In packet data transmission, the time between successfully received packets is called the interarrival time, and randomness in packet interarrival times is called jitter. In real-time packet data communications, jitter is undesirable. One measure of jitter is the standard deviation of the packet interarrival time. From Problem 2.6.5, calculate the jitter σT. How large must the successful transmission probability q be to ensure that the jitter is less than 2 milliseconds?

Problem 2.6.5

A source wishes to transmit data packets to a receiver over a radio link. The receiver uses error detection to identify packets that have been corrupted by radio noise. When a packet is received error-free, the receiver sends an acknowledgment (ACK) back to the source. When the receiver gets a packet with errors, a negative acknowledgment (NAK) message is sent back to the source. Each time the source receives a NAK, the packet is retransmitted. We assume that each packet transmission is independently corrupted by errors with probability q.

(a) Find the PMF of X, the number of times that a packet is transmitted by the source.

(b) Suppose each packet takes 1 millisecond to transmit and that the source waits an additional millisecond to receive the acknowledgment message (ACK or NAK) before retransmitting. Let T equal the time required until the packet is successfully received. What is the relationship between T and X? What is the PMF of T ?