymatroids. For , the problem is NP-hard, and a -approximation is known and is obtained by swapping as long as possible a subset of up to elements from the current solution by a set with one more element.
Here we give a simple analysis of the more particular two-for-one repeated swapping heuristic, obtaining a tight (weaker) -approximation.
{"title":"Analysis of the two-for-one swap heuristic for approximating the maximum independent set in a k-polymatroid","authors":"Adrian Calinescu , Gruia Călinescu","doi":"10.1016/j.orl.2024.107217","DOIUrl":"10.1016/j.orl.2024.107217","url":null,"abstract":"<div><div>Let <span><math><mi>f</mi><mo>:</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>N</mi></mrow></msup><mo>→</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> be a polymatroid (an integer-valued non-decreasing submodular set function with <span><math><mi>f</mi><mo>(</mo><mo>∅</mo><mo>)</mo><mo>=</mo><mn>0</mn></math></span>). A <em>k</em>-polymatroid satisfies that <span><math><mi>f</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>≤</mo><mi>k</mi></math></span> for all <span><math><mi>e</mi><mo>∈</mo><mi>N</mi></math></span>. We call <span><math><mi>S</mi><mo>⊆</mo><mi>N</mi></math></span> <em>independent</em> if <span><math><mi>f</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>e</mi><mo>∈</mo><mi>S</mi></mrow></msub><mi>f</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></span> and <span><math><mi>f</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>></mo><mn>0</mn></math></span> for all <span><math><mi>e</mi><mo>∈</mo><mi>S</mi></math></span>. Such a set was also called a <em>matching</em>. Finding a maximum-size independent set in a 2-polymatroid has been studied and polynomial-time algorithms are known for linear polymatroids. For <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>, the problem is NP-hard, and a <span><math><mo>(</mo><mo>(</mo><mn>2</mn><mo>/</mo><mi>k</mi><mo>)</mo><mo>−</mo><mi>ϵ</mi><mo>)</mo></math></span>-approximation is known and is obtained by swapping as long as possible a subset of up to <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>log</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo></mo><mo>(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> elements from the current solution by a set with one more element.</div><div>Here we give a simple analysis of the more particular two-for-one repeated swapping heuristic, obtaining a tight (weaker) <span><math><mo>(</mo><mn>2</mn><mo>/</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span>-approximation.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107217"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-03DOI: 10.1016/j.orl.2024.107219
Dujuan Zhou
In statistics, sample size determination (SSD) is of fundamental interest. In this paper, we focus on Bayesian sample size analysis, under the well-known ACC and WOC criteria, for queueing systems. Our study is based on a different method from the literature studies that is supported by the fact that observed data (sample or samples) from the population in applications can be significantly different from samples generated from the selected prior distribution.
{"title":"A new sampling approach for Bayesian sample size analysis in applications of queueing models","authors":"Dujuan Zhou","doi":"10.1016/j.orl.2024.107219","DOIUrl":"10.1016/j.orl.2024.107219","url":null,"abstract":"<div><div>In statistics, sample size determination (SSD) is of fundamental interest. In this paper, we focus on Bayesian sample size analysis, under the well-known ACC and WOC criteria, for queueing systems. Our study is based on a different method from the literature studies that is supported by the fact that observed data (sample or samples) from the population in applications can be significantly different from samples generated from the selected prior distribution.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107219"},"PeriodicalIF":0.8,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-28DOI: 10.1016/j.orl.2024.107218
Zhe Yang , Xinyu Yang
This paper provides a generalization of [17] to strategy-form games with infinitely many nontransferable and transferable utilities. We first prove the existence of cooperative equilibria for strategy-form games with finitely many nontransferable and transferable utilities. By aid of above result, we finally obtain the cooperative equilibrium existence theorem in strategy-form games with infinitely many nontransferable and transferable utilities.
{"title":"Cooperative equilibria of strategy-form games with infinitely many nontransferable and transferable utilities","authors":"Zhe Yang , Xinyu Yang","doi":"10.1016/j.orl.2024.107218","DOIUrl":"10.1016/j.orl.2024.107218","url":null,"abstract":"<div><div>This paper provides a generalization of <span><span>[17]</span></span> to strategy-form games with infinitely many nontransferable and transferable utilities. We first prove the existence of cooperative equilibria for strategy-form games with finitely many nontransferable and transferable utilities. By aid of above result, we finally obtain the cooperative equilibrium existence theorem in strategy-form games with infinitely many nontransferable and transferable utilities.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"58 ","pages":"Article 107218"},"PeriodicalIF":0.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.orl.2024.107216
Lu Yu
We prove three results on the existence and the structure of Nash equilibria for quasisupermodular games. They all require certain continuity as assumption. The first result is purely order-theoretic, where we assume a continuity introduced by Shannon. The second continuity hypothesis is a mixture in the following sense. We require another order-theoretic continuity defined by Milgrom and Roberts, which we show to be only a half of Shannon's condition. As compensation, we also require a weak topological continuity proposed by Tian and Zhou. The last continuity supposition is purely topological, which is a slightly stronger continuity due to Tian and Zhou. The last theorem simultaneously generalizes Zhou's theorem on supermodular games and Calciano's theorem on quasisupermodular games.
{"title":"Nash equilibria of quasisupermodular games","authors":"Lu Yu","doi":"10.1016/j.orl.2024.107216","DOIUrl":"10.1016/j.orl.2024.107216","url":null,"abstract":"<div><div>We prove three results on the existence and the structure of Nash equilibria for quasisupermodular games. They all require certain continuity as assumption. The first result is purely order-theoretic, where we assume a continuity introduced by Shannon. The second continuity hypothesis is a mixture in the following sense. We require another order-theoretic continuity defined by Milgrom and Roberts, which we show to be only a half of Shannon's condition. As compensation, we also require a weak topological continuity proposed by Tian and Zhou. The last continuity supposition is purely topological, which is a slightly stronger continuity due to Tian and Zhou. The last theorem simultaneously generalizes Zhou's theorem on supermodular games and Calciano's theorem on quasisupermodular games.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"58 ","pages":"Article 107216"},"PeriodicalIF":0.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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