In this paper, we focus on applications having quantitative QoS (Quality of Service) requirements on their end-to-end response time. Two types of quantitative QoS garantees can be delivered by a network, deterministic and probabilistic. The deterministic approach is based on a worst case analysis. The probabilistic approach uses a mathematical model to obtain the probability that the response time exceeds a given value. We assume that flows are scheduled according to non-preemptive FP/FIFO. The packet with the highest fixed priority is scheduled first. If two packets share the same fixed priority, the packet arrived first on the node considered is scheduled first. We compare deterministic and probabilistic QoS guarantees and introduce the c...