Optimal Control of Queues in Queueing Systems with Limited Performance
Abstract
Purpose: For queuing systems with infinite servers, there is no detailed study of the analogues of the threshold nature of the optimal
policy queueing systems established for queuing systems with non-homogeneous infinite servers. At the same time, the model systems with infinite servers provide a satisfactory description of the computing nodes with multi-threading. The aim of this study is to discover the threshold nature of optimal policy control queueing systems for infinite servers with the performance of a server depending on the amount of the requests in the system. Methods: To describe queuing, we use processes with discrete time and a finite number of states. In describing the outgoing flow, an autoregressive scheme is used. Results: An approach was proposed to the solution of the basic equations of the model. A simulation experiment was carried out to test the hypothesis of the threshold nature of queue management. In the approximation of the processes with discrete time, equations of autoregression and moving average were derived to describe the incoming and outgoing flows of the queueing process. It is assumed that the order of closure compliance coincides with the order in which they are received to be performed. To test the hypothesis of the existence of an optimal queueing discipine, simulation experiments were conducted. In the experiments, the intensity of the incoming flow took values both less and greater than the performance of the system, meeting only one requirement. The simulation experiments showed that the mean time a requirement spends in the system depends on the allowed queue size and the intensity of the incoming stream. Thus, to improve the performance for a given flow rate, we need to uniquely determine the lower bound for the queue value, starting from which the performance of the system does not grow. Practical relevance: The proposed mathematical and simulation models can be used for studying single and multi-phase systems with various distributions of run-time requirements and various patterns of productivity drop.
