A multi-tier linking approach to analyze performance of autonomous vehicle-based storage and retrieval systems

Develop a general performance analysis model for vehicle-based warehousing systems.Estimate the first and second moment of inter-departure times from a load-dependent queue.Link multiple semi-open queuing networks using parametric decomposition approach.Validate the modelling approach using detailed simulations. To improve operational flexibility, throughput capacity, and responsiveness in order fulfillment operations, several distribution centers are implementing autonomous vehicle-based storage and retrieval system (AVS/RS) in their high-density storage areas. In such systems, vehicles are self-powered to travel in horizontal directions (x- and y- axes), and use lifts or conveyors for vertical motion (z-axis). In this research, we propose a multi-tier queuing modeling framework for the performance analysis of such vehicle-based warehouse systems. We develop an embedded Markov chain based analysis approach to estimate the first and second moment of inter-departure times from the load-dependent station within a semi-open queuing network. The linking solution approach uses traffic process approximations to analyze the performance of sub-models corresponding to individual tiers (semi-open queues) and the vertical transfer units (open queues). These sub-models are linked to form an integrated queuing network model, which is solved using an iterative algorithm. Performance estimates such as expected transaction cycle times and resource (vehicle and vertical transfer unit) utilization are determined using this algorithm, and can be used to evaluate a variety of design configurations during the conceptualization phase.

[1]  Yves Dallery,et al.  Approximate Analysis of General Open Queuing Networks with Restricted Capacity , 1990, Perform. Evaluation.

[2]  Charles J. Malmborg,et al.  An Approximate Solution for Semi-Open Queueing Network Model of an Autonomous Vehicle Storage and Retrieval System , 2013, IEEE Transactions on Automation Science and Engineering.

[3]  Ward Whitt.  Towards better multi-class parametric-decomposition approximations for open queueing networks , 1994, Ann. Oper. Res..

[4]  Debjit Roy,et al.  Queuing models to analyze dwell-point and cross-aisle location in autonomous vehicle-based warehouse systems , 2015, Eur. J. Oper. Res..

[5]  Sunderesh S. Heragu,et al.  Analysis of manufacturing systems via single-class, semi-open queuing networks , 2011 .

[6]  W. H. M. Zijm,et al.  AMVA‐based solution procedures for open queueing networks with population constraints , 2000, Ann. Oper. Res..

[7]  Debjit Roy,et al.  A simulation framework for studying blocking effects in warehouse systems with autonomous vehicles , 2016 .

[8]  Charles J. Malmborg,et al.  Simulation based experimental design to identify factors affecting performance of AVS/RS , 2010, Comput. Ind. Eng..

[9]  Charles J. Malmborg,et al.  Performance modelling of autonomous vehicle storage and retrieval systems using class-based storage policies , 2008, Int. J. Comput. Appl. Technol..

[10]  Benjamin Avi-Itzhak,et al.  Approximate Queuing Models for Multiprogramming Computer Systems , 1973, Oper. Res..

[11]  Tone Lerher.  Travel time model for double-deep shuttle-based storage and retrieval systems , 2016 .

[12]  Charles J. Malmborg,et al.  A network queuing approach for evaluation of performance measures in autonomous vehicle storage and retrieval systems , 2009, Eur. J. Oper. Res..

[13]  Debjit Roy,et al.  Stochastic models for unit-load operations in warehouse systems with autonomous vehicles , 2015, Ann. Oper. Res..

[14]  Charles J. Malmborg,et al.  Design models for unit load storage and retrieval systems using autonomous vehicle technology and resource conserving storage and dwell point policies , 2007 .

[15]  Charles J. Malmborg,et al.  Variance-based approximations of transaction waiting times in autonomous vehicle storage and retrieval systems , 2009 .

[16]  Yang Liu,et al.  Modeling and evaluating the AVS/RS with tier-to-tier vehicles using a semi-open queueing network , 2014 .

[17]  Debjit Roy,et al.  Blocking Effects in Warehouse Systems With Autonomous Vehicles , 2014, IEEE Transactions on Automation Science and Engineering.

[18]  Gunter Bolch,et al.  Queueing Networks and Markov Chains , 2005 .

[19]  Myron Hlynka,et al.  Queueing Networks and Markov Chains (Modeling and Performance Evaluation With Computer Science Applications) , 2007, Technometrics.

[20]  Charles J. Malmborg.  Conceptualizing tools for autonomous vehicle storage and retrieval systems , 2002 .

[21]  Debjit Roy,et al.  Solving semi-open queuing networks with time-varying arrivals: An application in container terminal landside operations , 2018, Eur. J. Oper. Res..

[22]  Sunderesh S. Heragu,et al.  Simulation-based regression analysis for the rack configuration of an autonomous vehicle storage and retrieval system , 2010 .

[23]  Goran Dukic,et al.  Travel time model for shuttle-based storage and retrieval systems , 2015 .

[24]  W. Whitt,et al.  The Queueing Network Analyzer , 1983, The Bell System Technical Journal.

[25]  Charles J. Malmborg.  Interleaving dynamics in autonomous vehicle storage and retrieval systems , 2003 .

[26]  Gino Marchet,et al.  Analytical model to estimate performances of autonomous vehicle storage and retrieval systems for product totes , 2012 .

[27]  Charles J. Malmborg,et al.  An efficient cycle time model for autonomous vehicle storage and retrieval systems , 2008 .

[28]  Debjit Roy,et al.  Semi-open queuing networks: a review of stochastic models, solution methods and new research areas , 2016 .

[29]  Charles J. Malmborg,et al.  Analytical models for analysis of automated warehouse material handling systems , 2011 .

[30]  Debjit Roy,et al.  Performance analysis and design trade-offs in warehouses with autonomous vehicle technology , 2012 .