On a non-Markovian queueing problem under a control operating policy and start-up times

Arun Borthakur; Ruby Gohain

Aplikace matematiky (1982)

  • Volume: 27, Issue: 4, page 243-250
  • ISSN: 0862-7940

Abstract

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A non-Markovian queueing system with Poisson input is studied under a modified operating rule called “control operating policy” in which the server begins “start-up” only when the queue length reaches a fixed number n ( 1 ) . By using the supplementary variable technique, the distribution of the queue length (excluding those being served) in the form of a generating function is obtained. As a special case, a Markovian queueing system with exponential start-up is discussed in detail to analyse the economic behaviour of the system.

How to cite

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Borthakur, Arun, and Gohain, Ruby. "On a non-Markovian queueing problem under a control operating policy and start-up times." Aplikace matematiky 27.4 (1982): 243-250. <http://eudml.org/doc/15245>.

@article{Borthakur1982,
abstract = {A non-Markovian queueing system with Poisson input is studied under a modified operating rule called “control operating policy” in which the server begins “start-up” only when the queue length reaches a fixed number $n(\ge 1)$. By using the supplementary variable technique, the distribution of the queue length (excluding those being served) in the form of a generating function is obtained. As a special case, a Markovian queueing system with exponential start-up is discussed in detail to analyse the economic behaviour of the system.},
author = {Borthakur, Arun, Gohain, Ruby},
journal = {Aplikace matematiky},
keywords = {control operating policy; distribution of the queue length; economic behaviour of systems; control operating policy; distribution of the queue length; economic behaviour of systems},
language = {eng},
number = {4},
pages = {243-250},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a non-Markovian queueing problem under a control operating policy and start-up times},
url = {http://eudml.org/doc/15245},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Borthakur, Arun
AU - Gohain, Ruby
TI - On a non-Markovian queueing problem under a control operating policy and start-up times
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 4
SP - 243
EP - 250
AB - A non-Markovian queueing system with Poisson input is studied under a modified operating rule called “control operating policy” in which the server begins “start-up” only when the queue length reaches a fixed number $n(\ge 1)$. By using the supplementary variable technique, the distribution of the queue length (excluding those being served) in the form of a generating function is obtained. As a special case, a Markovian queueing system with exponential start-up is discussed in detail to analyse the economic behaviour of the system.
LA - eng
KW - control operating policy; distribution of the queue length; economic behaviour of systems; control operating policy; distribution of the queue length; economic behaviour of systems
UR - http://eudml.org/doc/15245
ER -

References

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  1. K. R. Baker, A Cost Function for a Markovian Production - Inventory System Under Base-Stock Level Control, Technical Memo No. 707, January; (1970). (1970) 
  2. K. R. Baker, A Note on Operating Policies for the Queue M/M/1 with Exponential Start-ups, INFOR, Vol. 11, No. 1, February; (1973). (1973) Zbl0247.60057MR0339803
  3. D. P. Heyman, Optimal Operating Policies for M/G/1 Queueing System, O.R. Vol. 16, No. 2, March-April; (1968). (1968) Zbl0164.47704

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