With Negative Customers With Bernoulli Feedback Geom/geom/1 Discrete-time Queuing Model

As in computer networks and communication systems, customers (parts or information packets, etc.) are transmitted by separate way, that is, all events are based on discrete-time,discrete-time queuing systems are more realistic than continuous-time queuing systems . Negative customers can be seen as misuses or disaster of the system , generally they are constraints of the system. They can kill the positive customers (that is, the usual customers)of the systerm. Queueing systerms with feedback mechanism also have very broad application. Bernoulli feedback is common, a lot of literature study the queue with Bernoulli feedback .This article based on three different killing mechanisms of negative customers, studies the Geom/Geom/1 discrete-time model with negative customers and Bernoulli feedback. The three killing mechanisms are RCE-inimmune servicing, RCE-immune servicing and DST. In this paper, using the general theory of Markov chain, I find the ergodicity conditions of the three killing mechanisms, probability generating function of the systerm size and the custerms in the waiting line, then I get the explicit formulae for the stationary distribution and other parameters. And I also make some numerical analysis to the queues with feedback and without it.