A communication channel of capacity

Mbps $($megabits per second$)$ is

shared by a group of

N

T

i

users. Here, the channel capacity is the rate at which infor

mation can be transmiRed over the channel. Each user, User $,$ either transmits at a rate

of

i

Mbps or becomes idle with no transmission, where $<=1,2,3,,>.$ Unless stated

otherwise, the transmission activity of a user is independent with that of another. In a

certain time period, the probability that User transmits is $,$ where

i

pi

The

channel is saturated when the total transmission rate of all users equals to the channel

capacity or higher.

$0<$ pi

$<=1$

Let

A

S

$.$

and be the number of users who are transmiRing concurrently and the total

transmission rate of all users, respectively. There is no overhead in sharing the channel.