Probability-time characteristics of MjGj1j1 queueing system with renovation

The queueing system in which the losses of incoming customers (tasks) are possible due to the introduction of a special renovation mechanism is under consideration. The renovation mechanism means that the task at the moment of the end of its service with some probability may empty the buffer and leave the system, or with an additional probability may just leave the system without emptying the buffer. The queueing system consists of the server with general service time distribution and the buffer of unlimited capacity. The incoming flow of tasks is a Poisson one. The embedded upon the end of service times Markov chain is constructed and under the assumption of the existence of a stationary regime for the embedded Markov chain the formula for the probability generation function is derived. In addition, the next probability characteristics (based on the embedded Markov chain) are obtained: The probability of the system being empty, the probability of a task in the buffer to be dropped (not to be dropped), the probability distribution of served (dropped) tasks. Also the average numbers of customers in the system, dropped customers and served customers (based on the embedded Markov chain) are derived as the service waiting time distribution for non-dropped tasks and the average service waiting time for non-dropped tasks. © Copyright 2017 for the individual papers by the papers' authors.