Ausbeutung einer bekannten wiener-hopf-faktorisierung beim wartemodell g/g/1 und einer mit ihm zusammenhängenden irrfahrt

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Abstract
The auhtor considers the random walk where are independeat random variabies with the common distribution K The charact,eristic function (e.i.) is decomposed according to (1.7). If either x + or x - are rational simple expressiond for important characteristic and gencrstive functiens are derix.red which are use ful for the description of the behaviour of the random walk. The novel featme lies ill the fact that most results hold in cither direction. E. g. the generative function which appears in the POLLACZEK SPITZIEN identity is rational if and only if x + is rational. Moreover the e.f .w(s) of is stucliecl; i t proves rational if and only if x + is rational. I n the waiting model G/G/1 the c. f. of the idletime is rational if and only if x - is rational. At last the author establishes the conditions under which x + or x - are rational in the model G/G/l. For instance if the servjce time has a rational c. f. then x + is rational; but the inverse conclusion holds only under additional assumptions. This is due to the fact that a rational c. f . may have meromorphic factors. From the methodological point of view this paper is a continuation of 1151; the main difference is that here we make use of the WIENEE-HOPF- factorisation (1 6) as an essedial tool while i t mw completely unnecessary in [15].

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