Full Paper Proc. of Int. Conf. on Advances in Computer Engineering 2012 the sample population it is working with is normally distributed. The proposed algorithm is presented in Fig. 1 where rate estimation is performed on a per aggregate basis.
significance exists in the difference of the means of the agile and stable estimated rates. Statistical significance is indicated if the returned p-value is less than 0.0027 (or 0.27%). This value is chosen (as opposed to typical values i.e. 0.05 used by statistical t-tests) to reflect the characteristics of the 3sigma rule used by the flip-flop (i.e. in a normal distribution 99.73% of values lie within 3 standard deviations of the mean) but eliminates the assumption that the sample population is normally distributed and eliminates the need to estimate a standard deviation value. Although a significance level of 0.27% covers a wide distribution it allows for good agility and stability. If statistical significance is indicated then the agile estimated rate is used as the output estimated rate to allow for the system to reflect this persistent change in traffic. Otherwise the stable estimate is used. Overall it is the premise of the authors that the proposed algorithm will produce accurate estimations from the use of the TSW and EWMA (with dynamic weight) rate estimators. The TSW will produce agile results whereas the EWMA will produce stable results. The t-test statistical controller will allow a persistent change in traffic to be detected, allowing the output estimated rate to alter between agile and stable estimated rates thereby allowing changes in the actual data rate of the traffic in a timely and accurate manner whilst also allowing short term changes in traffic behaviour to be ignored. IV. SIMULATION ANALYSIS AND EVALUATION The purpose of this section is to compare the performance of the proposed SARE algorithm to the flip-flop filter in terms of accuracy, agility, stability and cost. However as both of these algorithms are comprised of a combination of TSW and EWMA rate estimation techniques these need to be analysed initially. Furthermore, as the proposed SARE algorithm uses an EWMA algorithm with dynamic weight and quantitative analysis of this algorithm in terms of agility, stability and accuracy does not exist this also needs to be investigated. (Henceforth we will refer to an EWMA with a static weight as EWMA(static) and an EWMA with a dynamic weight as EWMA(dynamic).) This analysis will validate the choice of traffic rate estimation techniques used in the proposed SARE algorithm. The overall performance of the SARE and flip-flop algorithms will then be presented.
Figure 1. Proposed SARE Algorithm
avg_rate_agile denotes the estimated agile traffic rate. avg_rate_stable denotes the estimated stable traffic rate. avg_rate is the estimated rate used on output. win_length is the window length of time of the TSW. T is the period of time over which the EWMA decays its estimated rate. interpk_time is the inter-arrival time of packets. pk_size is the packet size. t-test represents a t-test statistical controller. alpha is the alpha level used for the statistical t-test. p is the value used to determine if there is statistical significance in the output of the controller. Two rate estimation techniques are used in SARE, a TSW to determine an agile estimated rate and a EWMA to determine a stable estimated rate. The TSW is configured with a small win_length for agility. The EWMA uses a dynamic weight that is a function of interpk_time and T as in [10] with a large T value for stability. At each packet arrival both agile and stable estimated traffic rates are updated. Since each measurement reveals the latest estimate of the rate, it can determine if the latest estimations demonstrate a statistical significance in a change of input traffic. This is achieved by the use of a (one sample) statistical t-test controller [9]. The most recent estimates are input into this controller whose purpose is to determine if a persistent change in traffic has been detected and not just a transient change. A t-test is performed on the agile estimated rates (with degrees of freedom (dof) that allow for transient spikes or short bursts of traffic to be ignored) and the mean of the stable rates. This t-test returns a p-value that indicates whether a statistical Š 2012 ACEEE DOI: 02.ACE.2012.03.4
A. Simulation Setup The network simulator OPNET is used for implementation of the algorithms in a high speed DOCSIS network [13]. The MINITAB software package is used to validate analysis [14]. The network topology is shown in Fig. 2 with one Cable Modem Termination System (CMTS) acting as the FTP/TCP server and Cable Modems (CMs) as the clients. The downstream data rate is 10Mbps. Three different traffic scenarios are set up, each using different traffic sources of CBR, Poisson and Pareto traffic. CBR and Poisson traffic is used to precisely quantify the behaviour of the estimator whereas Pareto traffic is used to mimic a realistic environment and to stress the estimators with traffic changes. All traffic used for simulation analysis is 3