Lab 3: Little’s Law
The law itself is named after John Little – an MIT
professor who first mathematically proved the law in
1961. The law existed beforehand, but until Little
there wasn’t a set mathematical definition of it or
proof for its validity.
Little defined the law while doing operations
research on traffic control signals, hence the basis of
it as a way to analyse queueing systems.
A Mobile Network Operator provides network access to the users using the base stations
they have in the city. Based on their analysis they realised that 3 base stations will be
under maintenance at any given time. The rate at which the base stations entered
maintenance was also calculated to be roughly every 7 days.
1. What is λ, L?
L = number of base stations in WIP (maintenance) = 3
λ = arrival/departure rate = 1 every 7 days = 1/7 days
2. Calculate the average amount of time spent in maintenance (W)?
W = L / λ = 3 / (1/7 days)
W = 3 / λ (1/7 days)
W = 21 days