{"title":"串联队列服务中负载平衡和区分任务的高效分配","authors":"Mohammad Delasay, Mustafa Akan","doi":"10.1007/s10479-024-06202-2","DOIUrl":null,"url":null,"abstract":"<p>Within service systems, tasks can encompass diverse functionalities. In a two-phase queuing model featuring two customer priority classes, our study discerns two distinct task functionalities executed by the first-phase server (referred to as the <i>auxiliary</i> server). These tasks aim to facilitate priority-based service by the second-phase server (referred to as the <i>expert</i>). <i>Load-balancing</i> tasks aim to alleviate the expert’s workload, while <i>differentiation</i> tasks seek to enhance accurate customer prioritization in the second phase by reducing misclassifications. With customers queuing for both the auxiliary server and the expert in tandem, our investigation focuses on determining the optimal allocation of the auxiliary server’s time between these load-balancing and differentiation tasks. Through queuing optimization, we aim to minimize customers’ expected total delay cost. In scenarios where the auxiliary server is allowed to perform only one task type (either load-balancing or differentiation), we delineate the optimal solutions based on specific functional forms dictating the server’s efficiency in executing each task type. These solutions strike a balance between excess phase capacities and the square root of marginal cost-to-saving ratios arising from each task type. Additionally, we partially characterize the optimal solution in scenarios permitting both load-balancing and differentiation tasks. Notably, under high system loads, executing load-balancing tasks proves more efficient than differentiation tasks. However, the relationship between the optimal task durations and system load showcases a non-monotonic pattern. As AI decision support products increasingly enable expert providers to delegate “routine” tasks to mid-level providers, our study sheds light on the efficient allocation of different tasks to different provider types to minimize delay costs in service systems.</p>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":null,"pages":null},"PeriodicalIF":4.4000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Efficient allocation of load-balancing and differentiation tasks in tandem queue services\",\"authors\":\"Mohammad Delasay, Mustafa Akan\",\"doi\":\"10.1007/s10479-024-06202-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Within service systems, tasks can encompass diverse functionalities. In a two-phase queuing model featuring two customer priority classes, our study discerns two distinct task functionalities executed by the first-phase server (referred to as the <i>auxiliary</i> server). These tasks aim to facilitate priority-based service by the second-phase server (referred to as the <i>expert</i>). <i>Load-balancing</i> tasks aim to alleviate the expert’s workload, while <i>differentiation</i> tasks seek to enhance accurate customer prioritization in the second phase by reducing misclassifications. With customers queuing for both the auxiliary server and the expert in tandem, our investigation focuses on determining the optimal allocation of the auxiliary server’s time between these load-balancing and differentiation tasks. Through queuing optimization, we aim to minimize customers’ expected total delay cost. In scenarios where the auxiliary server is allowed to perform only one task type (either load-balancing or differentiation), we delineate the optimal solutions based on specific functional forms dictating the server’s efficiency in executing each task type. These solutions strike a balance between excess phase capacities and the square root of marginal cost-to-saving ratios arising from each task type. Additionally, we partially characterize the optimal solution in scenarios permitting both load-balancing and differentiation tasks. Notably, under high system loads, executing load-balancing tasks proves more efficient than differentiation tasks. However, the relationship between the optimal task durations and system load showcases a non-monotonic pattern. As AI decision support products increasingly enable expert providers to delegate “routine” tasks to mid-level providers, our study sheds light on the efficient allocation of different tasks to different provider types to minimize delay costs in service systems.</p>\",\"PeriodicalId\":8215,\"journal\":{\"name\":\"Annals of Operations Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Operations Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://doi.org/10.1007/s10479-024-06202-2\",\"RegionNum\":3,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1007/s10479-024-06202-2","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
Efficient allocation of load-balancing and differentiation tasks in tandem queue services
Within service systems, tasks can encompass diverse functionalities. In a two-phase queuing model featuring two customer priority classes, our study discerns two distinct task functionalities executed by the first-phase server (referred to as the auxiliary server). These tasks aim to facilitate priority-based service by the second-phase server (referred to as the expert). Load-balancing tasks aim to alleviate the expert’s workload, while differentiation tasks seek to enhance accurate customer prioritization in the second phase by reducing misclassifications. With customers queuing for both the auxiliary server and the expert in tandem, our investigation focuses on determining the optimal allocation of the auxiliary server’s time between these load-balancing and differentiation tasks. Through queuing optimization, we aim to minimize customers’ expected total delay cost. In scenarios where the auxiliary server is allowed to perform only one task type (either load-balancing or differentiation), we delineate the optimal solutions based on specific functional forms dictating the server’s efficiency in executing each task type. These solutions strike a balance between excess phase capacities and the square root of marginal cost-to-saving ratios arising from each task type. Additionally, we partially characterize the optimal solution in scenarios permitting both load-balancing and differentiation tasks. Notably, under high system loads, executing load-balancing tasks proves more efficient than differentiation tasks. However, the relationship between the optimal task durations and system load showcases a non-monotonic pattern. As AI decision support products increasingly enable expert providers to delegate “routine” tasks to mid-level providers, our study sheds light on the efficient allocation of different tasks to different provider types to minimize delay costs in service systems.
期刊介绍:
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.