Calculation of Loss Probability in a Finite Size Partitioned Buffer for Quantitative Assured Service

Abstract

Abstract-This paper proposes an approximate yet accurate approach to calculate the loss probabilities in a finite size partitioned buffer system for the achievement of a quantitative assured service in differentiated services networks. The input is modeled as a fractional Brownian motion (FBM) process including J classes of traffic with different packet loss requirements. A first-in firstout buffer partitioned with J −1 thresholds is used to provide J loss priorities. Heuristic expressions of the loss probabilities for all the J classes are derived, and validated by computer simulations. The proposed loss calculation technique is then extended to a general input process by using the recently proposed traffic substitution technique, where both long-range dependent and short-range dependent input sources are equivalent to a properly parameterized FBM. We also apply the loss calculation to admission control, where the partition thresholds are optimally configured for quality of service guarantee and maximal resource utilization. Computer simulation results demonstrate that resource allocation based on the accurate finite buffer loss analysis results in much more efficient resource utilization than that based on the classic large-buffer overflow approximation.Index Terms-Fractional Brownian motion (FBM), long-range dependence (LRD), loss probability, quantitative assured service, traffic substitution.

QoS provisioning performance of IntServ, DiffServ and DQS with multiclass self‐similar traffic

“…The comparison results among various FBM generation methods, that is, the conditionalised random midpoint displacement algorithm ( RMD 3,3 ) and the fast Fourier transform, and the method based on aggregating a large number of ON–OFF sources with infinite‐variance sojourn times showed that the RMD 3,3 algorithm outperformed the other two because of its relatively lower computational complexity and trace quality . Indeed, RMD 3,3 algorithm is widely used to generate FBM‐based sequences for comparison between simulation and analytical results relative to self‐similar and long‐range dependent Internet traffic . Therefore, in this paper, we generate the FBM‐based self‐similar traffic sequences through RMD 3,3 .…”

“…Internet traffic especially real‐time traffic is self‐similar and long‐range dependent . Studies have shown that the properties of self‐similar traffic have significant effects on QoS provisioning. Therefore, an analytical performance model with this type of traffic is necessary for the previous three QoS schemes.…”

Quality-of-Service Analysis of Queuing Systems with Long-Range-Dependent Network Traffic and Variable Service Capacity

“…It was proven in [18] that for a queuing system subject to multiple LRD traffic flows and constant service capacity, the actual service rate received by individual traffic flows can be reasonably modelled as an LRD fBm process. Further, in [31] it was demonstrated that both LRD and SRD processes can be well substituted by a properly parameterized Gaussian process.…”

“…Here, is non-negative constant and is often chosen to be 0 as this allows to compute efficiently. Particularly, for a Gaussian traffic flow with mean arrival rate and variance 2 , can be calculated as follows [31], [34]:…”

Analysis of Finite Buffer Queue: Maximum Entropy Probability Distribution With Shifted Fractional Geometric and Arithmetic Means

“…An appropriate mathematical framework for the analysis of such systems is generally based on either M/G/1 type system with service time exhibiting the power law or the stochastic differential equation (SDE) driven by the fractional Brownian motion (fBM) [3]. Modeling input traffic by fBM, Cheng, Zhuang and Wang [4] have calculated the loss probability in finite-size partitioned buffer. Using the network traffic studies to model aggregate traffic by a stationary Gaussian process [5], [6], Kim An alternative approach is based on the use of Jaynes' maximum entropy principle [7] subject to partial information available in the form of specified moments.…”