In this work we analyze an open queueing network with batch services. In more detail, the arrival process is Poissonian and each node consists of a single server and an infinite waiting queue. Arrivals are served in fixed-size batches: if the number of customers in a node is less than the predefined batch size, the server remains idle, otherwise he will select the required number of customers, which then will be served as a unique batch with exponentially distributed service time. In this paper we show that, under suitable conditions on the routing matrix, such queueing network is equivalent, in terms of stationary distribution, to a Jackson network with single-server nodes and state-dependent service rates. Finally, the goodness of the proposed approach is confirmed by comparing analytical and simulation results.