Receiver Buffer Behavior for the Selective-Repeat ARQ Protocol

Abstract It is well known that the Selective-Repeat ARQ protocol has, among all error detection and retransmission schemes, the best throughput efficiency. However, this protocol has the disadvantage that data blocks may be received out of order, such that some reordering is required at the receiver side, before the blocks can be delivered to their destination. In order to accomplish this reordering, the receiver must dispose of a theoretically infinite amount of buffer space for the storage of correctly received blocks which cannot be delivered yet. The purpose of the paper is to study the statistical behavior of this receiver buffer, under the assumption of independent transmission errors. The study results in an explicit expression for the probability generating function of the number of blocks stored in the receiver buffer (observed at the discrete time epochs when blocks arrive at the receiver side), under the (worst-case) assumption that data blocks are available without interruption at the transmitter side. From this expression several interesting characteristics, such as the mean and variance of the buffer occupancy and the overflow probability of the buffer (if finite) can be derived with arbitrary accuracy.