On two modifications of E-r/E-s/1/m queuing system subject to disasters

Abstract

The paper deals with modelling a finite single-server queuing system with the server subject to disasters. Inter-arrival times and service times are assumed to follow the Erlang distribution defined by the shape parameter r or s and the scale parameter rλ or sμ respectively. We consider two modifications of the model − server failures are supposed to be operate-independent or operate-dependent. Server failures which have the character of so-called disasters cause interruption of customer service, emptying the system and balking incoming customers when the server is down. We assume that random variables relevant to server failures and repairs are exponentially distributed. The constructed mathematical model is solved using Matlab to obtain steady-state probabilities which we need to compute the performance measures. At the conclusion of the paper some results of executed experiments are shown.