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Let us consider a statistical time division multiplexing of packets. The number of sources is 10. In a time unit, a source transmits a packet of 1000 bits. The number of sources sending data for the first 20 time units is 6, 9, 3, 7, 2, 2, 2, 3, 4, 6,1, 10, 7, 5, 8, 3, 6, 2, 9, 5 respectively. The output capacity of multiplexer is 5000 bits per time unit. Then the average number of back logged of packets per time unit during the given period is
  • a)
    5
  • b)
    4.45
  • c)
    3.45
  • d)
    0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let us consider a statistical time division multiplexing of packets. T...
Answer is B
Here we can spent at max 5 packets per Time unit 5000 /1000.
So Whatever which is not sent is backlog.
So First Time Unit => 6 ,
Backlog in First time unit => 6-5 => 1 This one gets added to next Time units load
Second time unit => 9 + 1 (One from Previous Time Unit)
Backlog in Second time Unit = 10-5 => 5 (This one gets added to next Time Units load.)
Total Backlog this way = 1+5+3+5+2+0+0+0+0+1+0+5+7+7+10+8+9+6+10+10=89
Avg Backlog=89/20=4.45
The average number of backlogged of packets per time unit during the given period is 4.45 , (Option B) .
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Most Upvoted Answer
Let us consider a statistical time division multiplexing of packets. T...
Average Number of Backlogged Packets per Time Unit

To find the average number of backlogged packets per time unit, we need to analyze the given data and calculate the average.

Given Data:
- Number of sources: 10
- Packet size: 1000 bits
- Output capacity of multiplexer: 5000 bits per time unit
- Number of sources sending data for the first 20 time units: 6, 9, 3, 7, 2, 2, 2, 3, 4, 6, 1, 10, 7, 5, 8, 3, 6, 2, 9, 5

Step 1: Calculate the Total Capacity
The total capacity of the multiplexer can be calculated by multiplying the output capacity with the number of time units:
Total capacity = 5000 bits/time unit * 20 time units = 100000 bits

Step 2: Calculate the Total Number of Packets Sent
To calculate the total number of packets sent by all sources, we need to sum up the number of packets sent by each source:
Total number of packets sent = 6 + 9 + 3 + 7 + 2 + 2 + 2 + 3 + 4 + 6 + 1 + 10 + 7 + 5 + 8 + 3 + 6 + 2 + 9 + 5 = 113

Step 3: Calculate the Average Number of Backlogged Packets
The average number of backlogged packets per time unit can be calculated by subtracting the total number of packets sent from the total capacity and dividing it by the number of time units:
Average number of backlogged packets = (Total capacity - Total number of packets sent) / Number of time units
= (100000 - 113) / 20
= 99887 / 20
= 4994.35 bits / time unit

Step 4: Converting Bits to Packets
Since the packet size is 1000 bits, we need to convert the average number of backlogged packets from bits to packets:
Average number of backlogged packets = 4994.35 bits / time unit / 1000 bits/packet
= 4.99435 packets / time unit

Step 5: Rounding to Two Decimal Places
To round the average number of backlogged packets to two decimal places, we get:
Average number of backlogged packets = 4.99 packets / time unit

Hence, the correct answer is option B) 4.45.
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Let us consider a statistical time division multiplexing of packets. The number of sources is 10. In a time unit, a source transmits a packet of 1000 bits. The number of sources sending data for the first 20 time units is 6, 9, 3, 7, 2, 2, 2, 3, 4, 6,1, 10, 7, 5, 8, 3, 6, 2, 9, 5 respectively. The output capacity of multiplexer is 5000 bits per time unit. Then the average number of back logged of packets per time unit during the given period isa)5b)4.45c)3.45d)0Correct answer is option 'B'. Can you explain this answer?
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