Modeling Local Area Network Traffic with Markovian Traffic Models P. Salvador, A. Nogueira, R. Valadas Institute of Telecommunications / University of Aveiro, 3810-193 Aveiro, Portugal; e-mail: salvador@av.it.pt ; nogueira@av.it.pt ; rv@ua.pt Tel: 234.377900 Fax: 234.377901 Abstract In this work, we assess the suitability of some Markovian models and their associated fitting procedures to describe IP traffic exhibiting long-range dependence. We resort to traffic traces measured at the Institute of Telecommunications – Aveiro Pole. The models under analysis are special cases of Markov Modulated Poisson Processes (MMPPs): 2-MMPP, CMPP (Circulant Markov Poisson Process) and (2 ⊕ M/2)- MMPP. These models are evaluated by comparing the density function, the autocovariance and the loss rate queuing behavior of the measured traces and of traces generated from the fitted models. Results show a good agreement for both the CMPP and (2 ⊕ M/2)-MMPP but a reasonable mismatch for the 2-MMPP model. I. INTRODUCTION An efficient design and control of telecommunications networks needs to take into account the main characteristics of the supported traffic. Therefore, it is important to measure packet flows and to describe them through appropriate traffic models. A traffic model is a mathematical description of a specific traffic type. Traffic modeling comprises three steps: (i) selection of one or more models that may provide a good description of the traffic type, (ii) estimation of parameters for the selected models, and (iii) statistical testing for election of one of the considered models and analysis of its suitability to describe the traffic type under analysis. Parameter estimation is based on a set of statistics (e.g. mean, variance, density function or autocovariance function) that are measured or calculated from observed data. The actual set of statistics used in the inference process depends on the impact that those statistics may have in the main performance metrics of interest. An effective traffic model has to reproduce the first and second order statistics of the original traffic trace. The density function defines the first order statistics whereas the second order statistics can be accounted for by the autocovariance function. The second order statistics play an important role in traffic modeling, because traffic correlation is an important factor in packet losses due to buffer and bandwidth limitations. In recent years it has been clearly shown through experimental evidence that network traffic may exhibit properties of self-similarity or LRD. These characteristics have significant impact on network performance. Matching the LRD is only required within the time scales specific to the system under study. One of the consequences of this result is that more traditional traffic models such as Markovian models can still be used to model traffic exhibiting LRD. The use of Markovian models also benefits from the existence of several mathematical tools for assessing queuing behavior, such as average delay and packet loss ratio. In this work, we assess the suitability of some Markovian models and their associated fitting procedures to describe LAN traffic measured at the Institute of Telecommunications - Aveiro Pole, which is mainly dominated by TCP/IP data packets originated from HTTP connections. In order to do this, we compare the first and second order statistics of measured traffic traces and of traffic traces generated from the fitted models, as well as their queuing behaviors in terms of packet loss ratio. The rest of the paper is organized as follows. Section 2 gives an overview of the collected data traces and of the measurement set-up. In section 3, we present the selected traffic models and associated fitting procedures. Finally, in section 4, we discuss the results. II. OVERVIEW OF THE TRAFFIC TRACES In this paper we analyze IP traffic generated by a medium size research institution (around 50 users). In order to do this we carried out some traffic measurements at the Ethernet link connecting the network of the Institute of Telecommunications – Aveiro Pole (IT) and the campus network of the University of Aveiro (UA) using a traffic analyzer (HP J2300D Internet Advisor). Figure 1 depicts the experimental set-up used for the collection of the data traces. Router Hub IT - Aveiro network UA network Switch HP J2300D Internet Advisor Ethernet link (10Mbps) Figure 1 - Experimental set-up used in the traffic measurements. Name Measured at: Trace7 9 00am Morning, September 7 th , 2000 Trace7 9 00pm Afternoon, September 7 th , 2000 Trace8 9 00am Morning, September 8 th , 2000 Trace8 9 00pm Afternoon, September 8 th , 2000 Trace11 9 00am Morning, September 11 th , 2000 Table 1 – Measured traffic traces. Five different traces were collected, as described in Table 1. The measurements were carried out in three different days, trying to capture different daily periods, a morning period