@misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {Individual Overflow and Freed Carried Traffics for a Link with Trunk Reservation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6615}, number = {01-35}, abstract = {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.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the Moments of the Overflow and Freed Carried Traffic for the GI/M/C/0 System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6355}, number = {01-09}, abstract = {In circuit switching networks call streams are characterized by their mean and peakedness (two-moment method). The \$GI/M/C/0\$ system is used to model a single link, where the \$GI\$-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a \$GI/M/C/0\$ system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d.\ holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used rigorously. The main result of this paper is an efficient algorithm for computing the moments of the freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.}, language = {en} }