Dynamic control of a tandem system with abandonments

Zayas‐Cabán, Gabriel; Xie, Jingui; Green, Linda V.; Lewis, Michael M.

doi:10.1007/s11134-016-9489-7

Cited by 18 publications

(20 citation statements)

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“…(g) The dynamic control of queueing behavior: blocking by Blackburn [39] and Economou and Kanta [106]; reneging and impatience by Li et al [220] and Anderson [20]; and abandonment by Down et al [102], Legros et al [215], Larrañaga et al [209] and Zayas-Cabán et al [341].…”

Section: Objective Three: Dynamic Control Under Different Service Mecmentioning

confidence: 99%

See 1 more Smart Citation

An Overview for Markov Decision Processes in Queues and Networks

Fan

et al. 2019

Stochastic Models in Reliability, Network Security and System Safety

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Markov decision processes (MDPs) in queues and networks have been an interesting topic in many practical areas since the 1960s. This paper Provides a detailed overview on this topic and tracks the evolution of many basic results. Also, this paper summarizes several interesting directions in the future research. We hope that this overview can shed light to MDPs in queues and networks, and also to their extensive applications in various practical areas.One main purpose of this paper is to provide an overview for research on MDPs in queues and networks in the last six decades. Also, such a survey is first related to several other basic studies, such as, Markov processes, queueing systems, queueing networks, Markov decision processes, sensitivity-based optimization, stochastic optimization, fluid and diffusion control. Therefore, our analysis begins from three simple introductions:1 Markov processes and Markov decision processes, queues and queueing networks, and queueing dynamic control. (a) Markov processes and Markov decision processesThe Markov processes, together with the Markov property, were first introduced by a Russian mathematician: Andrei Andreevich Markov in 1906. See Markov [238] for more details. From then on, as a basically mathematical tool, the Markov processes have extensively been discussed by many authors, e.g., see some excellent books by Doob [99], Karlin [175], Karlin and Taylor [176], Chung [80], Anderson [21], Kemeny et al. [181], Meyn and Tweedie [241], Chen [77], Ethier and Kurtz [110] and so on. In 1960, Howard [165] is the first to propose and discuss the MDP (or stochastic dynamic programming) in terms of his Ph.D thesis, which opened up a new and important field through an interesting intersection between Markov processes and dynamic programming (e.g., see Bellman and Kalaba [32]). From then on, not only are the MDPs an important branch in the area of Markov processes, but also it is a basic method in modern dynamic control theory. Crucially, the MDPs have been greatly motivated and widely applied in many practical areas in the past 60 years. Readers may refer to some excellent books, for example, the discrete-time MDPs by Puterman [261], Glasserman and Yao [143], Bertsekas [33], Bertsekas and Tsitsiklis [34], Hernádez-Lerma and Lasserre [155, 156], Altman [9], Koole [193] and Hu and Yue [166]; the continuous-time MDPs by Guo and Hernández-Lerma [145]; the partially observable MDPs by Cassandra [67] and Krishnamurthy [196]; the competitive MDPs (i.e., stochastic game) by [127]; the sensitivity-based optimization by Cao [58]; some applications of MDPs by Feinberg and Shwartz (Eds.) [122]and Boucherie and Van Dijk (Eds.) [44]; and so on. (b) Queues and queueing networksIn the early 20th century, a Danmark mathematician: Agner Krarup Erlang, published a pioneering work [109] of queueing theory in 1909, which started the study of queueing theory and traffic engineering. Over the past 100 years, queueing theory has been regarded as a key mathematical tool not only for analyzing practical s...

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Section: Objective Three: Dynamic Control Under Different Service Mecmentioning

confidence: 99%

“…(1) MDPs of two-station tandem queues Ghoneim and Stidham [140], Nishimura [247], Farrar [113], Iravani et al [167], Ahn et al [5] and Zayas-Cabán et al [341].…”

Section: Mdps Of Queueing Network With Special Structurementioning

confidence: 99%

An Overview for Markov Decision Processes in Queues and Networks

Fan

et al. 2019

Stochastic Models in Reliability, Network Security and System Safety

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“…He shows that the switching policy for the flexible server is monotone with respect to the number of jobs in the system. Zayas‐Cabán, Xie, Green, and Lewis () extend the server scheduling literature for two‐stage tandem queueing systems by considering customer impatience. As a result of customer impatience, uniformization is not possible since the transition rates are unbounded.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal control policies in service systems with limited information on the downstream stage

Ansari

Iravani

Qi-feng

2019

Naval Research Logistics

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Existing models in multistage service systems assume full information on the state of downstream stages. In this paper, we investigate how much the lack of such information impacts jobs' waiting time in a two‐stage system with two types of jobs at the first stage. The goal is to find the optimal control policy for the server at the first stage to switch between type‐1 and type‐2 jobs, while minimizing the long‐run average number of jobs in the system. We identify control policies and corresponding conditions under which having no or partial information, the system can still capture the most benefit of having full information.

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“…Many hospital systems (e.g., Lutheran Medical Center and UW Health) have implemented interventions known as "split flow" models to improve patient flow in the Emergency Departments (EDs) (cf., [21,29,49,50]). Unlike a typical ED, a split flow model stations an advanced practice provider (APP) rather than a nurse at patient intake (i.e., before or during triage).…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the ED split flow model, we consider the assignment of servers between two phases of service in a two-stage tandem queue. This and related models have been studied in the case when one or more job classes require service at multiple service stations in tandem by one or more servers (cf., [1][2][3][4][5][6][7][8]15,17,18,20,25,27,35,37,41,42,46,49]). Servers decide where to allocate efforts to optimize performance criteria on quality of service and/or congestion.…”

Section: Introductionmentioning

confidence: 99%

Scheduling servers in a two-stage queue with abandonments and costs

Zayas‐Cabán¹,

Cochran

2022

Prob. Eng. Inf. Sci.

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We consider the assignment of servers to two phases of service in a two-stage tandem queueing system when customers can abandon from each stage of service. New jobs arrive at both stations. Jobs arriving at station 1 may go through both phases of service and jobs arriving at station 2 may go through only one phase of service. Stage-dependent holding and lump-sum abandonment costs are incurred. Continuous-time Markov decision process formulations are developed that minimize discounted expected and long-run average costs. Because uniformization is not possible, we use the continuous-time framework and sample path arguments to analyze control policies. Our main results are conditions under which priority rules are optimal for the single-server model. We then propose and evaluate threshold policies for allocating one or more servers between the two stages in a numerical study. These policies prioritize a phase of service before “switching” to the other phase when total congestion exceeds a certain number. Results provide insight into how to adjust the switching rule to significantly reduce costs for specific input parameters as well as more general multi-server situations when neither preemption or abandonments are allowed during service and service and abandonment times are not exponential.

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Dynamic control of a tandem system with abandonments

Cited by 18 publications

References 18 publications

An Overview for Markov Decision Processes in Queues and Networks

An Overview for Markov Decision Processes in Queues and Networks

Optimal control policies in service systems with limited information on the downstream stage

Scheduling servers in a two-stage queue with abandonments and costs

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