Let A and B be two stations attempting to transmit on Ethernet. Each has a steady queue of frames ready to send. A's frames will be numbered A₁, A₂ and so on, and B's similarly. Let T= 51.2 µs be the exponential backoff = base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times OxT and 1xT, respectively, meaning 'A' wins the race and transmits A₁, while B waits. At the end of this transmission, B will attempt to transmit B, while A will attempt to transmit A₂. These first attempts will collide, but now A backs off for either OxT or 1xT while B backs off for time equal to one of OxT......3xT. Give the probability that A wins the second backoff race.

Let A and B be two stations attempting to transmit on Ethernet. Each has a steady queue of frames ready to send. A's frames will be numbered A₁, A₂ and so on, and B's similarly. Let T= 51.2 µs be the exponential backoff = base unit. Suppose A and B simultaneously attempt to send frame 1, collide, and happen to choose backoff times OxT and 1xT, respectively, meaning 'A' wins the race and transmits A₁, while B waits. At the end of this transmission, B will attempt to transmit B, while A will attempt to transmit A₂. These first attempts will collide, but now A backs off for either OxT or 1xT while B backs off for time equal to one of OxT......3xT. Give the probability that A wins the second backoff race.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.4: The M/m/1/gd/∞/∞ Queuing System And The Queuing Formula L = Λw

Problem 7P

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