Optimum Discarding in a Bufferless System

This paper considers queueing systems without buffer. The problem is finding an optimum discipline that gives the minimal number of request discards in a given interval or the minimum discard probability. In the case of a single server fed by an arbitrary request input flow, it is proved that the discipline that discards the request having the maximum residual life is optimal. This result is extended to the system with more than one server. For G/G/1/0, it is given a condition under which the discipline that discards the request in service minimizes the discard probability. Also for a G/G/1/0, we state the problem of finding optimum discipline in terms of the discrete age Markov chain. The problem of minimization of one-step discard probability is stated. It is solved for a system with C servers and general point process of new arrivals.