Note On the Busy Period in the Case of Infinite Means

Cover Note On the Busy Period in the Case of Infinite Means
Note On the Busy Period in the Case of Infinite Means
Herman Hanisch
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:j^? ;tXi. :'£3'2 av^/C^jS . ;r{^ t^-J ^U ^.^iiViS!. Florid c-: -asvnoo oriar o:f bo. -i. Els'x \:ii. --GcI::i sasiciq . ■vsp. Taeup 'x9fi:fone -lol >. I-... -- HB 11, --fl: snois 9Qj\"S3R io'> tS'DJSqs Kiaso I; BSfl .^Jbs&qe fine • item arrives at before service on it has been completed, the server suffers a probability a of being disabled (absorbed). In the terminology of the moving queue, theorem 1 has the following formulation: THEOREM 2. Let G(x) be the distribution function of the distanc...e betvjeen adjacent elements and P(x) the service time distribution. Let p(b) denote the probability of serving in- finitely many members of the assembly line, if service on the first elements begins v/hen it is b units av;ay from the barrier.
If a > 0, |Xp = |j.^ = 00, and lim sup Q(s) > 0, then p(b) = for s ^ o all b > 0.
, ( ; ;')iiJ;g5i:f la jo ^ ■ . , ■■', 8 31bliop;raphy [l] Hanisch, H. And Hlrsch, V/. M. , Properties of a transient queue, Comm. On Pure and Applied Mathematics, No.


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