Опубликована: Янв. 1, 2021
Yuri Bizzoni, Stefania Degaetano-Ortlieb, Katrin Menzel, Elke Teich. Proceedings of the 5th Joint SIGHUM Workshop on Computational Linguistics for Cultural Heritage, Social Sciences, Humanities and Literature. 2021.
Язык: Английский
Probability in the Engineering and Informational Sciences, Год журнала: 2025, Номер unknown, С. 1 - 26
Опубликована: Фев. 21, 2025
In this paper, we investigate the number of customers that overlap or coincide with a virtual customer in an Erlang-A queue. Our analysis starts fluid and diffusion limit differential equations to obtain mean variance queue length. We then develop precise approximations for waiting times using limits polygamma function. Building on this, introduce novel approximation scheme calculate overlapping customers. This method facilitates assessment transient risks complex service systems, offering useful tool providers mitigate significant overlaps during pandemic seasons.
Язык: Английский
Процитировано
0
International Transactions in Operational Research, Год журнала: 2025, Номер unknown
Опубликована: Апрель 21, 2025
Abstract The double‐ended matching queueing model has wide applicability across various real‐life scenarios. In this paper, we analyze fluid models of bilateral queues with time‐varying arrivals. contains contents general patience time distributions in a task queue and worker queue, aiming to approximate the characteristics systems. We first prove existence uniqueness solution model. When arrival rates both tasks workers are constant, determine steady‐state lengths abandonment proportions for sides system. Furthermore, demonstrate that converges an equilibrium state starting from any initial state. For situations involving rates, satisfactory results numerical experiments validate reliability describing Finally, explore problems within systems provide tailored solutions
Язык: Английский
Процитировано
0
Production and Operations Management, Год журнала: 2021, Номер 30(11), С. 4236 - 4257
Опубликована: Июнь 29, 2021
We investigate the trade‐off between acquisition and retention efforts when customers are sensitive to quality of service they receive, that is, whether get timely access a company's resources requested. model problem as multi‐class queueing network with new returning customers, time‐dependent arrivals, abandonment. derive its fluid approximation; system ordinary linear differential equations continuous, piecewise smooth, right‐hand sides. Based on model, we propose novel approach determine optimal stationary staffing levels for customer queues in anticipation future time‐varying dynamics. Using accessibility proxy investment, demonstrate how apply our two families arrival functions motivated by real‐world applications: an advertising campaign clinical setting. In numerical study, creates policies maximize throughput while balancing more effectively (i.e., equitable abandonment from each class) than commonly used near‐stationary methods such variants square‐root policies. Our confirms intimately linked; this has been found empirical studies but not captured operations literature. suggest environments, focusing either alone is sufficient maintain high quality.
Язык: Английский
Процитировано
13
Probability in the Engineering and Informational Sciences, Год журнала: 2023, Номер 38(1), С. 21 - 27
Опубликована: Фев. 23, 2023
Abstract Imagine, you enter a grocery store to buy food. How many people do overlap with in this store? much time each person the In paper, we answer these questions by studying times between customers infinite server queue. We compute closed form steady-state distribution of pair and number that an arriving customer will with. Finally, define residual process counts overlapping queue for at least $\delta$ units its distribution.
Язык: Английский
Процитировано
5
Frontiers in Artificial Intelligence, Год журнала: 2021, Номер 4
Опубликована: Июнь 1, 2021
Endeavors to computationally model language variation and change are ever increasing. While analyses of recent diachronic trends frequently conducted, long-term accounting for sociolinguistic less well-studied. Our work sheds light on the temporal dynamics use British 18th century women as a group in transition across two situational contexts. findings reveal that formal contexts adapt register conventions, while informal they act innovators influencing others. adopted from other disciplines, our methods inform (historical) novel ways. These include periodization by Kullback-Leibler divergence determine periods relevant features variation, event cascades influencer models.
Язык: Английский
Процитировано
9
SSRN Electronic Journal, Год журнала: 2018, Номер unknown
Опубликована: Янв. 1, 2018
Customer arrival patterns observed in the real world typically exhibit strong seasonal effects. It is therefore natural to ask: Can a nonhomogeneous Poisson process (NHPP) with rate function that simple sum of sinusoids provide an adequate description reality? If so, how can sinusoidal NHPP be used improve performance service systems? We empirically validate model consistent arrivals data from two settings great interest operations: Patient emergency department and customer calls bank call centre. This finding provides rigorous justification for use assumption many existing queuing models. also clarify why more suitable than standard when underlying pattern aperiodic (e.g., does not follow weekly cycle). illustrated using car dealership, via naturalistic staffing simulation based on On other hand, if periodic, we explain both models should perform comparably. Even then, still necessary managers verify indeed step seldom performed applications.
Язык: Английский
Процитировано
5
SSRN Electronic Journal, Год журнала: 2018, Номер unknown
Опубликована: Янв. 1, 2018
We study customer service chat (CSC) systems with generally distributed and patience times by developing measure-valued processes to model analyze the system dynamics. first prove that these are tight in many-server asymptotic regime then show their limits satisfy a set of fluid equations. establish invariant states use obtain (non-asymptotic) approximations for various performance metrics CSC steady state. also demonstrate accuracy using extensive numerical experiments. These allow us impact time distributions on devise effective dynamic routing policies.
Язык: Английский
Процитировано
4
Applied Mathematical Modelling, Год журнала: 2024, Номер 128, С. 492 - 516
Опубликована: Янв. 7, 2024
Язык: Английский
Процитировано
0
SSRN Electronic Journal, Год журнала: 2024, Номер unknown
Опубликована: Янв. 1, 2024
This paper explores agent multitasking over time in customer service environments, particularly within livechat settings. Multitasking, a ubiquitous occurrence various professional sectors, is typically assumed to have constant effect conditional on the level. We go beyond this conventional approach by examining temporal dynamics of and their effects performance. Through collaboration with third-party contact center, we analyze interactions across different retail brands, focusing both multibranding, where agents manage tasks for multiple brands simultaneously. Our findings reveal that handling chats simultaneously increases average chat duration, diminishing marginal as number concurrent grows. explore implications these insights proposing "pile-on" heuristic, which assigns new already engaged multitasking, rather than evenly distributing agents. method can lead reduction duration increased idle time. study contributes operations management literature illustrating dynamic nature challenging traditional perceptions suggesting intensity play crucial roles shaping operational efficiency, show how work assignment strategies influence outcomes.
Язык: Английский
Процитировано
0
2018 Winter Simulation Conference (WSC), Год журнала: 2021, Номер unknown
Опубликована: Дек. 12, 2021
Processor sharing queues are used in a variety of settings telecommunications and internet applications known for being fair. In this paper, we study the possibility accurately predicting response times real time G/G/1 processor queue. To end, combine stochastic simulation with supervised learning machine methods. We show that many current algorithms can perform well at real-time.
Язык: Английский
Процитировано
2