On the convergence of workload in a service system to Brownian motion with switching variance

Some modification of the service system model introduced by I. Kaj and M. S. Taqqu is considered. This model describes the dynamics in time and space of various system loads created by a set of service processes. In the model under consideration two types of resource, each having its own load distribution, are used. Such a model can be identified with the presence of two operators of resource. At the time of the failure of the active operator one can switch to another operator whose resource has distribution loads different from the first operator. We prove a limit theorem on the convergence of finite-dimensional distributions of the integral workload process with two types of resource to Brownian motion with switching variance.