Equivalence relations in the approximations for the M/G/s/s + r queue

This paper investigates some equivalence relations among previously established approximations for the steady-state distribution in an M/G/s queue with finite waiting spaces. The focus is on four approximations developed by Hokstad 1], Tijms and van Hoorn 2], Miyazawa 3] and Kimura 4]. These approximations have been obtained by completely different approaches and they have different expressions. Equivalence theorems show conditions under which some of the approximations coincide.