Levente Bodrog

A Markovian canonical form of second-order matrix-exponential processes

Besides the fact that - by definition - matrix-exponential processes (MEPs) are more general than Markovian arrival processes (MAPs), only very little is known about the precise relationship of these processes in matrix notation. For the first time, this paper proves the persistent conjecture that - in two dimensions - the respective sets, MAP(2) and MEP(2), are indeed identical with respect to the stationary behavior. Furthermore, this equivalence extends to acyclic MAPs, i.e., AMAP(2), so that AMAP(2)[reverse not equivalent]MAP(2)[reverse not equivalent]MEP(2). For higher orders, these equivalences do not hold. The second-order equivalence is established via a novel canonical form for the (correlated) processes. An explicit moment/correlation-matching procedure to construct the canonical form from the first three moments of the interarrival time distribution and the lag-1 correlation coefficient shows how these compact processes may conveniently serve as input models for arrival/service processes in applications.

Analytical TCP throughput model for high-speed downlink packet access

This study deals with the throughput analysis of data services over high-speed downlink packet access (HSDPA) systems. The achievable throughput is calculated with an approximate analytical method based on the Padhye model that has two input parameters: the packet loss probability and the transmission control protocol (TCP) round trip time. The proposed solution is to calculate these parameters with an equivalent queuing network model of the HSDPA system that takes into account the possible congestion points in the system and the protocol layers that have dominant impact on the delay and packet drop. The modelling considerations and the analysis method are described in detail. Finally, the model is validated with a performance study of the HSDPA system that is executed with detailed NS2- based simulations too. The proposed method is found to be reasonably accurate requiring less computational effort than the simulations.

Packet Loss Analysis of Load-Balancing Switch with ON/OFF Input Processes

Lately, the number of Internet users and, correspondingly, the amount of traversing traffic is growing extremely fast. In spite of the fact that transmission links --- mostly optical fibres --- have high capacity, the internet routers still remain a point of traffic bottleneck. The construction of highly scalable switches for high-speed transmission still remains a real challenge for designers. In this paper we focus our efforts on the analysis of Load-Balancing Birkhof-von Neumann switch which is lately considered to be a highly efficient distributed switch with simple control and high scalability. Due to the fact that Internet traffic represents an asynchronous traffic which supports a variety of applications, we have introduced the analysis of possible loss inside the load-balanced switch under consideration of variable size packets and finite central stage buffers previously in [1]. Although the analysis has showed some interesting features of the switch, it has exponential complexity of

A tool support for automatic analysis based on the tagged customer approach

O\left(N^N\right)

Scalable Model for Packet Loss Analysis of Load-Balancing Switches with Identical Input Processes

which makes that model inapplicable for the switches with large number of ports, N . The main goal of this paper is to approximate the switch analysis with lower complexity, i.e.,

Phase-Type Distributions

O\left(2^N\right)

Canonical Form Based MAP(2) Fitting

which can be useful for evaluation of packet loss in the larger load-balanced switches.

Packet loss minimization in load-balancing switch

The analysis of performance models based on the tagged customer approach is composed by two main steps. The first one is the stationary analysis of a Markov chain and the second one is the transient analysis of another Markov (reward) model whose initial distribution is derived from the result of the first step. To the best of our knowledge none of the existing performance analysis tools allow the automatic evaluation of these performance models. This paper presents an extension of the MRMSolve tool for automatic execution of the two steps procedure. The theoretical background of this extension is well established and the implementation is built mainly on the existing Markov model analysis functions of MRMSolve, hence the contribution lies in the availability of the automatic analysis tool. To demonstrate the modeling abilities and the practical importance of the new tool we present the MRMSolve models of (G. Fodor, et al., May 2002) and (R. Gaeta, et al., 2005). Based on these MRMSolve models one can automatically generate the performance measures presented in G. Fodor, et al., May 2002) and (R. Gaeta, et al., 2005)

Moment characterization of matrix exponential and Markovian arrival processes

In this paper we present a scalable approximate model for packet loss analysis in load-balancing Birkhof-von Neumann switch with finite buffers and variable length packets assumption. We also present a numerical method to solve the model for large switches (up to the size ~30) equipped with large buffers (up to the buffer size ~1000). With regards to previously introduced models the main contribution of our model is its scalability in terms of the switch size as its computational complexity is linear with the number of ports. Contrary to previous models we assumed homogeneous input processes in this paper.

Current results and open questions on PH and MAP characterization

Both analytical (Chap. 6) and simulation- and experimentation-based (Chap. 17) approaches to resilience assessment rely on models for the various phenomena that may affect the system under study. These models must be both accurate, in that they reflect the phenomenon well, and suitable for the chosen approach. Analytical methods require models that are analytically tractable, while methods for experimentation, such as fault-injection (see Chap. 13), require the efficient generation of random-variates from the models. Phase-type (PH) distributions are a versatile tool for modelling a wide range of real-world phenomena. These distributions can capture many important aspects of measurement data, while retaining analytical tractability and efficient random-variate generation. This chapter provides an introduction to the use of PH distributions in resilience assessment. The chapter starts with a discussion of the mathematical basics. We then describe tools for fitting PH distributions to measurement data, before illustrating application of PH distributions in analysis and in random-variate generation.