Queues are commonly used in network systems. For example, e$-$mail is placed in

queues while it is waiting to be sent and after it arrives at the recipient's mailbox.

A problem occurs, however, if the outgoing mail processor cannot send one or

more of the messages in the queue. For example, a message might not be sent

because the recipient's system is not available.

Write an e$-$mail simulator that processes mail at an average of $20$ messages per

minute. As messages are received, they are placed in a queue. For the simulation,

assume that the messages arrive at an average rate of $30$ messages per minute.

Remember, the messages must arrive randomly, so you will need to use a random

number generator to determine when messages are received.

Each minute, you can dequeue up to $20$ messages and send them. Assume that

up to $25\%$ of the messages in the queue cannot be sent in any processing cycle.

Again, you will need to use a random number to determine whether a given

message can be sent. If it cannot be sent, put it back at the end of the queue or

enqueue it$.$

Run the simulator for $15$ minutes, tracking the number of times each message

had to be requeued. At the end of the simulation, print the statistics that show:

$1$ The total messages processed.

$2$ The average arrival rate, that is$,$ the average number of messages arriving

per minute.

$3$ The average number of messages sent per minute.

$4$ The average number of messages in the queue in a minute.

$5$ The number of messages sent on the first attempt, the number of messages

sent on the second attempt, and so forth.

$6$ The average number of times messages had to be requeued $($do not include

the messages sent the first time in this average.$)$

NOTE: Since the question is to assess your understanding of the concept of

Queue, you are NOT allowed to use the library of the language that implement

queue. You need to write the codes $($implementation$)$ of Queue for this exercise.

$($See point $($iii$).)$

Sample Output:

Please enter the total minutes to run: $30$

Total number of messages processed : $565$

Average arrival rate $,$:$29\mathrm{.}60$

Average number of messages sent per minute : $28\mathrm{.}7$

Average number of messages in the queue per minute :$65\mathrm{.}07$

Number of messages sent on $1$st attempt : $391$

Number of messages sent on $2$nd attempt

Number of messages sent on $3$rd attempt

Number of messages sent on $4$th attempt

Number of messages sent on $5$th attempt

: $87$

: $18$

:$4$

Average number of times messages had to be requeued :$1\mathrm{.}30$

Note: These are just sample answers to show the output format required from

your program. They are NOT necessarily the output that your program must

produce because the numbers shown were randomly generated.