RESUMEN

A single link in a circuit-switched network is considered. The link has C circuits, R of which are reserved for the primary traffic. Offered calls arrive in independent Poisson streams with mean rates $\lambda$ and $\nu$ for the primary and secondary traffic, respectively, and corresponding independent and exponentially distributed holding times with means 1 and $1/\kappa$. Both primary and secondary calls require 1 circuit. A primary call is blocked on arrival if all C circuits are busy, whereas a secondary call is blocked if more than C-R-1 circuits are busy. Blocked calls are lost to the link. It is assumed that R=O(1) and $\lambda\gg 1$, $\nu=O(\lambda)$ and C=O($\lambda$), and that the link is either underloaded, corresponding to $\lambda + \nu/\kappa < C$, or overloaded, corresponding to $\lambda+\nu/\kappa > C$. Asymptotic approximations to the blocking probabilities B1 and B2 of the primary and secondary calls, respectively, are derived. Numerical results are presented to illustrate the accuracy of the approximations.