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 solved 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 in 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.
M/M/1 Queuing model with ordinary maintenance and breakdowns
BRAGLIA, MARCELLO
1993-01-01
Abstract
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 solved 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 in 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
