G-networks with synchronised arrivals

We consider G-networks in which customers arrive simultaneously in several queues. We denote this new signal as synchronised arrivals. Under some conditions on the arrivals on the boundary of the state space, and the ergodicity condition, we prove that these networks have a product-form steady-state distribution. We show the link between this new signal and the positive signals introduced by Chao, Miyazawa and Pinedo.