Optimal Control of a Single Queue with Retransmissions: Delay-Dropping Tradeoffs

TL;DR

This paper models and analyzes the optimal control of a single queue with retransmissions, aiming to balance delay and dropping costs under no channel state information, proposing policies that optimize QoS trade-offs.

Contribution

It formulates a Markov Decision Problem for queue management with retransmissions, proving the existence of an optimal policy and introducing near-optimal <L,K>-policies for delay-dropping trade-offs.

Findings

Optimal deterministic stationary policy exists.

K-truncated ARQ is nearly optimal under certain queue conditions.

Suboptimal policies perform close to the optimal in delay-dropping trade-offs.

Abstract

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.