# A cooperative quay crane-based stochastic model to estimate vessel handling time

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## Abstract

Having a good estimate of a vessel’s handling time is essential for planning and scheduling container terminal resources, such as berth positions, quay cranes (QCs) and transport vehicles. However, estimating the expected vessel handling time is not straightforward , because it depends on vessel characteristics, resource allocation decisions, and uncertainties in terminal processes. To estimate the expected vessel handling time, we propose a two-level stochastic model. The higher level model consists of a continuous-time Markov chain (CTMC) that captures the effect of QC assignment and scheduling on vessel handling time . The lower level model is a multi-class closed queuing network that models the dynamic interactions among the terminal resources and provides an estimate of the transition rate input parameters to the higher level CTMC model. We estimate the expected vessel handling times for several container load and unload profiles and discuss the effect of terminal layout parameters and crane service time variabilities on vessel handling times. From numerical experiments, we find that by having QCs cooperate, the vessel handling times are reduced by up to 15 %. The vessel handling time is strongly dependent on the variation in the QC service time and on the vehicle travel path topology.

## Keywords

Vessel sojourn time Cooperating QCs Markov chain Closed queuing network## Notes

### Acknowledgments

We are thankful to the Research and Publications Office at Indian Institute of Management Ahmedabad and Erasmus Smartport for supporting this research. We are thankful to the referees for the comments in improving the exposition of this paper.

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