CONTENTS1. Introduction................................................................................... 52. Palm's system............................................................................. 63. The system GI/M/N with losses................................................ 84. Takács' machine repair system............................................... 115. Cyclic queueing systems.......................................................... 166. Generalization of Takács' system...............................................
The bivariate negative binomial distribution is introduced using the Marshall-Olkin type bivariate geometrical distribution. It is used to the estimation of the distribution of the number of accidents in standard data.
Let us consider two independent renewal processes generated by appropriate sequences of life times. We say that a renewal time is accepted if in the time between a signal and the preceding one, some signal of the second process occurs. Our purpose is to analyze the sequences of accepted renewals. For simplicity we consider continuous and discrete time separately. In the first case we mainly consider the renewal process rarefied by the Poisson process, in the second we analyze the process generated...
In the memoirs of Professor Hugo Steinhaus the problem of estimation of the war casualties of German Army during the SecondWorldWar on the base of contemporary press obituaries is mentioned.A ssuming the inflated geometric probability distribution function for the size of German family, introducing some transformations of this random variable and taking into account the probability distribution function of the contens of obituaries we propose in the note a solution of the problem.
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