M/M/1 Occupancy Probability

Problem

Steady-state probability that an M/M/1 queue with arrival rate lam and service rate mu contains exactly n customers:

P(N = n) = (1 - rho) * rho^n with rho = lam / mu.

Return 0.0 when rho >= 1 (unstable queue) or for invalid inputs.

Hint

The geometric steady state exists only when the arrival rate is below the service rate.

case 1

in: [1,2,0]

expected: 0.5

case 2

in: [1,2,1]

expected: 0.25

case 3

in: [2,3,0]

expected: 0.33333333333333337

case 4

in: [1,1,0]

expected: 0

case 5

in: [0,2,3]

expected: 0

Starter codePython

def mm1_occupancy_probability(lam, mu, n):
    # Your code here
    pass

5 test cases · run your code against them in the editor