Little’s Law

Little’s Law applies to parallel computing but has its origins in the world of economics and queuing theory. The law appears deceptively simple but provides a probability distribution independent way of analyzing the load on stable systems. The law states that the average number of customers in a stable system is the product of the average arrival rate and the time each customer spends in the system. In terms of a formula, it appears as follows:

» L = kW
» L is the average number of customers in a stable system
» k is the average arrival rate
» W is the time a customer spends in the system

To understand this a bit further, consider a simple system, say a small gas station with cash-only payments over a single counter. If four customers arrive every hour at this gas station and each customer takes about 15 minutes (0.25 hours) at the gas station, there should be an average of only one customer at any point in time at this station. If more than four customers arrive at the same station, it becomes clear that it would lead to bottlenecks in the system. If gas station customers get frustrated by waiting longer than normal and leave without fi lling up, you are likely to have higher exit rates than arrival rates and in such a situation the system would become unstable.

Viewing a system in terms of Little’s Law, it becomes evident that if a customer or an active
process, when translated to parallel programs, takes a certain amount of time, say W, to complete
and the maximum capacity for the system allows handling of only L processes at any time, then the arrival rate cannot be more than L/W per unit of time. If the arrival rate exceeds this value, the system would be backed up and the computation time and volume would be impacted.

Source of Information : NoSQL


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