On a probability distribution of a truck queue length in a large shovel-truck system

Abstract

Abstract Recent achievements in the description of operation of shovel-truck system rely on construction of two basic models. The first one, the probability distribution of a working truck number per one working shovel may be considered as the principle of reduction of cyclic, closed machinery system for given distribution of states into the elementary system: shovel-trucks one. The second is the G/G/l queueing model under the heavy traffic conditions as the model of operation for the shovel-trucks system. This paper shows a new model being a generalization of the above two. The mass probability function for the number of trucks at the shovel and the probability distribution of a truck queue length, both under the heavy traffic conditions are determined. Additionally, a full set of assumptions needed to fulfil in order to be allowed to use these functions is listed together with comments of both practical and theoretical nature.