Problem $2$:

Consider the figure below, which shows the arrival of$10$ messages$$for transmission at different multiple access wireless nodes at times

t $=<0\mathrm{.}4,1\mathrm{.}2,1\mathrm{.}7,2\mathrm{.}7,3\mathrm{.}2,3\mathrm{.}7,3\mathrm{.}8,4\mathrm{.}1,4\mathrm{.}3,4\mathrm{.}8>$and$$each transmission requires exactly one time unit. For this question, you need to provide explanation to justify your answers to the items below.$$

A$.$ Suppose all nodes are implementing the Aloha protocol.

For each message, indicate the time at which each transmission begins.$$

Which messages transmit successfully?$$

B$.$Suppose all nodes are implementing the Slotted Aloha protocol.

For each message, indicate the time at which each transmission begins.

Which messages transmit successfully?$$

C$.$Suppose all nodes are implementing Carrier Sense Multiple Access $($CSMA$),$ but without collision detection.

Suppose that the time from when a message transmission begins until it is beginning to be received at other nodes is $0\mathrm{.}4$ time units. $($Thus if a node begins transmitting a message at t$=2\mathrm{.}0$ and transmits that message until t$=3\mathrm{.}0,$ then any node performing carrier sensing in the interval $[2\mathrm{.}4,3\mathrm{.}4]$ will sense the channel busy.$)$ For each message, indicate the time at which each message transmission begins, or indicate that message transmission does not begin due to a channel that is sensed busy when that message arrives.

Which messages transmitted successfully?$$

D$.$ Suppose all nodes are implementing Carrier Sense Multiple Access $($CSMA$),$ with collision detection $($CSMA$/$CD$).$

Suppose that the time from when a message transmission begins until it is beginning to be received at other nodes is $0\mathrm{.}4$ time units, and assume that a node can stop transmission instantaneously when a message collision is detected. $($Thus if a node begins transmitting a message at t$=2\mathrm{.}0$ and transmits that message until t$=3\mathrm{.}0,$ then any node performing carrier sensing in the interval $[2\mathrm{.}4,3\mathrm{.}4]$ will sense the channel busy.$)$ For each message, indicate the time at which each message transmission begins, or indicate that message transmission does not begin due to a channel that is sensed busy when that message arrives.

Which messages transmitted successfully?

At what time did each message stop transmitting due to a collision.