In this problem, we consider sending real$-$time voice from Host A to Host B over a packetswitched

network $($VoIP$).$ Host A converts analog voice to a digital $64$ kbps bit stream on the fly.

Host A then groups the bits into $56-$byte packets. There is one link between Hosts A and B; its

transmission rate is $2$ Mbps and its propagation delay is $10$ msec. As soon as Host A gathers a

packet, it sends it to Host B$.$ As soon as Host B receives an entire packet, it converts the

packet$$s bits to an analog signal. How much time elapses from the time a bit is created $($from the

original analog signal at Host A$)$ until the bit is decoded $($as part of the analog signal at Host B$)?$

P$8.$ Suppose users share a $3$ Mbps link. Also suppose each user requires $150$ kbps when

transmitting, but each user transmits only $10$ percent of the time. $($See the discussion of packet

switching versus circuit switching in Section $1\mathrm{.}3.)$

a$.$ When circuit switching is used, how many users can be supported?

b$.$ For the remainder of this problem, suppose packet switching is used. Find the probability

that a given user is transmitting.

c$.$ Suppose there are $120$ users. Find the probability that at any given time, exactly n users

are transmitting simultaneously. $($Hint: Use the binomial distribution.$)$

d$.$ Find the probability that there are $21$ or more users transmitting simultaneously.