Blocking Probabilities for an Underloaded or Overloaded Link with Trunk Reservation

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 exponentically 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 is large, nu=O(lambda) and C=O(lambda), and that the link is either underloaded or overloaded. Asymptotic approximations to the blocking probabilities of the primary and secondary calls are derived. Numerical results are presented to illustrate the accuracy of the approximations.