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References in periodicals archive ?
The repair times follow a general distribution [B.sub.2](y) with Laplace-Stieltjes transform [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (s) and nth moments [[beta].sub.2,n].
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the Laplace-Stieltjes transform of the time a customer stays in the service station and [rho] = [lambda][[beta].sub.1,1] is the load of the system.
Proof: First note that [sg.sub.n](1/s) is an O-regularly varying function and observe that [s.sup.-1][g.sub.n](s) is the Laplace-Stieltjes transform of the function [[integral].sup.x.sub.0] dt [f.sup.[infinity].sub.t] [y.sup.n] dF (y).
Write [[??].sub.j] for the Laplace-Stieltjes transform of [absolute value of [Y.sub.j]].
and hence that Assertion (b) holds, where W has the Laplace-Stieltjes transform on the right-hand side of (84), and its density function is
The right-hand side is the (bilateral) Laplace-Stieltjes transform of a random variable S which has the Gumbel type distribution function exp(-[e.sup.-[alpha]x]).