On convergence of multidimensional workload with dominant service duration to a stable process

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.