In this paper, we concentrate on a multi-relay network in which the source and the relays are equipped with limited buffers, and we study the maximum supportable arrival rates with buffer overflow quality of service (QoS) guaranteed at all buffered nodes. To this end, the effective capacity (EC) function of such a network is derived as a function of individual QoS exponents of the source and relays denoted by $\theta _S$ , $\theta _{R_1}$ , $\ldots$ , $\theta _{R_N}$ . To reduce the computational complexity, a closed form expression for the EC is computed. Then, a time slot allocation algorithm is proposed based on the defined EC function. To show the results, both scenarios of heterogeneous and homogeneous queuing at the relays are investigated. The behavior of derived EC and the proposed algorithm are evaluated by some numerical results. It is shown for $\theta _S>\theta _R$ , EC remains constant versus $\theta _R$ and varies versus $\theta _S$ and vice versa, meaning that among $\theta _S$ and $\theta _R$ , the higher one is determinative in the amount of $E_C(\theta _S,\theta _R)$ . Also, it is found that the majority of resources is allocated to the node with a more stringent QoS constraint.