Question

Consider a packet of length \(L\) which begins at end system A and travels over three links to a destination end system. These three links are connected by two packet switches. Let \(d_{\vec{r}} s_{\vec{i}}\), and \(R_{i}\) denote the length, propagation speed, and the transmission rate of link \(i\), for \(i=1,2,3\). The packet switch delays each packet by \(d_{p \text { moc }}\). Assuming no queuing delays, in terms of \(d_{i} s_{i} R_{i}\), ( \(i=1,2,3\) ), and \(L\), what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, the propagation speed on all three links is \(2.5\). \(10^{8} \mathrm{~m} / \mathrm{s}\), the transmission rates of all three links are \(2 \mathrm{Mbps}\), the packet switch processing delay is \(3 \mathrm{msec}\), the length of the first link is \(5,000 \mathrm{~km}\), the length of the second link is \(4,000 \mathrm{~km}\), and the length of the last link is \(1,000 \mathrm{~km}\). For these values, what is the end-to-end delay?

Short answer

The total end-to-end delay is 64 milliseconds.

Step-by-step solution

Identify and Express Components of Delay

The total end-to-end delay is the sum of transmission delays, propagation delays, and processing delays at the switches. Transmission delay for each link is given by \( \frac{L}{R_i} \). Propagation delay for each link is \( \frac{d_i}{s_i} \). The processing delay at each switch is \( d_{p \text{ moc}} \). Thus, the total delay for three links and two packet switches is: \[ \sum_{i=1}^{3} \left(\frac{L}{R_i} + \frac{d_i}{s_i}\right) + 2 \times d_{p \text{ moc}} \]

Calculate Transmission Delays

The transmission rate \( R_i \) for each link is 2 Mbps, and the packet length is 1,500 bytes (or 12,000 bits). Calculate the transmission delay for each link using \( \frac{L}{R_i} = \frac{12,000}{2 \times 10^6} \) seconds for each link. This simplifies to 0.006 seconds or 6 milliseconds per link.

Calculate Propagation Delays

Each link has a different length \( d_i \) but the same propagation speed \( s_i = 2.5 \times 10^8 \) m/s. Calculate the propagation delay for:- Link 1: \( \frac{5,000,000}{2.5 \times 10^8} = 0.02 \) seconds (20 milliseconds)- Link 2: \( \frac{4,000,000}{2.5 \times 10^8} = 0.016 \) seconds (16 milliseconds)- Link 3: \( \frac{1,000,000}{2.5 \times 10^8} = 0.004 \) seconds (4 milliseconds)

Account for Switch Processing Delays

Each packet switch delays the packet by 3 milliseconds. With two packet switches, the total processing delay is \(2 \times 3 = 6 \) milliseconds.

Sum All Delays for Total End-to-End Delay

Add up all the calculated delays:- Transmission delays: \(3 \times 6 \) milliseconds = 18 milliseconds- Propagation delays: 20 ms + 16 ms + 4 ms = 40 milliseconds- Processing delays: 6 millisecondsTotal end-to-end delay = 18 ms + 40 ms + 6 ms = 64 milliseconds.

Key concepts

Transmission Delay

Imagine sending a letter to a friend. The time it takes to write and send the letter is similar to transmission delay in networking. Transmission delay refers to the time required to push all packet bits onto the link. It depends on the packet's size and the transmission rate of the link.

To calculate this delay, we use the formula \( \frac{L}{R} \), where \( L \) is the packet length in bits and \( R \) is the transmission rate in bits per second. For example, if you send a 12,000-bit packet over a link with a 2 Mbps rate, the transmission delay is \( \frac{12,000}{2,000,000} = 0.006 \) seconds, or 6 milliseconds. Each link along the packet's path contributes to the overall transmission delay.

Propagation Delay

Propagation delay is like the travel time of a car on a highway. This delay occurs when a signal travels from the sender to the receiver over a physical medium, like a fiber optic cable. It's influenced by two main factors: the distance between the two points and the speed at which the signal travels.

We calculate it using \( \frac{d}{s} \), where \( d \) is the distance in meters and \( s \) is the propagation speed (typically close to the speed of light in the medium). For instance, a 5,000 km link with a speed of \( 2.5 \times 10^8 \) m/s results in a propagation delay of \( \frac{5,000,000}{2.5 \times 10^8} = 0.02 \) seconds or 20 milliseconds. Remember, this delay only depends on the medium and distance, not packet size.

Processing Delay

Processing delay consists of the time routers or switches use to process the packet header information. It is like a customs officer checking and stamping a passport. This delay arises from various tasks, such as error checking and routing decisions, executed at each network device.

In typical cases, processing delay is a small, nearly constant duration, often a few milliseconds. In our scenario, each packet switch adds a processing delay of 3 milliseconds. Since there are two switches in the path, the total processing delay will be \( 2 \times 3 \) milliseconds = 6 milliseconds. Understanding processing delay is crucial for assessing how switches and routers impact our data transfers.

Network Performance

Network performance is an umbrella term that encompasses various metrics like throughput, latency, and packet loss. It tells us how well the network serves its users. In particular, the sum of transmission, propagation, and processing delays affects how fast and efficiently a network operates.

End-to-end delay is one of the significant components of network performance, determining the time data takes to travel from sender to receiver. In our example, all delays combined (18 ms for transmission, 40 ms for propagation, and 6 ms for processing) resulted in a total end-to-end delay of 64 milliseconds. Keeping these delays optimized is vital for smooth and efficient network services.

• Throughput: Measures data rate over the network.
• Latency: Refers to delay in data transfer.
• Packet Loss: Indicates lost data packets during transfer.

Ensuring good network performance involves a balance of these parameters to meet the required levels of service.