Geodesic
On convergence of multidimensional workload with dominant service duration to a stable process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 121-134

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A service system model introduced by I. Kai and M. S. Takku is considered. We prove a limit theorem on the convergence of finite-dimensional distributions of the total workload process with a multidimensional resource to the corresponding distributions of a multidimensional stable process. The situation is considered when the service durations prevails over the values of multidimensional resources. 
@article{ZNSL_2020_495_a6,
     author = {E. S. Garai},
     title = {On convergence of multidimensional workload with dominant service duration to a stable process},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--134},
     publisher = {mathdoc},
     volume = {495},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a6/}
}
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E. S. Garai. On convergence of multidimensional workload with dominant service duration to a stable process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 121-134. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a6/