On a tandem queue with batch service and its applications in wireless sensor networks

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Abstract

We present a tandem network of queues 0, …, s -1. Customers arrive at queue 0 according to a Poisson process with rate λ. There are s independent batch service processes at exponential rates μ0, …, μs−1. Service process i , i = 0, … , s -1, at rate μi is such that all customers of all queues 0, …, i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of μi appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.
Original languageEnglish
Pages (from-to)81
Number of pages93
JournalQueueing systems
Volume87
Issue number1-2
DOIs
Publication statusPublished - 2 Jun 2017

Fingerprint

Batch Service
Tandem Queues
Queue
Wireless Sensor Networks
Wireless sensor networks
Sensors
Data fusion
Decentralized
Sensor networks
Customers
Scheduling
Sensor
Product Form
Steady-state Distribution
Queueing Model
Data Fusion
Optimal Allocation
Poisson process
Waiting Time
Sensor Networks

Keywords

  • Tandem network of queues with Batch Service
  • Wireless Sensor Network
  • Broadcasting
  • Scheduling

Cite this

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title = "On a tandem queue with batch service and its applications in wireless sensor networks",
abstract = "We present a tandem network of queues 0, …, s -1. Customers arrive at queue 0 according to a Poisson process with rate λ. There are s independent batch service processes at exponential rates μ0, …, μs−1. Service process i , i = 0, … , s -1, at rate μi is such that all customers of all queues 0, …, i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of μi appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.",
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On a tandem queue with batch service and its applications in wireless sensor networks. / Mitici, Michaela; Goseling, Jasper ; van Ommeren, Jan C.W.; de Graaf, Maurits ; Boucherie, Richard.

In: Queueing systems, Vol. 87, No. 1-2, 02.06.2017, p. 81.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Mitici, Michaela

AU - Goseling, Jasper

AU - van Ommeren, Jan C.W.

AU - de Graaf, Maurits

AU - Boucherie, Richard

PY - 2017/6/2

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N2 - We present a tandem network of queues 0, …, s -1. Customers arrive at queue 0 according to a Poisson process with rate λ. There are s independent batch service processes at exponential rates μ0, …, μs−1. Service process i , i = 0, … , s -1, at rate μi is such that all customers of all queues 0, …, i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of μi appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.

AB - We present a tandem network of queues 0, …, s -1. Customers arrive at queue 0 according to a Poisson process with rate λ. There are s independent batch service processes at exponential rates μ0, …, μs−1. Service process i , i = 0, … , s -1, at rate μi is such that all customers of all queues 0, …, i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of μi appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.

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KW - Scheduling

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