Question

Suppose two hosts \(\mathrm{A}\) and \(\mathrm{B}\) are connected via a router \(\mathrm{R}\). The \(\mathrm{A}-\mathrm{R}\) link has infinite bandwidth; the \(R-B\) link can send one packet per second. \(R\) 's queue is infinite. Load is to be measured as the number of packets per second sent from A to B. Sketch the throughput-versus-load and delay-versus-load graphs, or if a graph cannot be drawn, explain why. Would another way to measure load be more appropriate?

Short answer

Throughput increases linearly with load until 1 packet per second, then stays constant. Delay increases sharply once load exceeds 1 packet per second.

Step-by-step solution

Understanding the Problem

Two hosts, A and B, are connected via a router R. The A-R link has infinite bandwidth, while the R-B link can send one packet per second. The goal is to analyze the throughput and delay with respect to the load (number of packets per second sent from A to B).

Define Throughput

Throughput is defined as the rate at which packets are successfully delivered from A to B through R. Since the R-B link can only handle one packet per second, the maximum throughput is 1 packet per second.

Define Load

Load is the number of packets per second sent from A to B. If A sends more than one packet per second, packets will accumulate in R's queue because the R-B link can only transmit one packet per second.

Sketch Throughput-versus-Load Graph

For load (x-axis) less than or equal to 1 packet per second, throughput (y-axis) equals the load since all sent packets can be delivered. For load greater than 1 packet per second, throughput remains constant at 1 packet per second because the R-B link can only handle this rate. The graph starts at the origin and forms a straight line with a slope of 1 until the load hits 1, then becomes a horizontal line.

Define Delay

Delay is the time it takes for a packet to travel from A to B. For load less than or equal to 1 packet per second, the delay is minimal since there is no queue buildup. Beyond this load, packets will queue at R, increasing the delay.

Sketch Delay-versus-Load Graph

For load (x-axis) less than or equal to 1 packet per second, the delay (y-axis) is low and remains relatively constant. As load exceeds 1 packet per second, the delay grows rapidly because more packets are queued at R, forming a graph that sharply increases after the load of 1 packet per second.

Evaluate Load Measurement

In this context, measuring load as the number of packets per second is appropriate because it directly influences the throughput and delay characteristics observed in the network.

Key concepts

Throughput Measurement

Throughput is the rate at which packets are successfully transmitted from one host to another.
In our exercise, throughput is the number of packets delivered from Host A to Host B through Router R.

Since the A-R link has infinite bandwidth, it does not limit throughput. However, the R-B link only allows one packet per second to pass through.
This means that even if A sends multiple packets per second, the R-B link is the bottleneck, restricting the maximum throughput to one packet per second.

Thus, the throughput-versus-load graph starts at the origin, climbs linearly with a slope of 1 until it hits a load of 1 packet per second.
Beyond this point, the line becomes horizontal, indicating that the throughput remains constant at 1 packet per second, regardless of any additional load.

Delay Measurement

Delay refers to the time it takes for a packet to travel from the source to the destination.
It is influenced by many factors, including propagation delay, transmission delay, and queuing delay.

In the given problem, the delay is related to how packets queue at Router R.
For loads less than or equal to 1 packet per second, the delay is minimal because the packets can be transmitted immediately over the R-B link.
However, when the load exceeds 1 packet per second, packets start accumulating in Router R's queue.
This queued congestion leads to increased delay.
The delay-versus-load graph, therefore, starts low and relatively constant but then increases sharply as the load surpasses the 1 packet per second threshold.
It highlights a rapid growth in delay, primarily due to queuing.

Packet Transmission

Packet transmission involves sending data packets across a network from one host to another.
In our scenario, Host A sends packets to Host B through Router R.

The efficiency of transmission depends on the bandwidth of network links and the capabilities of Router R.
Since the A-R link has infinite bandwidth, there’s no delay in transmitting packets from A to R.
However, the R-B link can only handle one packet per second, making it the throttling point.
This restriction means any packet from A to B must wait for its turn to be transmitted if the load exceeds 1 packet per second.
Understanding this concept is crucial for network performance analysis, as it shows how bottlenecks can impede efficient data transfer and lead to increased latency.

It's also important to know the impact of queue management in routers, as it affects packet delivery and network throughput.
Good management can help reduce delays and improve the overall performance of the network.