  A single queue incorporating a retransmission protocol is investigated,
assuming that the sequence of per effort success probabilities in the Automatic
Retransmission reQuest (ARQ) chain is a priori defined and no channel state
information at the transmitter is available. A Markov Decision Problem with an
average cost criterion is formulated where the possible actions are to either
continue the retransmission process of an erroneous packet at the next time
slot or to drop the packet and move on to the next packet awaiting for
transmission. The cost per slot is a linear combination of the current queue
length and a penalty term in case dropping is chosen as action. The
investigation seeks policies that provide the best possible average packet
delay-dropping trade-off for Quality of Service guarantees. An optimal
deterministic stationary policy is shown to exist, several structural
properties of which are obtained. Based on that, a class of suboptimal
<L,K>-policies is introduced. These suggest that it is almost optimal to use a
K-truncated ARQ protocol as long as the queue length is lower than L, else send
all packets in one shot. The work concludes with an evaluation of the optimal
delay-dropping tradeoff using dynamic programming and a comparison between the
optimal and suboptimal policies.
