Problem $6[10$ points$]$

A set of $\backslash ($ N $\backslash )$ users shares a common medium of a fixed capacity $\backslash ($ C $\backslash )$ and bandwidth $\backslash ($ B $\backslash ).$ Describe the preferred multiplexing method under the following traffic models. Defend your choice by explaining why the selected multiplexing method better suits the traffic model $($advantages and disadvantages of competing solutions$).$

$($a$)[\backslash (\backslash$mathbf$\{3\}\backslash )$ points$]$: All users are backlogged and have traffic to send at all times. For example, the users are live streams from $\backslash ($ N $\backslash )$ cameras sharing the same medium.

$($b$)[\backslash (\backslash$mathbf$\{3\}\backslash )$ points$]$: Traffic at each user arrives at varying rates and follows different distributions. Some users have higher average rates, and those rates may vary with time.

$($b$)[4$ points$]$: A hybrid of the two models above. Some users have constant traffic, whereas others receive a random traffic pattern following different probability distributions.