In the TCP protocol, a packet transmitted across a network is re-transmitted in case it goes lost (dropped). If the re-transmitted packet is also lost, another re-transmission is performed and so on. The sender however can specify a maximum re-transmission count R, after which no re-transmissions is attempted, and the connection is considered to be interrupted. The considered network is rather experimental, and as such the probability that a packet is lost is 0.8. Answer the following questions.

1. a) Assuming R = +, how many transmissions (including re-transmissions and the original packet) on average need to be performed before a packet is successfully sent?

2. b) If we have that R = 8, what is the probability that attempting to send 8 different packets (each has to reach destination and may require re-transmission) will result in the connection being interrupted?

The same network is used by an application using UDP instead of TCP. In UDP, no re-transmission is attempted for lost packets. Answer the following.

c) What is the probability that 32 or more consecutive packets are dropped? d) What is the probability that when sending 64 packets, only one of them is received at destination?

e) What is the probability that when sending 64 packets, 3 or more will be correctly sent? f) What is the average number of packets that will be correctly delivered before a drop occurs?

g) What is the average number of packets that will be correctly delivered out of a batch of 128 packets?