Multiple Class G-Networks with Jumps back to Zero

We consider multiple class G-networks of processor sharing queues with negative customers which destroy all the customers in a queue. We prove that these networks have a product form solution for steady-state distribution. These networks may have some applications in reliability or performability as the negative customers may clearly model breakdown of computer or communication systems. We also show that under simple assumptions these networks always have a stationary distribution. Finally, we present some asymptotic results on the average number of customers and the average sojourn time when the arrival rate goes to innnity.