The existence of good probabilistic models for the job arrival process and the delay components introduced at different stages of job processing in a Grid environment is important for the improved understanding of the Grid computing concept. In this study, we present a thorough analysis of the job arrival process in the EGEE infrastructure and of the time durations a job spends at different states in the EGEE environment. We define four delay compo- nents of the total job delay and model each compo- nent separately. We observe that the job inter-arrival times at the Grid level can be adequately modelled by a rounded exponential distribution, while the total job delay (from the time it is generated until the time it completes execution) is dominated by the computing element’s register and queuing times and the worker node’s execution times. Further, we evaluate the efficiency of the EGEE environment by comparing the job total delay performance with that of a hypothetical ideal super-cluster and conclude that we would obtain similar performance if we submitted the same workload to a super-cluster of size equal to 34% of the total average number of CPUs participating in the EGEE infrastructure. We also analyze the job inter-arrival times, the CE’s queuing times, the WN’s execution times, and the data sizes exchanged at the kallisto.hellasgrid.gr cluster, which is node in the EGEE infrastructure. In contrast to the Grid level, we find that at the cluster level the job arrival process exhibits self-similarity/long-range dependence. Final- ly, we propose simple and intuitive models for the job arrival process and the execution times at the cluster level.