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Joint distribution of waiting time and queue size for single server queues

CONTENTS1. Introduction...................................................................52. Preliminaries................................................................113. Departure process......................................................194. Joint distribution of waiting time and queue size..........325. New forms of Little's formula.......................................38References.....................................................................53

The phenomenon of the Steinhaus Seminar on Applied Mathematics: Topics

Władysław Szczotka — 2019

Antiquitates Mathematicae

This article presents the subject of the Applied Mathematics Seminar, conducted in 1948-1960 by Professor Hugon Steinhaus in Wrocław and is an important supplement to the analysis presented in the work of Szczotka (2018). This topic is illustrated by a more detailed discussion of some of the works on this subject and some of the results obtained by the participants of the Seminar. The results are well-founded in mathematical journals.

The case of the Steinhaus seminar on applied mathematics. Outline of the concept

Władysław Szczotka — 2018

Antiquitates Mathematicae

This article is devoted to the Seminar on Applied Mathematics, conducted in 1948-1960 by Professor Hugo Steinhaus in Wroclaw. It is based on the protocols of this Seminar so far not discussed anywhere. Many facts related to Professor Hugo Steinhaus can be found easily in the literature, also in the diary of the professor (2016). Steinhaus was an outstanding mathematician. He wrote his doctoral thesis under the direction of David Hilbert at the University of Göttingen. Already at that time, he was...

The phenomenon of the Steinhaus Seminar on Applied Mathematics: Topics

Władysław Szczotka — 2019

Antiquitates Mathematicae

This article presents the subject of the Applied Mathematics Seminar, conducted in 1948-1960 by Professor Hugon Steinhaus in Wrocław and is an important supplement to the analysis presented in the work of Szczotka (2018). This topic is illustrated by a more detailed discussion of some of the works on this subject and some of the results obtained by the participants of the Seminar. The results are well-founded in mathematical journals.

Covariance structure of wide-sense Markov processes of order k ≥ 1

Arkadiusz KasprzykWładysław Szczotka — 2006

Applicationes Mathematicae

A notion of a wide-sense Markov process X t of order k ≥ 1, X t W M ( k ) , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of X t is the k-dimensional process x t = ( X t - k + 1 , . . . , X t ) . The covariance structure of X t W M ( k ) is considered in the general case and in the periodic case. In the general case it is shown that X t W M ( k ) iff x t is a k-dimensional WM(1) process and iff the covariance function of x t has the triangular property....

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