A discrete-time queueing network approach to performance evaluation of autonomous vehicle storage and retrieval systems

An approach for a performance calculation of shuttle-based storage and retrieval systems with multiple-deep storage

“…The open queueing network is used to take account of the interactions between lifts and shuttles. Again, there are approaches that are not validated through simulation, e.g., Heragu et al [11], Wang et al [29], and approaches that are validated through simulation: Marchet et al [23], Ekren et al [8], and Epp et al [9]. The restriction of these approaches is that they evaluate the waiting times between lifts and shuttles.…”

“…The system that is investigated in this paper is a tier-captive single-aisle SBS/RS for double-deep storage, as shown in [23] Tier-captive SCC OQN (yes) Single-deep Ekren et al [7] Tier-captive SCC/DCC SIM Single-deep Lerher et al [21] Tier-captive SCC/DCC SIM Single-deep Marchet et al [24] Tier-captive SCC SIM Single-deep Lerher [14] Tier-captive SCC/DCC CTM (no) Single-deep Sari et al [25] Tier-captive SCC/DCC CTM (yes) Single-deep Kartnig et al [12] Tier-captive DCC SQ (yes) Single-deep Trummer et al [27] Tier-captive SCC/DCC SIM Single-deep Lerher et al [18] Tier-captive SCC/DCC CTM (no) Single-deep Lerher et al [20] Tier-captive DCC SIM Single-deep Ekren et al [6] Tier-captive DCC SIM Single-deep Wang et al [29] Tier-captive SCC/DCC OQN (no) Single-deep Lerher [15] Tier-captive SCC/DCC CTM (yes) Double-deep Eder et al [4] Tier-captive SCC/DCC SQLC (yes) Single-deep Eder et al [3] Tier-captive SCC/DCC SQLC (yes) Double-deep Lerher et al [22] Tier-captive SCC/DCC CTM (no) Single-deep Lerher et al [17] Tier-captive SCC/DCC SIM Single-deep Lerher et al [19] Tier-captive SCC/DCC SIM Single-deep Borovinšek et al [1] Tier-captive SCC/DCC CTM (no) Single-deep Ekren et al [8] Tier-captive SCC/DCC OQN (yes) Single-deep Lerher [16] Tier-captive DCC SIM Single-deep Epp et al [9] Tier-captive SCC/DCC OQN(yes) Single-deep Eder et al [5] Tier-captive SCC/DCC SQLC (yes) Single-deep Kriehn et al [13] Tier-captive SCC/DCC SIM Single-deep Ha et al [10] Tier-captive SCC SIM Single-deep Eder [2] Tier -There are different transfer times from and to the shuttle depending on the depth of the rack. -There is no difference in time between the transfer of totes to and from the lifts.…”

Analytical model to estimate the performance of shuttle-based storage and retrieval systems with class-based storage policy

“…A single-aisle model was deemed fit for determining the performance of SBS/RS, as the storage and retrieval transactions among all aisles were evenly distributed [7,8,13]. For this study, the presented approach is based on the approach by Eder [2], which employs an open queueing model with limited capacity (M|G|1|K) and with three main parts determining the throughput, namely the interarrival time to Shuttle velocity w N / w X Probability of order a tote in zone N / area X w NX Probability that a tote from zone N is situated in area X one single tier, the service time of the shuttles, and the open queueing model M|G|1|K.…”

“…Eder's [2] approach assumed that all tiers have the same exponentially distributed interarrival time; thus, to fulfil this, the approach was divided in different parts. Figures 6,7,8, and 9 show a class-based storage with three classes and zoning in the vertical direction. Figure 6 presents the arrivals into the different tiers, specifically, the three different zones with their probabilities of numbers of tiers into the respective zone n N = 20%/30%/50% and with their probabilities of numbers from the respective zone w N = 60%/30%/10%.…”

Parametric Study of Throughput Performance in SBS/RS Based on Simulation

“…For example, Marchet et al [14] presented an open queuing network approach to design an analytical model to estimate some performance measures (waiting and cycle time of transactions) to study SBS/RS and compared their experimental results with simulation results. Epp et al [15] presented a method for the calculation of the performance measures of a tier-captive single-aisle AVS/RS with general discrete inter-arrival and service times, modelled as a discrete-time open queuing network.…”