David Tung Chong Wong

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. Finally, the mean queueing delay are obtained via this function. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the Lambert-W function as well as explicit closed-form with basic queueing parameters. New result is presented. Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.