Optimisation of Servers with Different Quality of Services

A large class of modern servers are capable of providing services with different levels of quality. In general, more accurate output requires longer computation time, allowing the trade-off between quality of service and expected response time. In order to model a self-adaptive system that employs dynamic control of the quality of service, we study a queueing system with C classes of service, each of which is characterised by a quality of service and an expected service time. The routing of customers to classes occurs at the customer arrival epoch and depends on the number of customers in the system - specifically, on C - 1 thresholds that are parameters of the system. We aim at finding the values for these thresholds that maximise a reward function which we define based on the quality of provided service and expected response time. Differently from previous work, we consider processor sharing queueing discipline. We find the exact solution of the underlying Markov chain based model to be computationally too expensive for the purpose of maximising the reward function in a self-adaptive manner, and propose an approximate model which we use to maximise the reward function using deepest descent search.