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We consider a time slotted communication network with a base station (BS) anda user. At each time slot a fresh update packet arrives at the BS withprobability $p>0$. When the BS transmits an update packet for the first time,it goes through with a success probability of $q_1$. In all subsequentre-transmissions, the packet goes through with a success probability of $q_2$where $q_2>q_1$, due to the accumulation of observations at the receiver usedto decode the packet. When the packet goes through the first time, the age ofthe user drops to 1, while when the packet goes through in subsequenttransmissions, the age of the user drops to the age of the packet since itsgeneration. Thus, when the BS is in the process of re-transmitting an oldpacket, if it receives a new packet, it has to decide whether to re-transmitthe old packet with higher probability of successful transmission but resultingin higher age, or to transmit the new packet which will result in a lower ageupon successful reception but this will happen with lower probability. In thispaper, we provide an optimal algorithm to solve this problem.

To Re-transmit or Not to Re-transmit for Freshness