A computer router receives data packets that need to be transmitted to their destinations. The router operates in small time-slots that are such that on a given time-slot only two things can happen: either a packet is received or no packets are received. The probability that a packet is received during a given time-slot isp, independently of any other time-slots. Packets are stored in a waiting queue at the router until they are successfully transmitted to their destination; there is no limit to how many packets can be stored. On any given time-slot, the router will also attempt to send out one packet from the waiting queue to its destination. The probability that a packet is successfully transmitted during a time-slot isq, independently of any other attempts. A packet that arrives and finds no other packets in the waiting queue will wait until the next time-slot to be transmitted. LetXndenote the number of packets waiting to be transmitted at the beginning of thenthtime-slot. Note that the state space ofXnisS= {0, 1, 2, 3,...}