MediumProbabilitypr-209

M/M/1 Wait Exceedance Probability

Problem

For a stable M/M/1 queue, return the probability that a customer waits more than time t:

P(W > t) = rho * exp(-(mu - lam) * t).

Return 0.0 when the queue is unstable or inputs are invalid.

Hint

The waiting time is exponential with rate mu - lam, taken with probability rho.

case 1

in: [1,2,1]

expected: 0.18393972058572117

case 2

in: [1,2,0]

expected: 0.5

case 3

in: [2,4,2]

expected: 0.00915781944436709

case 4

in: [1,1,1]

expected: 0

Starter codePython

import math


def mm1_wait_exceed_probability(lam, mu, t):
    # Your code here
    pass

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