English

运筹学学报 >

2024 , Vol. 28 >Issue 3: 81 - 96

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2024.03.005

俞建教授八十华诞贺寿专辑

池化、专业化和自主完成任务如何影响平均队列长度

展开
  • 1. 剑桥大学嘉治商学院, 英国剑桥 CB2 1AG

收稿日期: 2024-04-25

  网络出版日期: 2024-09-07

版权

运筹学学报编辑部, 2024, 版权所有，未经授权。
收起

Effects of pooling, specialization, and discretionary task completion on queueing performance

Expand
  • 1. Judge Business School, University of Cambridge, CB2 1AG, Cambridge, the United Kingdom
江厚元, E-mail: h.jiang@jbs.cam.ac.uk

Received date: 2024-04-25

  Online published: 2024-09-07

Copyright

, 2024, All rights reserved, without authorization
Fold

摘要

在排队系统中, 池化、去池化/专业化和自主完成任务是典型的运营操作策略, 这些策略在医疗保健、电话服务中心和线上销售中有广泛应用。这些策略在不同的操作环境中可能有优劣之分。本文使用$M/M/1$和$M/M/2$排队模型研究池化、专业化和自主完成任务对平均队列长度的影响。我们推导出$M/M/2$排队系统的平均队列长度的解析式。通过计算实例展示池化、专业化和自主完成任务如何影响平均队列长度的变化。最后, 本文提出了几个猜想。

关键词： 排队系统; 池化; 专业化; 自主完成任务; 平均队列长度

本文引用格式

江厚元 . 池化、专业化和自主完成任务如何影响平均队列长度[J]. 运筹学学报, 2024 , 28(3) : 81 -96 . DOI: 10.15960/j.cnki.issn.1007-6093.2024.03.005

Abstract

Pooling, unpooling/specialization, and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare, call centers, and online sales. These strategies may have advantages and disadvantages in different operational environments. This paper uses the $M/M/1$ and $M/M/2$ queues to study the impact of pooling, specialization, and discretionary task completion on the average queue length. Closed-form solutions for the average $M/M/2$ queue length are derived. Computational examples illustrate how the average queue length changes with the strength of pooling, specialization, and discretionary task completion. Finally, several conjectures are made in the paper.

Key words： queuing systems; pooling; specialization; discretionary task completion; average queue length

参考文献

1 van Dijk N , van der Sluis E . Pooling is not the answer[J]. European Journal of Operational Research, 2009, 197, 415- 421.
2 Jiang H , Sodhi M S . Analyzing the proposed reconfiguration of accident-and-emergency facilities in england[J]. Production and Operations Management, 2019, 28 (7): 1837- 1857.
3 Tijms H C . A First Course in Stochastic Models[M]. New York: Wiley, 2003.
4 Song H , Tucker A , Murrell K L . The diseconomies of queue pooling: An empirical investigation of emergency department length of stay[J]. Management Science, 2015, 61 (12): 3032- 3053.
5 Weber R R , Jr. Stidham S . Optimal control of service rates in networks of queues[J]. Advanced Applied Probability, 1987, 19, 202- 218.
6 Cattani K , Schmidt G M . The pooling principle[J]. INFORMS Transactions on Education, 2005, 5 (2): 1- 12.
7 Alfaro J A , Corbett C J . The value of SKU rationalization in practice (The pooling effect under suboptimal inventory policies and nonnormal demand)[J]. Production and Operations Management, 2009, 12 (1): 12- 29.
8 Alptekinoglu A , Banerjee A , Paul A , et al. Inventory pooling to deliver differentiated service[J]. Manufacturing & Service Operations Management, 2012, 15 (1): 33- 44.
9 Benjaafar S , Cooper W L , Kim J S . On the benefits of pooling in production-inventory systems[J]. Management Science, 2005, 51 (4): 548- 565.
10 Gans N , Koole G , Mandelbaum A . Telephone call centers: Tutorial, review and research prospects[J]. Manufacturing and Service Operations Management, 2003, 5, 79- 141.
11 van Dijk N M. To pool or not to pool? The benefits of combining queueing and simulation [C]// Proceedings of the Winter Simulation Conference IEEE, 2002: 1469-1472.
12 van Dijk N M , Van der Sluis E . To pool or not to pool in call centers[J]. Production and Operations Management, 2008, 17, 1- 10.
13 Smith D R , Whitt W . Resource sharing for efficiency in traffic systems bell system[J]. Tech Journal, 1981, 60, 39- 55.
14 Hung D , Shunko M , Lucas M , et al. On the pooling of queues: How server behavior affects performance[J]. Production and Operations Management, 2018, 27, 1553- 1573.
15 Shunko M , Niederhoff J , Rosokha Y . Humans are not machines: The behavioral impact of queueing design on service time[J]. Management Science, 2018, 64, 453- 473.
16 Ata B , van Mieghem J A . The value of partial resource pooling: Should a service network be integrated or product-focused[J]. Management Science, 2009, 55 (1): 115- 131.
17 Hopp W J , Spearman M L . Factory Physics[M]. New York: McGraw-Hill/Irwin, 2000.
18 Mor A , Roels G , Song H . Pooling queues with strategic servers: The effects of customer ownership[J]. Operations Research, 2021, 69, 13- 29.
19 Nur S , Tu Y , Ziya S . Pooled vs. dedicated queues when customers are delay-sensitive[J]. Management Science, 2021, 67, 3785- 3802.
20 Bell S L , Williams R J . Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy[J]. Annals of Applied Probability, 2001, 11, 608- 649.
21 Cao P , He S , Huang J , et al. To pool or not to pool: Queueing design for large-scale service systems[J]. Operations Research, 2021, 69, 1866- 1885.
22 Morrison J A . Sojourn and waiting times in a single-server system with state-dependent mean service rate[J]. Quequeing Systems, 1989, 4, 213- 235.
23 Stidham S , Weber R R . Monotonic and insensitive optimal policies for control of queues with undiscounted costs[J]. Operations Research, 1989, 37, 611- 625.
24 Adusumilli K M , Hasenbein J J . Dynamic admission and service rate control of a queue[J]. Queueing Systems, 2010, 66, 131- 154.
25 Chan C W , Yom-Tov G , Escobar G . When to use speedup: An examination of service systems with returns[J]. Operations Research, 2014, 62 (2): 462- 582.
26 George J M , Harrison J M . Dynamic control of a queue with adjustable service rate[J]. Operations Research, 2001, 49, 720- 731.
27 Hopp W J , Iravani S , Yuen G Y . Operations systems with discretionary task completion[J]. Management Science, 2007, 53, 61- 77.
28 Lin C , Shang K , Sun P . Wait time-based pricing for queues with customer-chosen service times[J]. Management Science, 2023, 69, 2127- 2146.
Options
文章导航

/

〈 〉