Networks of queues with batch services, signals and product form solutions

Consider a network of queues with batch services at each node and signals. The nodes in the network have the feature that upon a service completion an entire batch of customers coalesce into a single customer. When a signal arrives at a node, it also triggers a batch of customers to leave as a single unit. The batch sizes are arbitrarily distributed. When a batch completes its service (or triggered to leave by a signal), it goes to another node either as a single customer of as a signal with given routing probabilties. The authros obtain the steady state probability for this network which turns out to be product form.