REPUBLIC OF SERBIA

MINISTRY OF DEFENCE

www.mod.gov.rs

MINISTRY OF DEFENCE

Material Resources Sector

Defensive Technologies Department

Military Technical Institute

www.vti.mod.gov.rs

THE APPLICATION OF THE TWO-DIMENSIONAL MARKOV PROCESS FOR VIDEO CONNECTIONS ANALYSIS

Boban Z. Pavlović

Military Academy, Belgrade, bobanpav@yahoo.com;

Vladimir Suša

Military AcademyBelgrade, vladimir.susha@gmail.com;

Jovan Bajčetić

Military Academy, Belgrade, bajce05@gmail.com;

Katarina Milovac

Military Academy, Belgrade, milovac.katrina@gmail.com

Abstract: The paper analyzes the calculation of blocking probabilities for video connections in wired telecommunication networks. We observed transmission through STS-3 link with 155.52 Mbps capacity. It is analyzed two video connections with bandwidth demands 50 Mbps and 34 Mbps, respectively. The traffic process becomes a pure birth and death process. The problem is graphically and analytically presented and solved in a form of the two-dimensional Markov process. Since connections is established through limited link capacity, it can be formed a finite number of connections. It is evidently that the birth and death process cannot be observed independently. Further analysis is done through the determination of all allowable states for this two-dimensional process. Each state is represented with corresponding probability which is obtained by solving the local balance equations for each node. Based on the calculated state probabilities, it is possible to find a numerous of different system parameters, such as the current link occupancy and average link occupancy. In further, we also defined the states that might cause blocking for first or second connections, as well as blocking both connections simultaneously. Due to aforementioned states, it is fully predictable to calculate the end-to-end blocking probabilities for observing video connections.

Keywords: video-connection, two-dimensional Markov chains, the probability of connection blocking, link occupancy.