The value of a network and Metcalfe's and Beckstrom's law

It has been argued that the value of a network is based on Metcalfe's law. Robert Metcalfe in 1980 formulated the concept that the value of any network is proportional to the square of connected users of a system. In the case of IoT, users may mean sensors or edge devices. Generally speaking, Metcalfe's law is represented as:

Where:

• V = Value of the network
• N = Number of nodes within the network

A graphical model helps to understand the interpretation as well as the Crossover Point, where a positive return on investment (ROI) can be expected:

Metcalfe's Law. Value of a network is represented as proportional to N². The cost of each node is represented as kN where k is an arbitrary constant. In this case, k represents a constant of $10 per IoT edge sensor. The key takeaway is the crossover point occurs rapidly due to the expansion of value and indicates when this IoT deployment achieves a positive ROI.

A recent example validating Metcalfe's law to the value of blockchains and cryptocurrency trends was recently conducted. We will go much deeper into blockchains in the security chapter.

A recent white paper by Ken Alabi finds that blockchain networks also appear to follow Metcalfe’s law, Electronic Commerce Research and Applications, Volume 24, C (July 2017), page number 23-29. 

Metcalfe's law does not account for service degradation in the event of service degradation as the number of users and/or data consumption grows, but the network bandwidth does not. Metcalfe's law also doesn't account for various levels of network service, unreliable infrastructure (such as 4G LTE in a moving vehicle), or bad actors affecting the network (for example, denial of service attacks).

To account for these circumstances, we use Beckstrom's law:

Where:

• V_i,j: Represents the present value of the network for device i on network j
• i: An inpidual user or device on the network
• j: The network itself
• k: A single transaction
• B_i,j,k: The benefit that value k will bring to device i on network j
• C_i,j,k: The cost of a transaction k to a device i on network j
• r_k: The discount rate of interest to the time of transaction k
• t_k: The elapsed time (in years) to transaction k
• n: The number of inpiduals
• m: The number of transactions

Beckstrom's law teaches us that to account for the value of a network (for example, an IoT solution), we need to account for all transactions from all devices and sum their value. If the network j goes down for whatever reason, what is the cost to the users? This is the impact an IoT network brings and is a more representative real-world attribution of value. The most difficult variable to model in the equation is the benefit of a transaction B. While looking at each IoT sensor, the value may be very small and insignificant (for example, a temperature sensor on some machine is lost for an hour). At other times, it can be extremely significant (for example, a water sensor battery died and a retailer basement is flooded, causing significant inventory damage and insurance adjustments).  

An architect's first step in building an IoT solution should be to understand what value they are bringing to what they are designing. In the worst case, an IoT deployment becomes a liability, and actually produces negative value for a customer.