def expected_time_in_markov_state_ignoring_class_2_arrivals(
    state, lambda_1, mu, num_of_servers, system_capacity
):
    """
    The expected time of the Markov chain model at the state given.
    Note here that for a state (u,v) where v = system capacity (C) no class 1 arrival
    can occur and thus the rate at which the model leaves that state changes.
    """
    if state[1] == system_capacity:
        return 1 / (min(state[1], num_of_servers) * mu)
    return 1 / (min(state[1], num_of_servers) * mu + lambda_1)