Question

Suppose there is exactly one packet switch between a sending host and a receiving host. The transmission rates between the sending host and the switch and between the switch and the receiving host are \(R_{1}\) and \(R_{2}\), respectively. Assuming that the switch uses store-and-forward packet switching, what is the total end-to-end delay to send a packet of length \(L ?\) (Ignore queuing, propagation delay, and processing delay.)

Short answer

Total end-to-end delay is \( \frac{L}{R_1} + \frac{L}{R_2} \).

Step-by-step solution

Understand the Problem

In this problem, we're supposed to calculate the total end-to-end delay for a packet of length \( L \) sent from the sending host to the receiving host through one packet switch. The transmission rates are \( R_1 \) for the link between the sending host and the switch, and \( R_2 \) for the link between the switch and the receiving host. We are using store-and-forward packet switching, and we need to ignore queuing delays, propagation delays, and processing delays.

Calculate Transmission Delay Between Sending Host and Switch

The transmission delay for sending the packet from the sending host to the switch is calculated using the formula: \[ \text{Transmission Delay} = \frac{L}{R_1} \] where \( L \) is the packet length and \( R_1 \) is the transmission rate of the link between the sending host and the switch.

Calculate Transmission Delay Between Switch and Receiving Host

The transmission delay for sending the packet from the switch to the receiving host is given by: \[ \text{Transmission Delay} = \frac{L}{R_2} \] where \( L \) is the packet length and \( R_2 \) is the transmission rate of the link between the switch and the receiving host.

Calculate Total End-to-End Delay

The total end-to-end delay is the sum of the transmission delays calculated in Step 2 and Step 3. Hence, it is given by: \[ \text{Total Delay} = \frac{L}{R_1} + \frac{L}{R_2} \] This sum includes the time needed for the packet to be transmitted to the switch and then from the switch to the receiving host.

Key concepts

Transmission Rate

The transmission rate is a crucial concept in networking. It refers to the speed at which data can be transmitted over a network link. Measured in bits per second (bps), the transmission rate determines how quickly data packets, the building blocks of network communication, can be sent from one point to another. In packet switching, the transmission rate impacts the time it takes for a packet to be transmitted from one device to another. Understanding the transmission rate is essential because it directly affects the efficiency of data transfer. A higher transmission rate means data can be sent more quickly, reducing wait times in communication. On the contrary, a lower transmission rate results in a slower transfer, which might not be ideal for time-sensitive transmissions like video conferencing or online gaming. When working out problems related to packet switching, like in the original exercise, calculating how long it takes a packet of information to travel over each link requires knowledge of the respective transmission rates. These rates, represented as \( R_1 \) and \( R_2 \) for different segments of a network path, help in understanding and optimizing the network performance.

End-to-End Delay

End-to-end delay encompasses the total time taken for a packet to travel from the source to the destination. This delay includes several components, but in the context of our simplified exercise, we only consider the transmission delays since other factors (like queuing, propagation, and processing delays) are ignored.To solve for the end-to-end delay, we break it down into different segments:

• The first segment is from the sending host to the switch with a transmission delay of \( \frac{L}{R_1} \), where \( L \) is the packet length and \( R_1 \) is the transmission rate between these nodes.
• The second is from the switch to the receiving host, represented as \( \frac{L}{R_2} \).
• The total end-to-end delay is the sum of these two individual transmission delays, resulting in \( \frac{L}{R_1} + \frac{L}{R_2} \).

Understanding these calculations helps highlight how network elements and their individual performance characteristics contribute to the overall delay experienced by data packets. This insight is valuable for optimizing network infrastructure and improving communication efficiency.

Store-and-Forward

The store-and-forward technique is a fundamental mechanism in packet-switched networks. It involves storing the entire packet at each point (or node) in the network before forwarding it to the next point. This method ensures that packets are received in their entirety before being processed and sent on, minimizing errors and improving the reliability of data transmission.With store-and-forward, routers and switches within a network can examine the packet data, perform necessary checks, and make forwarding decisions. This approach, although slightly delayed due to the need to store the data fully, is beneficial for handling complex network protocols and ensuring data integrity, especially on noisy links or those with high error rates.In the context of the original exercise, store-and-forward means:

• The packet is first fully received and stored at the switch, incurring no additional delay beyond the transmission delay since queuing and processing are ignored.
• Once stored, the switch then forwards the packet to the receiving host at the given transmission rate, \( R_2 \).

This method is contrasted with other packet-switching strategies that might begin forwarding data before the entire packet is received, which can reduce latency but at the risk of greater transmission errors.