MATRIX GEOMETRIC SOLUTION OF UNRELIABLE SERVER M/M/1 QUEUEING SYSTEM WITH SECOND OPTIONAL SERVICE

An M/M/1 queueing system with second optional service and unreliable server is studied in existing paper. The customers arrive to the system according to Poisson process with state dependent rates depending upon the server's status. All customers demand the first essential service whereas only some of them demand the second optional service. A customer either may leave the system after the first essential service with probability (1- r), or at the completion of the first essential service go for second optional service with probability r (0 <= r <= 1) The matrix geometric technique is used for the analysis of the concerned queueing system. The sensitive analysis is also performed to examine the variation of the system perfounance characteristics with various input parameters.