Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Lee, Chihoon; Liu, Xin; Liu, Yunan; Zhang, Ling

doi:10.2139/ssrn.3367263

Cited by 3 publications

(6 citation statements)

References 27 publications

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“…for i = 1, 2, • • • , K and t ≥ 0. Since R(•) process depends on all the categories, we observe that the queue length processes as in (5) for each i are mutually coupled if we manage to cancel out the common R(•) process. Thus, we can simply call (5) the coupled queue length processes.…”

Section: Stochastic Modelmentioning

confidence: 99%

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Multi-component Matching Queues in Heavy Traffic

Xie¹

2022

Preprint

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We consider multi-component matching queue systems in heavy traffic. We assume a product made of K ≥ 2 distinct perishable components is mass produced under the assemble-to-order production strategy. These components arrive randomly over time at high speed at the assembling station, and they wait in their respective queues according to their categories until matched or their "patience" runs out. If all categories are available, matching occurs instantaneously, and thereafter the matched components leave immediately. For a sequence of such matching queue systems parameterized by n, when the arrival rates of all categories tend to infinity in concert as n tends to infinity, we obtain a weak convergence result for the queue length processes in heavy traffic under mild assumptions. We demonstrate that the heavy traffic limit of the appropriately scaled queue length vector is characterized by a coupled stochastic integral equation with a scalar-valued non-linear term. We prove some crucial properties of such a coupling behavior for certain coupled equations. We also exhibit that a generalized coupled stochastic integral equation admits a unique weak solution that has the strong Markov property. Moreover, we establish an asymptotic Little's law for each component queue, which reveals the asymptotic relationship between the queue length and its waiting time in the queue. We introduce an infinite-horizon discounted cost functional associated with the matching queue model with abandonment, where we consider two types of costs: a holding cost generated by storing the components in queues and a penalty cost generated by abandoned components. We show that the expected value of this cost functional for the nth system converges to that of the heavy traffic limiting process as n tends to infinity.

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Section: Stochastic Modelmentioning

confidence: 99%

“…[2]), production-inventory systems (cf. [3], [4], [5]), blood bank drives (cf. [6]), organ transplantation problems (cf.…”

Section: Introductionmentioning

confidence: 99%

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Multi-component Matching Queues in Heavy Traffic

Xie¹

2022

Preprint

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“…[19,29]), where one side of the queue represents inventory of products and the other side accepts the arrivals of orders. In a recent work [24], a production rate control problem is studied to minimize a finite horizon cost functional consisting of linear costs for inventory and waiting and a cost that penalizes rapid fluctuations of production rates. An asymptotic optimal production rate is developed under the fluid scaling given that the demand arrival rate is time and state dependent.…”

Section: Introductionmentioning

confidence: 99%

Admission Control for Double-ended Queues

Liu¹,

Weerasinghe²

2021

Preprint

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We consider a controlled double-ended queue consisting of two classes of customers, labeled sellers and buyers. The sellers and buyers arrive in a trading market according to two independent renewal processes. Whenever there is a seller and buyer pair, they are matched and leave the system instantaneously. The matching follows firstcome-first-match service discipline. Those customers who cannot be matched immediately need to wait in the designated queue, and they are assumed to be impatient with generally distributed patience times. The control problem is concerned with the tradeoff between blocking and abandonment, and its objective is to choose optimal queue-capacities (buffer lengths) for sellers and buyers to minimize an infinite horizon discounted linear cost functional which consists of holding costs, and penalty costs for blocking and abandonment.When the arrival intensities of both customer classes tend to infinity in concert, we use a heavy traffic approximation to formulate an approximate diffusion control problem (DCP), and derive an optimal threshold policy for the DCP. Finally, we employ the DCP solution to establish an easy-to-implement, simple asymptotically optimal threshold policy for the original queueing control problem.

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“…Büke and Chen [13] studied stabilizing admission control policies for the probabilistic matching systems. Lee et al [41] discussed optimal control of a time-varying double-ended production queueing model.…”

Section: Introductionmentioning

confidence: 99%

Matched Queues with Matching Batch Pair (m, n)

Liu¹,

Li²,

Zhang³

2020

Preprint

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In this paper, we discuss an interesting but challenging bilateral stochastically matching problem: A more general matched queue with matching batch pair (m, n) and two types (i.e., types A and B) of impatient customers, where the arrivals of A-and B-customers are both Poisson processes, m A-customers and n B-customers are matched as a group which leaves the system immediately, and the customers' impatient behavior is to guarantee the stability of the system. We show that this matched queue can be expressed as a novel bidirectional level-dependent quasi-birthand-death (QBD) process. Based on this, we provide a detailed analysis for this matched queue, including the system stability, the average stationary queue lengthes, and the average sojourn time of any A-customer or B-customer. We believe that the methodology and results developed in this paper can be applicable to dealing with more general matched queueing systems, which are widely encountered in various practical areas, for example, sharing economy, ridesharing platform, bilateral market, organ transplantation, taxi services, assembly systems, and so on.

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Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Cited by 3 publications

References 27 publications

Multi-component Matching Queues in Heavy Traffic

Multi-component Matching Queues in Heavy Traffic

Admission Control for Double-ended Queues

Matched Queues with Matching Batch Pair (m, n)

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