Stabilizing batch-processing networks

In a batch-processing network, multiple jobs can be formed into a batch to be processed in a single service operation. The network is multiclass in that several job classes may be processed at a server. Jobs in different classes cannot be mixed into a single batch. A batch policy specifies which class of jobs is to be served next. Throughput of a batch-processing network depends on the batch policy used. When the maximum batch sizes are equal to one, the corresponding network is called a standard-processing network, and the corresponding service policy is called a dispatch policy. There are many dispatch policies that have been proven to maximize the throughput in standard networks. This paper shows that any normal dispatch policy can be converted into a batch policy that preserves key stability properties. Examples of normal policies are given. These include static buffer priority (SBP), first-in-first-out (FIFO), and generalized round robin (GRR) policies.