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

摘要/Abstract

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

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

中图分类号:

O226

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（中英文）, 2024, 28(3): 81-96.

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

图/表 5

Table 1

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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]

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