# On a Functional Equation Arising in the Theory of Queues On a Functional Equation Arising in the Theory of Queues
Herman Hanisch
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Let "^ > N and x/2^ h(s, N) = -— 0, (s) > 5 - Q(0) = ( O/. N.. _ N [0, co ) Ut)dt ^ ^ - \ Moreover, since l-e~ 2m^, T > IT, and 2m^^, [N, oo ) To obt-ain an estimate of J"!:' (s) we write it in the form J^'-^s) = J (l-e^^ G(s)) J e"^* ln(t)|dt dG(T) = [0, N] (^, co ) / d-e^'' g'(s))(M(s)- / e"^^lii(t)|clt)dG('L ) = [0, -] io, t ] T'here J|^"^^s) = - J d-e^' G(s)) J e~^'^|pt(t)Idt dGC^ ), [0, 11] [0, 1:-] and ■^J^h.^ = ru. ) I (1 -^^ J^"'(3) =M(s) J d-e"' G(s)) dG( L ) .
[0, N] Now, |jj^, ^'
...^^(s)|

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