Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0780.90056
Braglia, M.
$M/M/1$ queueing model with ordinary maintenance and breakdowns. (English)
[J] RAIRO, Rech. Opér. 27, No.1, 1-21 (1993). ISSN 0399-0559

Summary: An $M/M/1$ system with ordinary maintenance and possibility of breakdowns is considered from a practical point of view. An appropriate equation for the probability of $n$ units in the system at any instant of time is written in terms of the Green function of the conventional $M/M/1$ model and solve by an iterative technique which imposes a periodic regime state. Some Monte Carlo simulations are used to assess the accuracy of the iterative process, i.e. verify that it really converges to the correct solution. Special attention is turned to the analysis of the error that is introduced if the different breakdowns that may occur during the service interval are replaced by a single cumulative waste of time. Numerical results are reported for the special cases in which this cumulative breakdown is placed at the beginning or at the end of the service interval, or is uniformly distributed. To some extent, part of the analysis is deliberately approximated, even if good accuracy is always preserved. The extension to the $M/G/1$ model is also considered.

MSC 2000:: *90B25 Reliability, etc.
90B22 Queues and service
60K25 Queueing theory

Keywords: $M/M/1$ system; maintenance; breakdowns; Green function; Monte Carlo simulations; $M/G/1$ model

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]