池化、专业化和自主完成任务如何影响平均队列长度

doi:10.15960/j.cnki.issn.1007-6093.2024.03.005

Abstract

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

CLC Number:

O226

Houyuan JIANG. Effects of pooling, specialization, and discretionary task completion on queueing performance[J]. Operations Research Transactions, 2024, 28(3): 81-96.

Figures/Tables 5

References 28

1	van Dijk N , van der Sluis E . Pooling is not the answer[J]. European Journal of Operational Research, 2009, 197, 415- 421. doi: 10.1016/j.ejor.2008.06.014
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. doi: 10.1111/poms.13020
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. doi: 10.1287/mnsc.2014.2118
5	Weber R R , Jr. Stidham S . Optimal control of service rates in networks of queues[J]. Advanced Applied Probability, 1987, 19, 202- 218. doi: 10.2307/1427380
6	Cattani K , Schmidt G M . The pooling principle[J]. INFORMS Transactions on Education, 2005, 5 (2): 1- 12. doi: 10.1287/ited.5.2.1
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. doi: 10.1287/mnsc.1040.0303
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. doi: 10.1287/msom.5.2.79.16071
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. doi: 10.3401/poms.1070.0007
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. doi: 10.1111/poms.12883
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. doi: 10.1287/mnsc.2016.2610
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. doi: 10.1287/mnsc.1080.0918
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. doi: 10.1287/opre.2020.2004
19	Nur S , Tu Y , Ziya S . Pooled vs. dedicated queues when customers are delay-sensitive[J]. Management Science, 2021, 67, 3785- 3802. doi: 10.1287/mnsc.2020.3663
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. doi: 10.1287/opre.2019.1976
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. doi: 10.1007/BF02100267
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. doi: 10.1287/opre.37.4.611
24	Adusumilli K M , Hasenbein J J . Dynamic admission and service rate control of a queue[J]. Queueing Systems, 2010, 66, 131- 154. doi: 10.1007/s11134-010-9192-z
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. doi: 10.1287/opre.2014.1258
26	George J M , Harrison J M . Dynamic control of a queue with adjustable service rate[J]. Operations Research, 2001, 49, 720- 731. doi: 10.1287/opre.49.5.720.10605
27	Hopp W J , Iravani S , Yuen G Y . Operations systems with discretionary task completion[J]. Management Science, 2007, 53, 61- 77. doi: 10.1287/mnsc.1060.0598
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. doi: 10.1287/mnsc.2022.4474

Queueing Features	Unpooling Systems: $ M/M/1 $ and $ M/M/1 $	Pooling System: $ M/M/2 $
No DTC, No Specialization	$ \lambda_1, \mu $	$ \lambda_1 + \lambda_2, \mu $ ^[3]
	$ \lambda_2, \mu $ ^[3]
No DTC, With Specialization	$ \lambda_1, \mu (1+\delta) $	$ \lambda_1 + \lambda_2, \mu $ ^[3]
	$ \lambda_2, \mu (1+\delta) $ ^[3]
With DTC, No Specialization	$ \lambda_1, \mu, \mu (1+\Delta) $	$ \lambda_1 + \lambda_2, \mu, \mu (1+\Delta) $
	$ \lambda_2, \mu, \mu (1+\Delta) $ ^[22]
With DTC, With Specialization	$ \lambda_1, \mu (1+\delta), \mu (1+\delta)(1+\Delta) $	$ \lambda_1 + \lambda_2, \mu, \mu (1+\Delta) $
	$ \lambda_2, \mu (1+\delta), \mu (1+\delta)(1+\Delta) $ ^[22]

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

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