M/M/1 Expected Queue Length

Problem

Expected number of customers in an M/M/1 system (including the one in service):

E[N] = rho / (1 - rho) with rho = lam / mu.

Return -1.0 when rho >= 1, since the queue grows without bound.

Hint

This is the mean of a geometric distribution on the number in system.

case 1

in: [1,2]

expected: 1

case 2

in: [2,4]

expected: 1

case 3

in: [1,4]

expected: 0.3333333333333333

case 4

in: [1,1]

expected: -1

Starter codePython

def mm1_expected_queue_length(lam, mu):
    # Your code here
    pass

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