Two-worker blocking congestion model with walk speed m in a no-passing circular passage system

• Construct a blocking model traveling with walk speed m in a circular-aisle warehouse.
• Derive a closed-form expression of two-worker blocking congestion.
• Estimate the blocking congestion in a practical walk speed system.
• Demonstrate the applicability to a bucket-brigade order picking situation.

This paper introduces a blocking model and closed-form expression of two workers traveling with walk speed m (m = integer) in a no-passing circular-passage system of n stations and assuming n = m + 2, 2m + 2, …. We develop a Discrete-Timed Markov Chain (DTMC) model to capture the workers’ changes of walk, pick, and blocked states, and quantify the throughput loss from blocking congestion by deriving a steady state probability in a closed-form expression. We validate the model with a simulation study. Additional simulation comparisons show that the proposed throughput model gives a good approximation of a general-sized system of n stations (i.e., n > 2), a practical walk speed system of real number m (i.e., m ⩾ 1), and a bucket brigade order picking application.