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'''Receiving site''':
* Upon reception of a <math>\text{request}(ts, i)</math> message, the receiving site <math>P_j</math> will:
** If site <math>P_j</math> does not have an outstanding <math>\text{grant}</math> message (that is, a <math>\text{grant}</math> message that has not been released), then site <math>P_j</math> sends a <math>\text{grant}(j)</math> message to site <math>P_i</math>.
** If site <math>P_j</math> has an outstanding <math>\text{grant}</math> message with a process with higher priority than the request, then site <math>P_j</math> sends a <math>\text{failed}(j)</math> message to site <math>P_i</math> and site <math>P_j</math> queues the request from site <math>P_i</math>.
** If site <math>P_j</math> has an outstanding <math>\text{grant}</math> message with a process with lower priority than the request, then site <math>P_j</math> sends an <math>\text{inquire}(j)</math> message to the process which has currently been granted access to the critical section by site <math>P_j</math>. (That is, the site with the outstanding <math>\text{grant}</math> message.)
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