On Ergodic Properties of Queues with Balking

The queues with balking are considered as simple queues with the time of employment of a server by a given customer depending on the waiting time. A sufficient condition for the existence of a limit distribution for these queues is given. The proof of this fact is based on the technique developed for the simple queue. The case when the queue satisfies some additional condition of monotony is considered. In this case a necesswy and sufficient condition for ergodicity is found. The necessity of the condition is proved by constructing some majorizing simple queue.