Question

If costs are recorded as 8-bit numbers in a 50-router network, and distance vectors are exchanged twice a second, how much bandwidth per (full-duplex) line is chewed up by the distributed routing algorithm? Assume that each router has three lines to other routers.

Short answer

The bandwidth per line is 100 bytes/s.

Step-by-step solution

Understand the Network Setup

The network consists of 50 routers. Each router is connected to three other routers, forming a part of a larger interconnected network structure. The network uses distance vector routing, exchanging routing information regularly among routers.

Determine the Size of the Distance Vector

Each router needs to maintain a distance vector containing the cost to reach every other router. Since there are 50 routers, each router's distance vector will hold 50 cost entries. Each cost is recorded using an 8-bit number.

Calculate the Size of a Single Distance Vector Exchange

The size of the distance vector for each router is 50 entries multiplied by 8 bits per entry. Thus, the size is 400 bits or 50 bytes.

Determine the Frequency and Total Transfers

Routers exchange their distance vectors twice every second. Since each router has three connections, every router sends out three vectors per exchange. Therefore, each router performs 2 (exchanges per second) x 3 (lines) = 6 transmissions per second.

Calculate Bandwidth Usage

Each transmission is 50 bytes. Thus, each router transmits 6 x 50 = 300 bytes every second. Each of the 50 routers will transmit through their 3 lines.

Calculate Total Bandwidth Per Line

The overall bandwidth utilized per line is the total traffic sent by each router divided by the three lines. So, the overall bandwidth usage per line is \[ \text{Total Bandwidth for each router per second} = 300 \times 50 \text{ bytes/s} = 15000 \text{ bytes/s} \]Each line carries a third of this total:\[ \text{Bandwidth per (full-duplex) line} = \frac{15000}{50 \times 3} \text{ bytes/s} = 100 \text{ bytes/s} \]

Key concepts

Cost Metrics

In Distance Vector Routing, cost metrics are essential for determining the most efficient path through a network. A cost metric assigns a numeric value to each link, representing the "cost" of sending data packets through that link. Common cost metrics may include:

• Transmission Delay: Time it takes for a packet to travel from source to destination.
• Bandwidth: Available data rate of a link.
• Hop Count: Number of routers a packet has to pass through to reach its destination.

For our network scenario with 50 routers, each cost value is an 8-bit number. This means each cost ranges from 0 to 255. After calculating and assigning cost values, routers can derive the best path for data packet transmission by comparing these cost metrics. Lower cost values usually indicate a preferred path, ensuring efficiency and speed across the network. Each router uses these metrics in its distance vector table to dynamically adjust to network changes.

Full-duplex Communication

Full-duplex communication is a network feature allowing data transmission in two directions simultaneously. Unlike half-duplex systems, where data can only travel in one direction at a time, full-duplex systems eliminate waiting times, boosting the efficiency of network communication. This capability is crucial in a setup with distance vector routing, as routers need to continuously and promptly exchange routing information to maintain an accurate view of the network status. By supporting simultaneous sending and receiving of distance vectors between connected routers, full-duplex communication ensures that information is up-to-date and reliable. This scheme maximizes bandwidth utilization, as each line can effectively manage sending and receiving data packets without delays caused by switching directions.

Router Network Topology

Router network topology refers to the arrangement and connections of routers within a network. The topology determines the paths available for data transmission and can have a significant impact on the efficiency and reliability of the network. In our exercise, each router connects to three other routers, forming a part of a mesh-like structure. This interconnected nature provides redundant paths, enhancing the network's robustness. If one path fails, data can still be relayed through other available routes. The fixed number of connections per router helps in managing the complexity of the network while facilitating efficient exchange of distance vectors. Such topologies enable dynamic routing adjustments as routers exchange vectors, reflecting any changes in the network in real-time. This flexibility helps in optimizing data flow, ensuring minimal delay and improved data handling across the network.