FBM Model Based Network-Wide Performance Analysis with Service Differentiation

ABSTRACT In this paper, we demonstrate that traffic modeling with the fractional Brownian motion (FBM) process is an efficient tool for end-to-end performance analysis over a network provisioning differentiated services (DiffServ). The FBM process is a parsimonious model involving only three parameters to describe the Internet traffic showing the property of selfsimilarity or long-range dependence (LRD). As a foundation for network-wide performance analysis, the FBM modeling can significantly facilitate the single-hop performance analysis. While accurate FBM based queueing analysis for an infinite/finite first-in-first-out (FIFO) buffer is available in the existing literature, we develop a generic FBM based analysis for multiclass single-hop analysis where both inter-buffer priority and intra-buffer priority are used for service differentiation. Moreover, we present both theoretical and simulation studies to reveal the preservation of the self-similarity, when the traffic process is multiplexed or randomly split, or goes through a queueing system. It is such self-similar preservation that enables the concatenation of FBM based single-hop analysis into a network-wide performance analysis

IP Traffic Statistics - A Markovian Approach

Data originating from non-voice sources is expected to play an increasingly important role in the next generation mobile communication services. To plan these networks, a detailed understanding of their traffic load is essential. Recent experimental studies have shown that network traffic originating from data applications can be self-similar, leading to a different queueing behavior than predicted by conventional traffic models. Heavy tailed probability distributions are appropriate for capturing this property, but including those random processes in a performance analysis makes it difficult and often impossible to find numerical results. In this thesis three related topics are addressed: It is shown that Markovian models with a large state space can be used to describe traffic which is self-similar over a large time scale, a Maximum Likelihood approach to fit parallel Erlang-k distributions directly to time series is developed, and the performance of a channel assignment procedure in a wireless communication network is evaluated using the above mentioned techniques to set up a Markovian model. Outcomes of the performance analysis are blocking probabilities and latency due to restrictions of the channel assignment procedure as well as estimations of the overall bandwidth that the system is required to offer in order to support a given number of users

GPS queues with heterogeneous traffic classes

We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic classes are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the light-tailed class for the situation where its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed class served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain pre-factor, which accounts for the interaction with the heavy-tailed class. Specifically, the pre-factor represents the probability that the heavy-tailed class is backlogged long enough for the light-tailed class to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario

Selfish traffic allocation for server farms

We study the price of selfish routing in noncooperative networks like the Internet. In particular, we investigate the price of selfish routing using the price of anarchy (a.k.a. the coordination ratio) and other (e.g., bicriteria) measures in the recently introduced game theoretic parallel links network model of Koutsoupias and Papadimitriou. We generalize this model toward general, monotone families of cost functions and cost functions from queueing theory. A summary of our main results for general, monotone cost functions is as follows: 1. We give an exact characterization of all cost functions having a bounded/unbounded price of anarchy. For example, the price of anarchy for cost functions describing the expected delay in queueing systems is unbounded. 2. We show that an unbounded price of anarchy implies an extremely high performance degradation under bicriteria measures. In fact, the price of selfish routing can be as high as a bandwidth degradation by a factor that is linear in the network size. 3. We separate the game theoretic (integral) allocation model from the (fractional) flow model by demonstrating that even a very small or negligible amount of integrality can lead to a dramatic performance degradation. 4. We unify recent results on selfish routing under different objectives by showing that an unbounded price of anarchy under the min-max objective implies an unbounded price of anarchy under the average cost objective and vice versa. Our special focus lies on cost functions describing the behavior of Web servers that can open only a limited number of Transmission Control Protocol (TCP) connections. In particular, we compare the performance of queueing systems that serve all incoming requests with servers that reject requests in case of overload. Our analysis indicates that all queueing systems without rejection cannot give any reasonable guarantee on the expected delay of requests under selfish routing even when the injected load is far away from the capacity of the system. In contrast, Web server farms that are allowed to reject requests can guarantee a high quality of service for every individual request stream even under relatively high injection rates

The pseudo-self-similar traffic model: application and validation

Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems