Abstract
A finite-buffer queueing system of the M/M/1/N type is used for modeling the operation of a single-machine production line with cyclic failure-free and repair periods. The arriving jobs enter randomly according to a Poisson process and are being processed individually with service times having the common exponential distribution. After an exponentially distributed working period a breakdown of the machine occurs, starting an exponentially distributed repair time during which the service process is stopped. At the completion epoch of the repair time a new working period begins and so on. A system of integral equations for conditional probability distributions of the number of jobs completely processed before the fixed time t (departure process) is built, using the concept of embedded Markov chain and the total probability law. Applying linear-algebraic approach the compact-form solution of the corresponding system written for double transforms of departure process is found.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
