TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Individual Overflow and Freed Carried Traffics for a Link with Trunk Reservation N2 - Two traffic streams $\Phi_1$, $\Phi_2$ are offered a link. The calls of $\Phi_i$ require exponential holding times with parameter $\mu$ and are accepted if less than $C_i$ trunks are occupied. Approximating the $\Phi_i$ by appropriate renewal processes meeting their first two moments, defined as the moments of the numbers of calls in virtual links of infinite capacity to which the traffic streams as freed traffics are virtually directed and where the calls get fresh exponential i.i.d.\ holding times with parameter $\mu$, stable recursive algorithms of complexity $O(\max(C_1,C_2))$ are derived for the first two defined as above moments of the individual overflow and freed carried traffics. The results offer a unified handling of both overflow and carried traffics in circuit switching networks with trunk reservation, providing a basis for new two-moment network dimensioning algorithms. T3 - ZIB-Report - 01-35 KW - trunk reservation KW - overflow traffic KW - freed carried traffic KW - factorial moments KW - peakedness KW - two-moment method KW - circuit switching network Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6615 ER - TY - GEN A1 - Brandt, Manfred T1 - Approximations for the Distribution Function of the Sum of iid Random Variables with Compact Support in R+ N2 - In this paper a unified approach to central and decentral approximations of the distribution function $F(x,n)$ of the sum of $n$ iid random variables with compact support in $I\!\!R_+$ is given. This approach yields direct Edgeworth expansion (especially the Central limit theorem) and indirect Edgeworth expansion (Theorem of Bahadur-Rao, large deviation results) within a unified framework. An approximative inversion of the LST of $F(x,n)$ (approximation of the complex inversion integral over a line by an integral over a proper bounded arc with a proper integrand) allows to get these approximations and moreover explicit error bounds. T3 - ZIB-Report - SC-95-33 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1990 ER -