Individual Overflow and Freed Carried Traffics for a Link with Trunk Reservation

Two traffic streams Φ₁, Φ₂ are offered a link. The calls of Φ_i require exponential holding times with parameter μ and are accepted if less than C_i trunks are occupied. Approximating the Φ_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 μ, stable recursive algorithms of complexity O(max (C₁,C₂)) 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 switched networks with trunk reservation, providing a basis for new two-moment network dimensioning algorithms.This work was supported by a grant from the Siemens AG.