Coupled queues with customer impatience

Evdokimova, Ekaterina; Turck, Koen De; Fiems, Dieter

doi:10.1016/j.peva.2017.10.002

Cited by 10 publications

(8 citation statements)

References 27 publications

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“…We will first show the uniqueness of the solution to (8), which further implies a unique solution to (7) by taking e → 0. If d < f then we rewrite (8)…”

Section: System Optimizationmentioning

confidence: 99%

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Fluid queues with synchronized output

Boxma

Kella

Ravner

2019

Operations Research Letters

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“…We will first show the uniqueness of the solution to (8), which further implies a unique solution to (7) by taking e → 0. If d < f then we rewrite (8)…”

Section: System Optimizationmentioning

confidence: 99%

“…In view of the complexity of the above-mentioned multiqueue models, numerical methods are usually employed for their analysis, or some relaxing assumptions are made (e.g. [18,19] and [8]). Approximations and asymptotic techniques have also been used (e.g.…”

Section: Introductionmentioning

confidence: 99%

Fluid queues with synchronized output

Boxma

Kella

Ravner

2019

Operations Research Letters

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“…The dynamics of our model in the memory-abundant regime are also related to the so-called averaging principle in establishing fluid approximation for Markov processes, where the evolution of a Markov process at a slow time scale is influenced by average behavior of a modulating process at a faster time scale (cf. Perry andWhitt (2011), Mandelbaum et al (1998), Evdokimova et al (2018), Coutin et al (2010); see also Darling and Norris (2008) for an overview.) However, in these models the underlying slow process is Markovian (e.g., queue lengths) and the modulating process a function of its value (e.g., the differences in queue lengths in Perry and Whitt (2011)).…”

Section: Related Literaturementioning

confidence: 99%

Reinforcement with Fading Memories

Yun

2018

Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems

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We study the effect of imperfect memory on decision making in the context of a stochastic sequential action-reward problem. An agent chooses a sequence of actions which generate discrete rewards at different rates. She is allowed to make new choices at rate β, while past rewards disappear from her memory at rate µ. We focus on a family of decision rules where the agent makes a new choice by randomly selecting an action with a probability approximately proportional to the amount of past rewards associated with each action in her memory.We provide closed-form formulae for the agent's steady-state choice distribution in the regime where the memory span is large (µ → 0), and show that the agent's success critically depends on how quickly she updates her choices relative to the speed of memory decay. If β µ, the agent almost always chooses the best action, i.e., the one with the highest reward rate. Conversely, if β µ, the agent chooses an action with a probability roughly proportional to its reward rate. 1

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“…This modification considerably complicates performance assessments, as the corresponding stochastic model now consists of two coupled 'queues': a decoupling inventory and an order backlog. See, e.g., [27][28][29][30] for other applications of coupled queueing systems and [31][32][33][34] for Markovian systems that include both queueing and inventory management. The performance of this hybrid MTS/MTO system is assessed when the same production capacity is used for MTS and MTO.…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

et al. 2020

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We present a comprehensive numerical approach with reasonably light complexity in terms of implementation and computation for assessing the performance of hybrid make-to-stock (MTS)/make-to-order (MTO) systems. In such hybrid systems, semi-finished products are produced up front and stored in a decoupling inventory. When an order arrives, the products are completed and possibly customised. We study this system in a stochastic setting: demand and production are modelled by random processes. In particular, our model includes two coupled Markovian queues: one queue represents the decoupling inventory and the other the order backlog. These queues are coupled as order processing can only occur when both queues are non-empty. We rely on matrix analytic techniques to study the performance of the MTO/MTS system under non-restrictive stochastic assumptions. In particular, we allow for arrival correlation and non-exponential setup and MTS and MTO processing times, while the hybrid MTS/MTO system is managed by an (s,S)-type threshold policy that governs switching from MTO to MTS and back. By some numerical examples, we assess the impact of inventory control, irregular order arrivals, setup and order processing times on inventory levels and lead times.

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Coupled queues with customer impatience

Cited by 10 publications

References 27 publications

Fluid queues with synchronized output

Fluid queues with synchronized output

Reinforcement with Fading Memories

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

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