On the Statistics of QoS Parameters over Heterogeneous Networks ⋆ A. Botta, A. Pescap´ e, and G. Ventre Universit´a degli Studi di Napoli, “Federico II” Via Claudio 21, Napoli, Italy {a.botta, pescape, giorgio}@unina.it Abstract. Offering real services with a specific Quality of Service (QoS) guarantee over heterogeneous networks is very challenging. To make it feasible a complete and robust real performance assessment of these scenarios is of paramount importance. This paper deals with a perfor- mance evaluation and measurement of a number of heterogeneous end- to-end (e2e) paths taking into account a wide range of statistics. An ac- tive measurement approach of UDP QoS parameters has been adopted for the studying of (i) proprieties we called concise statistics (mean, standard deviation, inter quantile range, minimum, maximum, and me- dian) and (ii) detailed statistics (Probability Density Function, Auto Correlation Function, Entropy, and log-log Complementary Cumulative Distribution Function). Used tools and traces are publicly available at www.grid.unina.it/Traffic/. Keywords : Monitoring and measurement systems, End-to-end QoS. 1 Introduction The perceived quality of Internet applications is primarily determined by para- meters like packet loss, delay, jitter, throughput, and available bandwidth. For this purpose, several reference documents containing constraints regarding these parameters have been defined [1], [2], [3], and research have focused on the effects of these parameters on real time traffic (i.e. telephony)[4]. Understanding the sta- tistics of QoS parameters is important (i) for the appropriate design of network algorithms (routing, flow control, streaming, ...), (ii) for the evaluation of net- work capability to support new value-added services (i.e. telephony, games), (iii) for the study of network performance, (iv) for developing algorithms to detect anomalies (attacks, misconfigurations, ...) and, finally, (v) for the definition of Service Level Agreements (SLAs). In literature there are a lot of works focused on the analysis of QoS parameters and more specifically on the delay (both One Way Delay (OWD) and Round Trip Time (RTT)) over backbone networks [5], [6], [7], [8], [9]. It is our opinion that with rapidly expanding core and backbone networks, performance parameters such as delay, jitter, bandwidth, and loss get ⋆ This work has been partially supported by the MIUR in the framework of the PRIN 2004 Quasar Project and by the E-Next European project.