A fact-finding petition may be withdrawn by the petitioning party in the case of a unilateral filing, or by agreement of both parties in the case of a joint filing, at any time prior to the appointment of a fact-finder. After the appointment of a fact-finder, a fact-finding petition may be withdrawn only by joint agreement of the parties. The parties shall compensate the fact-finder for such services performed in accordance with 456 CMR 21.17.