  In the relay based telecommunications with $K$ relays between the source and
destination, $K+1$ time or frequency slots are required for a single frame
transmission. However, without the relays, only one time or frequency slot is
used for a single frame transmission. Therefore, despite the benefits of
relaying systems, this type of communications is not efficient from the
spectral efficiency viewpoint. One solution to reduce this issue might be the
full-duplex (FD) relays. An old technique which is reconsidered recently to
improve the spectral efficiency of telecommunication systems. However, FD
relays have a certain complexity, so, some similar techniques such as
successive relays with nearly the same performance but less complexity is taken
into account now. In successive relaying systems, two relays between the source
and destination are employed which receive the transmitted frames from the
source and relay it to the destination successively. This structure generally
acts like an FD relays. In this paper, the effective capacity performance of an
amplify and forward (AF) successive relaying systems with power allocation
strategy at the relays are studied perfectly. However, while the inter-rely
interference (IRI) between two successive relays has to be managed well, the
power allocation and the effective capacity is derived under different
assumptions about the IRI. In this way, we assume weak or strong, short or
long-term constraints on the IRI. Then we extract the optimal transmitted power
at the relay to maximize the effective capacity under these constraints.
