## 1 Introduction  
The semiconductor industry has experienced outstanding advancements over the past five decades. There are two main factors driving these advancements. One is technology advancement and another is wafer size increment [1]. The technology advancements focused on minimizing the integrated circuit (IC) so as to pack more transistors into one IC chip to enhance its functionality. Following the Moore's rule, each of the wafer size transitions has nearly doubled the number of transistors in an IC chip [2]. The wafer size increments have led to the increase of IC dies. For example, for the last transition of wafer size from 200 mm diameter to 300 mm diameter, the IC dies resulting from one wafer has been increased as much as 2.25 times [1], which has enhanced the productivity considerably. Currently, the IC industry is transitioning from the 300 mm wafer to 450 mm wafer. A similar transitional benefit is expected. However, due to their increased size and weight, 450 mm wafers will introduce unprecedented challenges on a wafer fab in terms of wafer handling, transport, factory configuration and process automation [3]. A capable Automated Material Handling System (AMHS) suitable for 450 mm wafer production is definitely required [4; 5], and the AMHS plays an important role that can determine the success of wafer transition [6]. In the past, various kinds of AMHSs have been proposed to support wafer production. They include automatic guided vehicle (AGV), rail-guided vehicles (RGV), overhead shuttle system (OHS), overhead hoist transport (OHT) and conveyor [7]. Among these AMHS, OHT is the main system widely used in 300 mm wafer fabs. This kind of AMHS employs overhead transporters (such as vehicles) to directly access a stocker or a machine in a production line, with the efficiency of the OHT depending heavily on its control mechanism and the characteristics of its vehicles. The number of vehicles in the OHT is also critical as it can affect the performance of an OHT considerably; insufficient vehicles in an OHT can lead to long waiting times for lots while excessive vehicles will cause the traffic-jam problem [8]. The traffic jam problem can affect the performance of an AMHS considerably [9]. Compared to a vehicle-based AMHS, a conveyor-based AMHS can send a lot earlier due to the continuous flow of conveyor, which leads to the benefits of reduced waiting time and eventually shortened delivery time for lots. Another benefit found for a conveyor-based AMHS is that it can serve as a buffer for lots prior to their entering into a processing equipment. This can lead to the benefit of reduced number of stockers in an AMHS. One more benefit found for a conveyor-based AMHS is that it can maintain a higher entering rate of lots into a processing equipment [6; 10]. Due to these advantages, researchers have suggested using conveyor-based AMHSs for 450 mm wafer fabrication [9; 10]. In a wafer fab, a conveyor-based AMHS usually consists of two main parts: an Inter-bay loop and some Intra-bay loops. The Inter-bay loop is usually situated at the center of a factory and connects to several Intra-bay loops. The Intra-bay loops are used to transport lots within an Intra-bay while the Inter-bay loop transports lots between Intra-bays. In a conveyor-based AMHS, conveyors are the main device used to carry and transport wafers and these conveyors are moving along one direction. In an AMHS, it also includes sensors to detect lots so as to control the movements of these wafer lots. For instance, a get-out sensor is usually used at the end of the conveyor to detect wafer lots. In an Intra-bay, some similar machines are grouped with each machine equipped with a load/unload port for loading/unlading lots, one at a time. The load/unload port for 450 mm wafer production has been already standardized [11]. However, a traditional conveyor-based AMHS tends to encounter the traffic-jam problem due to the single direction movement of conveyors.