Fe b 20 08 Estimating Traffic Parameters with Rigorous Error Control ∗

To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating the arrival rate of Poisson processes and the average service time for servers under the assumption that the service time is exponential. In particular, we derive sample size (i.e., the number of i.i.d. observations) required to obtain an estimate satisfying a pre-specified relative accuracy with a given confidence level. A remarkable feature of this approach is that no a priori information about the parameter is needed. In contrast to conventional methods such as, standard error estimation and confidence interval construction, which only provides post-experimental evaluations of the estimate, this approach allows experimenters to rigorously control the error of estimation. 1 Traffic Model The assumption of Poisson arrivals is usually valid in modeling traffic in communications [1]. There is well-developed mathematical theory justifying such an assumption. Also, it is often assumed that the service time of a server in a queuing system is exponential. In the case of telephone traffic, the service time is the time for which a subscriber engages the equipment of interest. In a packet-switching network, the service time is the transmission time and is therefore proportional to the packet length. It is difficult to give a sound theoretical reason why service times should be exponential, but the fact in most cases they are very nearly exponential [1]. For design and analysis purpose, it is desirable to estimate accurately the load currently generated by each device inter-connected in a network. For example, the rate of packets generated by a terminal or the size of packets. ∗The author is currently with Department of Electrical Engineering, Louisiana State University at Baton Rouge, LA 70803, USA, and Department of Electrical Engineering, Southern University and A&M College, Baton Rouge, LA 70813, USA; Email: [email protected]