Data Communication

Question

A system uses the Stop-and-Wait ARQ Protocol, the bandwidth of the line is 1 Mbps. If each packet carries 1000 bits of data, how long does it take to send 1 million bits of data if the distance between the sender and receiver is 5000 Km and the propagation speed is 2 x 108 m/s? Ignore transmission, waiting, and processing delays. We assume no data or control frame is lost or damaged.

Answer 1

To calculate how long it takes to send 1 million bits of data using the Stop-and-Wait ARQ Protocol, we need to consider the following:

- Bandwidth (B): 1 Mbps = 1,000,000 bits per second.

- Packet size (P): 1000 bits per packet.

- Distance (d): 5000 km = 5,000,000 meters.

- Propagation speed (v): 2 x 10^8 meters per second.

- Total data to send (D): 1 million bits = 1,000,000 bits.

Step 1: Propagation Delay

The propagation delay is the time it takes for a signal to travel from the sender to the receiver. It's given by:

Propagation Delay = Distance / Propagation Speed

= 5,000,000 / (2 x 10^8)

= 0.025 seconds

= 25 ms

Step 2: Transmission Time Per Packet

The transmission time is the time it takes to send one packet over the channel, which is calculated as:

Transmission Time = Packet Size / Bandwidth

= 1000 / 1,000,000

= 0.001 seconds

= 1 ms

Step 3: Round-Trip Time (RTT)

The round-trip time (RTT) includes the time for the packet to travel to the receiver and the acknowledgment (ACK) to travel back to the sender:

RTT = 2 x Propagation Delay

= 2 x 0.025

= 0.05 seconds

= 50 ms

Step 4: Time Per Stop-and-Wait Cycle

For each cycle of Stop-and-Wait ARQ, the total time includes:

1. The transmission time to send a packet.

2. The RTT (since the sender waits for an acknowledgment).

Time Per Cycle = Transmission Time + RTT

= 0.001 seconds + 0.05 seconds

= 0.051 seconds

Step 5: Total Number of Cycles

The total data to be sent is 1,000,000 bits, and each packet carries 1000 bits, so the total number of cycles (packets) needed is:

Total Cycles = Total Data / Packet Size

= 1,000,000 / 1000

= 1000 packets

Step 6: Total Time to Send 1 Million Bits

Finally, the total time to send 1 million bits using Stop-and-Wait ARQ is:

Total Time = Total Cycles x Time Per Cycle

= 1000 x 0.051

= 51 seconds

Conclusion

It will take **51 seconds** to send 1 million bits of data using the Stop-and-Wait ARQ protocol, considering the given bandwidth, packet size, distance, and propagation speed.