def test_get_state_probabilities_array():
"""
Test to ensure that the sum of elements of the pi array equate to 1
"""
all_states = build_states(
threshold=3,
system_capacity=5,
buffer_capacity=4,
)
transition_matrix = get_transition_matrix(
lambda_2=0.1,
lambda_1=0.2,
mu=0.2,
num_of_servers=3,
threshold=3,
system_capacity=5,
buffer_capacity=4,
)
pi = get_steady_state_algebraically(
Q=transition_matrix, algebraic_function=np.linalg.solve
)
pi_array = get_markov_state_probabilities(
pi=pi, all_states=all_states, output=np.ndarray
)
assert round(np.nansum(pi_array), NUMBER_OF_DIGITS_TO_ROUND) == 1
def test_get_steady_state_algebraically_lstsq(a, b, c, d, e, f):
"""
Ensures that getting the steady state numerically using numpy's
lstsq function returns the steady state for different transition-like matrices
"""
Q = np.array([[-a - b, a, b], [c, -c - d, d], [e, f, -e - f]])
steady = get_steady_state_algebraically(Q=Q, algebraic_function=np.linalg.lstsq)
assert is_steady_state(state=steady, Q=Q)
def test_get_mean_number_of_individuals_examples():
"""
Some examples to ensure that the correct mean number of individuals are output
"""
all_states = build_states(threshold=4, system_capacity=20, buffer_capacity=20)
transition_matrix = get_transition_matrix(
lambda_2=0.2,
lambda_1=0.2,
mu=0.2,
num_of_servers=3,
threshold=4,
system_capacity=20,
buffer_capacity=20,
)
pi = get_steady_state_algebraically(
Q=transition_matrix, algebraic_function=np.linalg.solve
)
assert (
round(
get_mean_number_of_individuals_in_system(pi=pi, states=all_states),
NUMBER_OF_DIGITS_TO_ROUND,
)
== 2.88827497
)
assert (
round(
get_mean_number_of_individuals_in_service_area(pi=pi, states=all_states),
NUMBER_OF_DIGITS_TO_ROUND,
)
== 2.44439504
)
assert (
round(
get_mean_number_of_individuals_in_buffer_center(pi=pi, states=all_states),
NUMBER_OF_DIGITS_TO_ROUND,
)
== 0.44387993
)