Note on a tandem queue with delayed server release

W.M. Nawijn

Research output: Book/ReportReportProfessional

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Abstract

We consider a tandem queue with two stations. The first station is an $s$-server queue with Poisson arrivals and exponential service times. After terminating his service in the first station, a customer enters the second station to require service at a single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in station 1 is released. Two cases are considered. In the first case it is assumed that the service times in the second station are exponentially distributed. The solution of this model can be formulated using the matrix-geometric method. In the second case $s=2$ and, the service times are generally distributed. The model is analyzed using the supplementary variable technique, obtaining the relevant probability generating functions.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty of Mathematical Sciences
Number of pages15
ISBN (Print)0169-2690
Publication statusPublished - 2000

Publication series

NameMemorandum / Faculty of Mathematical Sciences
PublisherUniversity of Twente, Faculty of Mathematical Sciences
No.1531

Keywords

  • EWI-3351
  • IR-60818
  • METIS-141215
  • MSC-60K30

Cite this

Nawijn, W. M. (2000). Note on a tandem queue with delayed server release. (Memorandum / Faculty of Mathematical Sciences; No. 1531). Enschede: University of Twente, Faculty of Mathematical Sciences.
Nawijn, W.M. / Note on a tandem queue with delayed server release. Enschede : University of Twente, Faculty of Mathematical Sciences, 2000. 15 p. (Memorandum / Faculty of Mathematical Sciences; 1531).
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Nawijn, WM 2000, Note on a tandem queue with delayed server release. Memorandum / Faculty of Mathematical Sciences, no. 1531, University of Twente, Faculty of Mathematical Sciences, Enschede.

Note on a tandem queue with delayed server release. / Nawijn, W.M.

Enschede : University of Twente, Faculty of Mathematical Sciences, 2000. 15 p. (Memorandum / Faculty of Mathematical Sciences; No. 1531).

Research output: Book/ReportReportProfessional

TY - BOOK

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PY - 2000

Y1 - 2000

N2 - We consider a tandem queue with two stations. The first station is an $s$-server queue with Poisson arrivals and exponential service times. After terminating his service in the first station, a customer enters the second station to require service at a single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in station 1 is released. Two cases are considered. In the first case it is assumed that the service times in the second station are exponentially distributed. The solution of this model can be formulated using the matrix-geometric method. In the second case $s=2$ and, the service times are generally distributed. The model is analyzed using the supplementary variable technique, obtaining the relevant probability generating functions.

AB - We consider a tandem queue with two stations. The first station is an $s$-server queue with Poisson arrivals and exponential service times. After terminating his service in the first station, a customer enters the second station to require service at a single server, while in the meantime he is blocking his server in station 1 until he completes service in station 2, whereupon the server in station 1 is released. Two cases are considered. In the first case it is assumed that the service times in the second station are exponentially distributed. The solution of this model can be formulated using the matrix-geometric method. In the second case $s=2$ and, the service times are generally distributed. The model is analyzed using the supplementary variable technique, obtaining the relevant probability generating functions.

KW - EWI-3351

KW - IR-60818

KW - METIS-141215

KW - MSC-60K30

M3 - Report

SN - 0169-2690

T3 - Memorandum / Faculty of Mathematical Sciences

BT - Note on a tandem queue with delayed server release

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Nawijn WM. Note on a tandem queue with delayed server release. Enschede: University of Twente, Faculty of Mathematical Sciences, 2000. 15 p. (Memorandum / Faculty of Mathematical Sciences; 1531).