Multimode queueing network with random staying time of signals

An open queueing network with different types of customers and multimode service strategies is considered. Every node can operate in several modes corresponding to different degrees of its working capacity. There are signals in the network, which change the number of operating mode. Staying time of signals in each node is the random value having exponential distribution. The conditions of multiplicativity and an analytical view of stationary distribution of the network states probabilities are found.