Order Picking Systems: A Queue Model for Dimensioning the Storage Capacity, the Crew of Pickers, and the AGV Fleet
Table 1
The adopted notation.
Expected number of arrivals in a unit of time in the system for each AGV.
Expected number of arrivals in a unit of time when the system is in the state
System throughput.
Expected number of pallets served in a unit of time by a single picker
Expected number of pallets served per unit of time when the system is in state
Probability that a pallet is of type Pallet_end. Number of pallets that are in picking bay plus the number of those waiting in prequeue, that is the state of the system
Probability that the system is in the state at the time
Probability that the system switches from state to state in the time interval
Probability that the system is in the state in the equilibrium (i.e. stationary condition)
Traffic intensity of the system and use factor of the pickers
Size of the AGV fleet
Storage capacity of the picking bay
Number of pickers in the picking bay
Expected number of pallets in the system
Expected number of pallets in the system queue (i.e., waiting for the picking service both in prequeue and in the picking bay)
Expected number of AGVs waiting at the picking bay
Expected time of a pallet in the system
Expected time of a pallet in the system queue (that is waiting for the picking service both in prequeue and in the picking bay)
Expected time of AGV loads and unloads waiting at the picking bay
Maximum number of busy AGVs at the picking bay when the system is in state , which coincides with the maximum number of AGVs not really busy due to the presence of Pallet_end pallets in the picking bay
Expected number of busy AGVs at the picking bay when the system is in state . The number of free AGVs when the system is in state is therefore
