The existence of good probabilistic models for the job arrival process and job characteristics is important for the improved understanding of grid systems and the prediction of their performance. In this study, we present a thorough analysis of the job inter-arrival times, the waiting times at the queues, the execution times, and the data sizes exchanged at the kallisto.hellasgrid.gr cluster, which is part of the EGEE Grid infrastructure. By computing the Hurst parameter of the inter-arrival times we find that the job arrival process exhibits self-similarity/long-range dependence. We also propose simple and intuitive models for the job arrival process and the job execution times. The models proposed were validated and were found to be in very good agreement with our empirical measurements.