  In this paper, we study the merging and splitting of generalized counting
processes (GCPs). First, we study the merging of a finite number of independent
GCPs and then extend it to the case of countably infinite. The merged process
is observed to be a GCP with increased arrival rates. It is shown that a packet
of jumps arrives in the merged process according to the Poisson process. Also,
we study two different types of splitting of a GCP. In the first type, we study
the splitting of jumps of a GCP where the probability of simultaneous jumps in
the split components is negligible. In the second type, we consider the
splitting of jumps in which there is a possibility of simultaneous jumps in the
split components. It is shown that the split components are GCPs with certain
decreased jump rates. Moreover, the independence of split components is
established. Later, we discuss applications of the obtained results to
industrial fishing problem and hotel booking management system.
