Towards the Analysis of the Queuing System Operating in the Random Environment with Resource Allocation
Journal: Discrete and Continuous Models and Applied Computational Science (Vol.26, No. 4)Publication Date: 2018-12-21
Authors : Ivan Zaryadov; Vladimir Tsurlukov; Cravid Carvalho; Anna Zaytseva; Tatiana Milovanova;
Page : 303-320
Keywords : queuing system; random environment; Markov modulated Poisson process; Markov modulated service process; resource allocation; MMPP;
Abstract
The mathematical model of the system, that consists of a storage device and several homogeneous servers and operates in a random environment, and provides incoming applications not only services, but also access to resources of the system, is being constructed. The random environment is represented by two independent Markov processes. The first of Markov processes controls the incoming flow of applications to the system and the size of resources required by each application. The incoming flow is a Poisson one, the rate of the flow and the amount of resources required for the application are determined by the state of the external Markov process. The service time for applications on servers is exponential distributed. The service rate and the maximum amount of system resources are determined by the state of the second external Markov process. When the application leaves the system, its resources are returned to the system. In the system under consideration, there may be failures in accepting incoming applications due to a lack of resources, as well as loss of the applications already accepted in the system, when the state of the external Markov process controlling the service and provision of resources changes. A random process describing the functioning of this system is constructed. The system of equations for the stationary probability distribution of the constructed random process is presented in scalar form. The main tasks for further research are formulated.
Other Latest Articles
- The Method of Finding Algebraic Integral for First-order Differential Equations
- Parametric Study of the System with Active Queue Management Module
- RACH Session Initiation Procedure with Retranslations
- Optical Characterization of a Thin-Film Material Based on Light Intensity Measurements
- Simple Model of Nonlinear Spin Waves in Graphene Structures
Last modified: 2020-08-31 19:26:07