Let A and B be two stations attempting to transmit on an Ethernet. Each has a...

Let A and B be two stations attempting to transmit on an Ethernet. Each has a steady queue of frames ready to send; A’s frames will be numbered ?1, ?2 and so on, and B’s similarly. Let ? = 51.2 ???? be the exponential backoff base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times of 0 × ? and 1 × ?, respectively. As a result, Station A transmits ?1 while Station B waits. At the end of this transmission, B will attempt to retransmit ?1 while A will attempt to transmit ?2. These first attempts will collide, but now A backs off for either 0 × ? or 1 × ? (with equal probability), while B backs off for time equal to one of 0 × ?, 1 × ?, 2 × ? and 3× ? (with equal probability).

What is the probability that A wins all the ? backoff races. (? is a given constant)

Expert Solution

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venereology answered 5 hours ago

Let A and B be two stations attempting to transmit on an Ethernet. Each has a...

Let A and B be two stations attempting to transmit on an Ethernet. Each has a steady queue of frames ready to send; A’s frames will be numbered ?1, ?2 and so on, and B’s similarly. Let ? = 51.2 ???? be the exponential backoff base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times of 0 × ? and 1 × ?, respectively. As a result, Station A transmits ?1...

Let A and B be two stations attempting to transmit on an Ethernet. Each has a...

Let A and B be two stations attempting to transmit on an Ethernet. Each has a steady queue of frames ready to send; A’s frames will be numbered ?1, ?2 and so on, and B’s similarly. Let ? = 51.2 ???? be the exponential backoff base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times of 0 × ? and 1 × ?, respectively. As a result, Station A transmits ?1...

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Let A and B be two stations attempting to transmit on an Ethernet. Each has a...

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