A Bmap\G\1 Queue With Randomly Limited Feedback Operating In A Markovian Random Envrionment

Abstract

Feedback queues model, e.g., real-life systems, where the serving device is not absolutely reliable such that the repeated service of a customer can be required. In the present paper, the feedback queue with the batch markovian arrival and generally distributed service time is considered. Additionally, it is assumed that some markovian finite state random environment influences the arrival and the service processes as well as feedback probability. Moreover, it is assumed that the amount of service repetitions for a single customer is limited by a random variable. The stationary state distribution of the queue is calculated and numerical examples are presented.