Effective capacity across ab in the network shown is

General
1

effective capacity across ab in the network shown is

2

What is effective capacity across AB in the network shown?

The “effective capacity” of a network path, especially one between two points (like points A and B), refers to the maximum achievable data transfer rate considering any bottlenecks or constraints in the network. This measurement is crucial in network design for understanding the throughput and performance.

To calculate the effective capacity, follow these steps:

  1. Identify All Paths Between A and B:

    • List all possible paths between the two points. For example, if there are multiple routes from A to B, each must be considered separately.

  2. Determine Bandwidth for Each Path:

    • Analyze the available bandwidth of each link in the paths. Bandwidth can be defined as the maximum rate at which data can be transferred over a network link.

  3. Consider Serial Paths and Bottlenecks:

    • For paths in series, the effective capacity is dictated by the lowest bandwidth link within that path. This is because the slowest link will limit the overall throughput.

  4. Parallel Paths Analysis:

    • If there are parallel paths between A and B, the effective capacities of these paths can be summed to achieve the total capacity. This assumes traffic can be evenly distributed across the paths.

Let’s assume we have a simple network diagram with multiple paths between nodes A and B, with each path having individual bandwidth capacities. Here is a generalized formula to calculate the effective capacity.

Example Network:

Let’s envision the network as follows:

  • Path 1 through A-C-B with link capacities of A-C (100 Mbps) and C-B (150 Mbps).
  • Path 2 through A-D-B with link capacities of A-D (120 Mbps) and D-B (130 Mbps).

Step-by-Step Solution:

  1. Identify Paths and Link Bandwidths:

    • Path 1: A -> C -> B
      • Link A-C: 100 Mbps
      • Link C-B: 150 Mbps
    • Path 2: A -> D -> B
      • Link A-D: 120 Mbps
      • Link D-B: 130 Mbps

  2. Calculate Effective Capacity for Each Path:

    • For Path 1, the effective capacity is determined by the minimum of the two link bandwidths:
      $$ \text{Capacity of Path 1} = \min(100, 150) = 100 \text{ Mbps} $$
    • For Path 2, similarly:
      $$ \text{Capacity of Path 2} = \min(120, 130) = 120 \text{ Mbps} $$

  3. Combine Capacities of Parallel Paths:

    • Since both paths are parallel, the effective capacity of the network is the sum of the individual path capacities:
      $$ \text{Effective Capacity} = 100 \text{ Mbps} + 120 \text{ Mbps} = 220 \text{ Mbps} $$

Conclusion:

The effective capacity across AB in the given network, considering the paths and link constraints, would be 220 Mbps.

By breaking down the problem into steps and considering each link and path individually, we can determine the network’s overall effective capacity. This method ensures an accurate analysis of potential throughput in real-world scenarios.