On the asymptotic behavior of the distribution of a refusal moment in the \(GI| GI| 2| 0\) system. (English. Russian original) Zbl 0835.60081

Kushnir, O. O.

Theory Probab. Math. Stat. 47, 77-81 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 75-80 (1992).

Summary: Under certain sufficiently general restrictions on the parameters of the \(GI |GI |2 |0\) system, the first refusal moment in the system, after being appropriately normalized, is shown to have asymptotically the exponential distribution on fast servicing. The exponent of the distribution is expressed in terms of a solution of a certain integral equation and, also, bounded from the right and from the left. In a particular case its asymptotics is found.

MSC:

60K25	Queueing theory (aspects of probability theory)
60F99	Limit theorems in probability theory

Keywords:

probability of refusal; exponential distribution; integral equation; asymptotics