M/M/K systems with M-phase fluctuations of traffic intensity

The M/sup (m)//M/K and M/sup (m)//M/ infinity models with synchronous fluctuation of traffic intensity are considered. The phase process is assumed to make changes according to an irreducible m-phase Markov chain. In contrast to the model with asynchronous fluctuation of parameters, a phase change may occur only in synchronization with an arrival or beginning of service of a customer. The authors study the steady-state regime of their models and observe that closed-form solutions for the limiting probabilities are generally difficult to obtain. They give a necessary and sufficient condition for the steady state to be attained. Numerical examples are discussed that demonstrate the behavior of the system under different traffic conditions.<>