The Factorization of Queueing Equations and Their Interpretation

There are many queueing systems, including the M ^x /M ^y /c queue, the GI ^x /M/c queue and the M/D/c queue, in which the distribution of the queue length at certain epochs is determined by a Markov chain with the following structure. Except for a number of boundary states, all columns of the transition matrix are identical except for a shift which assures that there is always the same element occupying the main diagonal. This paper describes how one can find the equilibrium distribution for such Markov chains. Typically, this problem is solved by factorizing of a certain expression characterizing the repeated columns. In this paper, we show that this factorization has a probabilistic significance and we use this result to develop new approaches for finding the equilibrium distribution in question.     

Mössbauer study of iron reduction in hematite containing mineral originated from Aswan area in Egypt

Mössbauer spectroscopy was used to study iron reduction in mineral originated from Aswan area in Egypt. The Mössbauer spectra of samples heat treated at 1000 °C in hydrogen atmosphere show a gradually reduction process of hematite. The main phase of sample aged for 1 h is magnetite, while alpha-iron as well as some silicates and wustite type oxide can be detected in sample aged for 3 h. Further aging of sample results in dissolution of alloying elements /Si, Al/, being present in the samples. This process starts already in samples aged at 1000 °C for 4 h, but it is more expressive in minerals heat treated at 1200 °C or 1300 °C, when all paramagnetic phases disappeared.