Stochastic Modelling of Parallel Process Flows in Intra-logistics Systems

Many intra-logistics systems, such as automated container terminals, distribution warehouses, and crossdocks observe parallel process flows, which involve simultaneous (parallel) operations of multiple independent resources while processing a job. Due to the unknown service time of the job, stochastic modeling of the parallel process flows is quite complex. For modeling simplicity, researchers tend to assume sequential operations of the resources. This paper proposes a novel modeling approach using two-phase servers to model the simultaneous operations of resources. We develop a closed queuing network model to estimate the performance measures of a system which observes parallel process flows. To solve the resulting queuing network model, we construct two solution methods: an extended approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods using numerical experiments. Although both solution methods are quite accurate in estimating performance measures, the network aggregation dis-aggregation approach consistently performs best. We illustrate the proposed parallel modeling approach for two intra-logistic systems: an automated container terminal with automated guided vehicles and a robotic compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and a maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in underestimation of the throughput capacity up to 9%.