A refined queueing model for earthmoving operations

Abstract

The paper develops a queueing model that accurately reflects the variabilities in the plant cycle times as well as plant interaction in earthmoving operations of the shovel-truck or pusher-scraper types. Field data records are presented to establish the need and validity of the model. The model is based on finite source queueing theory although an equivalent two-stage cyclic queueing process is found to be a more preferable foundation for visualizing the solution process. A one-dimensional state definition is used for each of the stages in this cyclic queueing representation giving a total two-dimensional state definition for the whole earthmoving operation. Being two-dimensional it permits the ready drawing of the associated rate diagram from which the governing balance equations may be straightforwardly obtained. A numerical solution procedure is described for the solution of these balance equations. For comparison, the paper also presents an approximate model that is computationally easier but which is perhaps not as rational in its foundation as the full queueing model.

Keywords:

• queueing theory
• Erlang distributions
• earthmoving
• field data