Question

Consider a network in which all nodes are connected to three other nodes. In a single time step, a node can receive all transmitted broadcast packets from its neighbors, duplicate the packets, and send them to all of its neighbors (except to the node that sent a given packet). At the next time step, neighboring nodes can receive, duplicate, and forward these packets, and so on. Suppose that uncontrolled flooding is used to provide broadcast in such a network. At time step \(t\), how many copies of the broadcast packet will be transmitted, assuming that during time step 1 , a single broadcast packet is transmitted by the source node to its three neighbors.

Short answer

The number of copies sent at time step \(t\) is \(3 \times 2^{t-1}\).

Step-by-step solution

Initial Transmission

At time step 1, the source node sends the broadcast packet to its 3 neighbors. Hence, exactly 3 copies of the packet are transmitted at this step.

First Layer Transmission

At time step 2, each of these 3 receiving neighbors will forward the packet to its remaining 2 neighbors (since the packet is not sent back to the source node). Therefore, each of the 3 nodes will transmit to 2 nodes each, resulting in a total of \(3 \times 2 = 6\) copies transmitted.

Second Layer Transmission

At time step 3, each node receiving a packet will forward it to its 2 remaining neighbors (not sending it back to the sender). At least the 6 neighbors will each send to 2 others, leading to \(6 \times 2 = 12\) copies being transmitted.

General Formula Derivation

We notice that there's a pattern where at each time step \(t\), the total number of transmissions can be expressed as \(3 \times 2^{t-1}\). This arises from each previous layer transmitting twice as many copies as the step before.

Key concepts

Broadcast Packets

Broadcast packets are special types of data packets sent across a network to reach multiple recipients. The process of broadcasting means that a single broadcast packet is duplicated and distributed to several network nodes. Unlike unicasting, where data is sent from one sender to one receiver, broadcasting ensures that information is spread widely and simultaneously.

In the context of our network exercise, broadcasting plays a crucial role. When the source node sends a single broadcast packet at time step 1, it is duplicated and sent to three neighbors. This packet duplication ensures that more nodes are quickly reached without the need for re-sending the original data. This method is particularly efficient in networks where timely data delivery to multiple nodes is essential, such as in communication networks or sensor data aggregation systems.

Network Nodes

Network nodes are essential components of any communications network. A network node can be any device, like a computer, router, or switch, connected to a network. In our specific network scenario, each node is connected to three other network nodes, creating a symmetrical and balanced network topology.

Each node in this setup has the capability to perform specific actions. These include receiving packets, duplicating them, and then forwarding them to adjacent nodes. The simplicity in the node's task is key to understanding how networks efficiently handle large amounts of data. By sending information to multiple direct neighbors, each node contributes to the dissemination of broadcasting packets, promoting robust communication pathways across the entire network.

Uncontrolled Flooding

Uncontrolled flooding is a network broadcasting strategy where packets are sent from one node to all its neighboring nodes without any restriction on where subsequently moved packets go. This technique can rapidly spread information, which is vital in specific applications where all nodes must receive the data quickly.

However, the downside is that it can lead to network overload. When every node continuously duplicates and forwards the broadcast packet, it results in numerous copies being transmitted across the network, especially noticeable in our exercise as the number of broadcasts rises exponentially. This multiplicative effect can cause network congestion and inefficient use of bandwidth. Overall, while uncontrolled flooding ensures maximum reach, it also requires careful management to prevent network resource exhaustion.

Packet Transmission

Packet transmission refers to the process of sending data packets from one node to another across a network. It is at the core of data communication. The practice of packet transmission allows for the efficient transfer of data through various paths, ensuring the data reaches its intended destination.

In our network exercise, packet transmission occurs in sequential time steps. After the initial broadcast packet is sent from the source node, each subsequent node passes the packet to its neighbors. This orderly transmission follows the pattern outlined as \(3 \times 2^{t-1}\) transmissions at each time step \(t\). By understanding the pattern and flow of packet transmission, network engineers can better predict and manage network traffic, ensuring reliability and efficiency in diverse networking scenarios.