Controlling Arrival and Service of a Two-Removable-Server System Using Genetic Algorithm

This paper considers the optimal management problem of a M/M/2/K queueing system with controlling arrivals and services, in which (i) when the number of customers in the system reach its capacity, the arriving customers are not allowed to enter into the system until the number of customers drops to a certain threshold, and (ii) the number of working servers can be adjusted one at a time at arrival epochs or at service completion epochs depending on the system sizes. By applying Markov process, some important performance measures are derived. A cost model is developed to determine the optimal threshold values and the optimal service rate at a minimum cost. Some illustrative examples are provided and the genetic algorithm is employed to search for the joint optimal values of control arrival and service parameters for controllable queueing system.