Towards hypercube queuing models for dispatch policies with priority in queue and partial backup

•This work extends the hypercube queuing model to address users’ in-queue priorities.•The extended model also considers the partial backup of servers.•It is motivated by an emergency maintenance service of an agro-industry in Brazil.•To reduce the computational burden an approximate method is also developed.•The findings suggest promising perspectives for real-life applications. This work extends the hypercube queuing model to explicitly address users’ in-queue priorities, as well as the partial backup of servers. To reduce the computational burden an approximate method is also developed. The study is motivated by an emergency maintenance service system found within the agricultural stage of the sugarcane agro-industry in Brazil. An example is used to illustrate the issues of priority in queue and partial backup. In order to show the importance and effectiveness of our proposed models we conducted additional experiments by varying the user arrival rates as well as eliminating the in-queue priorities. The study shows that selected adaptations and extensions of both the hypercube model and the approximate method are capable of representing similar emergency systems. The findings from the illustrative examples suggest promising perspectives for real-life applications in sugar and ethanol plants, and other agro-industries.