Stochastic modeling of parallel process flows in intra-logistics systems: Applications in container terminals and compact storage systems

Many intra-logistics systems, such as automated container terminals, distribution warehouses, and cross-docks, observe parallel process flows, which involve simultaneous (parallel) operations of independent resources while processing a job. When independent resources work simultaneously to process a common job, the effective service requirement of the job is difficult to estimate. For modeling simplicity, researchers tend to assume sequential operations of the resources. In this paper, we propose an efficient modeling approach for parallel process flows using two-phase servers. We develop a closed queuing network model to estimate system performance measures. Existing solution methods can evaluate the performance of closed queuing networks that consist of two-phase servers with exponential service times only. To solve closed queuing networks with general two-phase servers, we propose new solution methods: an approximate mean value analysis and a network aggregation dis-aggregation approach. We derive insights on the accuracy of the solution methods from 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 modeling approach for two intra-logistic systems: a container terminal with automated guided vehicles and a shuttle-based compact storage system. Results show that approximating the simultaneous operations as sequential operations underestimates the container terminal throughput on average by 28% and at maximum up to 47%. Similarly, considering sequential operations of the resources in the compact storage system results in an underestimation of the throughput capacity up to 9%.