Loss tandem networks with blocking - a semi-Markov approach

Abstract

Loss tandem networks with blocking - a semi-Markov approachBased on the semi-Markov process theory, this paper describes an analytical study of a loss multiple-server two-station network model with blocking. Tasks arrive to the tandem in a Poisson fashion at a rate λ, and the service times at the first and second stations are non-exponentially distributed with means sAand sB, respectively. Between these two stations there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks (jobs) by the second station is temporarily suspended (blocking factor) and tasks must wait on the first station until the transmission process is resumed. Any new task that finds all service lines at the first station occupied is turned away and is lost (loss factor). Initially, in this document, a Markov model of the loss tandem with blocking is investigated. Here, a two-dimensional state graph is constructed and a set of steady-state equations is created. These equations allow the calculation of state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. In the next part of the paper, the algorithms for calculation of the main measures of effectiveness in the semi-Markov model are presented. Finally, the numerical part of this paper contains an investigation of some special semi-Markov models, where the results are presented of the calculation of the quality of service (QoS) parameters and the main measures of effectiveness.