Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

Abstract

We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

A Closed Queueing Networks Approach for an Optimal Heterogeneous Fleet Size of an Inter-Facility Bulk Material Transfer System

“…The queueing network model was used to estimate the system throughput, utilisation, and expected wait times. Yuan and Gong [79] and Otten et al [18] used mixed networks to model RMFS and find the optimal number of robots needed to achieve service levels in a warehouse. Munoz and Lee [80] conducted a study to determine the optimal number of trucks for a sugarcane harvesting field by modelling operations using a CQN.…”

“…Table 9 presents a comprehensive comparative analysis of queue response times between the analytical and simulation methods, explicitly focusing on selected multi-class nodes. The differences between these methodologies have been quantified by applying Equation (18). Furthermore, the calculated difference range serves as a critical metric to assess the acceptability of the disparities, adhering to the predefined criterion of ±8%.…”

“…Queueing networks are a pervasive and widely applied modelling framework in analysing and optimising MHS across diverse operational contexts. This modelling approach is instrumental in comprehensively assessing and refining MHS performance by considering a spectrum of operational considerations [16][17][18][19][20][21][22].…”

Robotic Mobile Fulfillment System: A Systematic Review

“…Each one of these categories has eleven papers. In the former, there is not much variety in terms of the technique, as most entries incorporate Semi-Open Queuing Networks [9], [58] or Multi-Class Closed Queuing Networks [40]. But for the latter, options are more diverse.…”