Large-deviations analysis of the fluid approximation for a controllable tandem queue
type: Item
instance of: scholarly article
title: Large-deviations analysis of the fluid approximation for a controllable tandem queue
zbMATH Open document ID: 1038.60088
author: Alexander Gajrat
author: Arie Hordijk
author: A. Ridder
published in: The Annals of Applied Probability
publication date: 2004-03-30T00:00:00Z
review text: The paper considers a discrete-time tandem queueing network of two single-server queues, Bernoulli \((\lambda)\) arrivals, Bernoulli (\(\mu_1\) and \(\mu_2\)) servers and infinite buffers. The state of the network at time \(n\) is \(\xi^n= (\xi^n_1, \xi^n_2)\), where \(\xi^n_i\) is the number of customers in buffer \(i\). At each moment of time \(n\), a server \(i\) either serves a customer from its buffer \((a^n_i=1)\) or is idle \((a^n_i= 0)\). The value function of the process under control \(a= \{(a^n_1, a^n_2),\, n= 0,1,\dots\}\) is defined as \[ V_a(x(N)):= E^a_{x(N)} \sum^{T_n}_{n=0} (\xi^n_1 c_1+ \xi^n_2 c_2), \] where \(E^a_{x(N)}(\cdot)\) denotes the expectation given initial state \(x(N)\) and control \(a\). The discrete optimal control is \(V_a(x(N))\to \min\). To solve this problem, a fluid approximation is constructed. This approximation is used to get the first term of the asymptotic of the value function of the optimal policy. The main theorem of the paper gives the next term of the asymptotic.
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 2063744
zbMATH Keywords: discrete-time tandem queueing network
zbMATH Keywords: fluid approximation
zbMATH Keywords: optimal policy
reviewed by: Oleg K. Zakusilo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1069786504
OpenAlex ID: W2132154039
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DOI: 10.1214/AOAP/1069786504
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description: scientific article; zbMATH DE number 2063744