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Mark M.

asked • 05/23/20

Not sure how to determine PMF

In random access communication protocols a population of users is contending for the use of a common channel to transmit their packets, without the control and supervision of a master station. In the sequel we assume that time is divided into timeslots. The communication channel can handle at most two packets in a timeslot. Because all users transmit packets when they themselves find appropriate, it will be possible of course that multiple users transmit a packet during the same time. If one or two users transmit a packet over the channel in a certain timeslot, then these transmissions are successfull. If three users transmit a packet over the channel in the timeslot, a small collision occurs and only one of the three packets is transmitted successfully. If four or more users transmit a packet in the timeslot, then a big collision occurs and all the packets transmitted in the timeslot are lost.


Suppose now that we have n users that always have packets to transmit over the channel. At the beginning of each timeslot each user, independently of all the other users, decides to transmit a packet with probability p = α/n for some α > 0.


Give the probability mass function PK(k; α, n) of the number of users, K, that transmit a packet over the communication channel in a certain timeslot in this case and evaluate it for n = 5, 10 and 100 and for α = 2.


Not sure how to determine the PMF here, could anyone help? Thanks!

Stanton D.

You'd probably start with a Poisson distribution, and modify for losses incurred when n>=3 users attempt transmission. (Or you might, as my Verizon service likes to do, simply permit some cross-channel bleed when the network gets full!)
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05/24/20

1 Expert Answer

By:

Tom K.

tutor
Note that we approach the Poisson with lambda = 2 for x's distribution.
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05/24/20

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