Queuing Theory-Based Design Methods for the Definition of Power Requirements in Manufacturing Systems

The attention paid to energy consumption is growing steadily, due to the costs associated with energy usage as well as the resulting environmental impacts. This work proposes an analytical method to assess the energy consumption and the power requirements of a productive system. By exploiting queuing theory, it is possible to achieve a probabilistic view of energy consumption. This method is useful to define the contractual power level and calculate the service level associated with it, so it is applicable as a decision-support tool during the design of productive systems, when it is not possible to have field-data (green-field design). Three different models are exploited, ordered by increasing complexity degree, can be described as: M/M/∞, Mn/M/∞, Mx/M/∞. The three models share the characteristic of the infinite number of servers, while the increasing complexity is due to the introduction of batch arrivals (i.e. Mn/M/∞) and the variability of the size of the arrival lot (i.e. Mx/M/∞). A connection is made between production variables and power used by machines to consider energy consumption. A numerical example shows the applicability of the method and highlights the different results obtained through the three models. In addition, analytical formulations are available for all three proposed models, thus no simulation process is needed