Genetic algorithm for optimal thresholds of an infinite capacity multi-server system with triadic policy

We consider an M/M/c queue with c = 2, in which the number of working servers can be adjusted one at a time at arrival epochs or at service completion epochs depending on the number of customers in the system. Analytic closed-form solutions of the infinite capacity M/M/2 queueing system operating under the triadic (0, Q, N, M) policy are derived. The total expected cost function per unit time is developed, to obtain the optimal operating (0, Q, N, M) policy and the optimal service rate, at minimum cost. Some illustrative examples are provided and the genetic algorithm is employed to search for the optimal management policy of the multi-server queueing system.