Level Dependent Band-QBD Processes: Steady State Solution and Applications
نویسندگان
چکیده
A class of Markov processes, called the Level Dependent Band-QBD Processes, is defined and introduced. An exact and efficient solution of these processes, using the spectral expansion method, is developed. The utility of these processes is illustrated through solving a non-trivial example, which is, the performance modelling of a multiserver system used for Web server software architecture.
منابع مشابه
General QBD Processes with Applications to Overload Control
In this paper we introduce a general class of level dependent Quasi-Birth-and-Death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of number of matrix quadratic equations. Our results will provide mixed-geometric solution for the stationary solution of level dependent chains. Applicat...
متن کاملSpectral Expansion Solution Methodology for QBD-M Processes and Applications in Future Internet Engineering
Quasi Simultaneous-Multiple Births and Deaths (QBD-M) Processes are used to model many of the traffic, service and related problems in modern communication systems. Their importance is on the increase due to the great strides that are taking place in telecommunication systems and networks. This paper presents the overview of the Spectral Expansion (SE) for the steady state solution of QBD-M pro...
متن کاملFolding algorithm: a computational method for finite QBD processes with level-dependent transitions
This paper presents a new computational method for steady state analysis of nite QBD-process with level-dependent transitions. The QBD state space is deened in two-dimension with N phases and K levels. Instead of formulating solutions in matrix-geometric form, the Folding-algorithm provides a technique for direct computation of P = 0, where P is the QBD generator which is an (NK)(NK) matrix. Ta...
متن کاملGeneralized QBD Processes, Spectral Expansion and Performance Modeling Applications
This paper suggests new queuing models, in the Markovian framework, which can tackle the presence of burstiness in the traffic and autocorrelations among the inter-arrival times of packets in the performance evaluation of next generation networks. These models are essentially based on certain generalizations of the Quasi Birth-Death (QBD) processes. Efficient steady state solution of these new ...
متن کاملKronecker-Based Infinite Level-Dependent QBD Processes
Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably infinite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its under...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004