For multiclass queueing networks, dispatch policies govern the assignment of servers to the jobs they process. Production policies perform the analogous task for queueing networks whose servers are subject to switch-over delays or setups, a model we refer to as setup 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 di#erent 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 bu#er priority (SBP), first-in--first-out (FIFO) and generalized round robin (GRR) policies. Keywords: batch processing, multiclass queueing networks, stability, throughput, fluid model, semiconductor wafer fabrication, furnace operation. 1

I would like to express my sincere gratitude to my advisor, Professor Jim Dai for his direction, support and feedback. His genius, patience and deep insights make it a pleasure to work with him. I also acknowledge the help and support of the other members of my committee, Professors Leon McGinnis, Richard Serfozo, John Vande Vate and Yang Wang. I would also thank the Virtual Factory Lab for providing computing resources during my four years research. Particularly, I thank Dr. Douglas Bodner for his support. My appreciation goes out to the entire school of ISyE at Georgia Tech, students and faculty, for their support and help. I would especially like to thank Ki-Seok Choi for his willingness to help me. In particular, I owe much to Zheng Wang who had the substantial tasks of proof-reading a draft of this thesis. On a more personal level, I would like to thank my friends, Jianbin Dai and Sheng Liu, for their help during my study at Georgia Tech. I would like to thank the National Science Foundation, which has supported my research through grants DMI-9457336 and DMI-9813345. I also thank Brooks Automations Inc., AutoSimulations division for donating AutoSched AP software and providing technical support. I can hardly imagine how this research could be done without the AutoSched AP software. Finally, I thank my family for their love and support throughout. Particularly, I thank my wife Miao Liu for her continuous support and encouragement. iii Contents Acknowledgements iii