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

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.

Modeling and performance analysis of shuttle-based compact storage systems under parallel processing policy

Short response time for order processing is important for modern warehouses, which can be potentially achieved by adopting appropriate processing policy. The parallel processing policy have advantages in improving performance of many autonomous storage and retrieval systems. However, researchers tend to assume a sequential processing policy managing the movement of independent resources in shuttle-based compact storage systems. This paper models and analyses a single-tier of specialized shuttle-based compact storage systems under parallel processing policy. The system is modeled as a semi-open queueing network with class switching and the parallel movement of shuttles and the transfer car is modeled using a fork-join queueing network. The analytical model is validated against simulations and the results show our model can accurately estimate the system performance. Numerical experiments and a real case are carried out to compare the performance of parallel and sequential processing policies. The results suggest a critical transaction arrival rate and depth/width ratio, below which the sequential processing policy outperforms the parallel processing policy. However, the advantage of sequential processing policy is decreasing with the increasing of shuttle number, transaction arrival rate and depth/width ratio. The results also suggest an optimal depth/width ratio with a value of 1.75 for minimizing the expected throughput time in the real system. Given the current system configurations, the parallel processing policy should be considered when the number of shuttles is larger than 2 or the transaction arrival rate is larger than 24 per hour.

Control of Fork-Join Processing Networks with Multiple Job Types and Parallel Shared Resources

A fork-join processing network is a queueing network in which tasks associated with a job can be processed simultaneously. Fork-join processing networks are prevalent in computer systems, healthcare, manufacturing, project management, justice systems, and so on. Unlike the conventional queueing networks, fork-join processing networks have synchronization constraints that arise because of the parallel processing of tasks and can cause significant job delays. We study scheduling in fork-join processing networks with multiple job types and parallel shared resources. Jobs arriving in the system fork into arbitrary number of tasks, then those tasks are processed in parallel, and then they join and leave the network. There are shared resources processing multiple job types. We study the scheduling problem for those shared resources (i.e., which type of job to prioritize at any given time) and propose an asymptotically optimal scheduling policy in diffusion scale.

Scheduling and Control of Queueing Networks

Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

Modeling Pilot Flight Performance in a Cognitive Architecture: Model Demonstration

Cognitive architecture models can support the simulation and prediction of human performance in complex human-machine systems. In the current work, we demonstrate a pilot model that can perform and simulate taxiing and takeoff tasks. The model was built in Queueing Network-Adaptive Control of Thought Rational (QN-ACTR) cognitive architecture and can be connected to flight simulators such as X-Plane to generate various data, including performance, mental workload, and situation awareness. The model results are determined in combination by the declarative knowledge chunks, production rules, and a set of parameters. Currently, the model can generate flight operation behavior similar to human pilots. We will collect human pilot data to examine further and validate model assumptions and parameter values. Once validated, such models can support interface evaluation and competency-based pilot training, providing a theory-based predictive approach complementary to human-in-the-loop experiments for aviation research and development.