Matrix-geometric solution for semi-open queuing network model of autonomous vehicle storage and retrieval system

Abstract

In this paper, we model the autonomous vehicle storage and retrieval system (AVS/RS) as a semi-open queuing network (SOQN) and apply a matrix-geometric method (MGM) for analyzing it. An AVS/RS is an automated material handling system for the high-rise pallet storage area of a warehouse and allows pallets to be stored and retrieved quickly and efficiently from their storage locations. It is an alternative to the traditional crane-based AS/RS (automated storage and retrieval system). A combination of lifts and autonomous vehicles store pallets into and retrieve them out of their respective rack storage locations. The crane based AS/RS typically utilizes aisle-captive, mast-mounted cranes that can access any storage location in an aisle via horizontal movement of the mast and vertical movement of the crane on the mast.In an SOQN, it is assumed that an arriving job or customer is paired with another device and the two visit all the stations that must process the job in the appropriate sequence. After all operations are completed on the job, it exits the system, but the device returns back to a device pool and awaits the next customer. Sometimes a job may have to wait for a device to arrive at the pool or a device may have to wait for a job to arrive. Although closed queuing networks (CQNs) and open queuing networks (OQNs) model systems that require pairing of an incoming job with a device, unlike the SOQN, they ignore the time that a device waits for a job or the time that a job waits for a device.In the context of an AVS/RS, the jobs correspond to storage/retrieval (S/R) transaction requests and the autonomous vehicles (AVs) correspond to the devices. Because an AV may sometimes have to wait for an S/R transaction or vice versa, we model the AVS/RS as an SOQN. We build the queuing network by deriving general travel times of pre-defined servers. We model the AVS/RS system as a single-class, multiple-server, SOQN. Then, we solve the network using the MGM and obtain its key performance measures. We apply the MGM technique for solving the SOQN model to a warehouse in France that uses AVS/RS.