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.

On the Estimation in Multi-server Multi-Core Open Queuing Networks

The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. We investigate the estimation in a multi-server multi-core open queueing networks and its applications to the theorems in heavy traffic conditions (fluid approximation, functional limit theorem, and law of the iterated logarithm) for a queue of jobs in a multi-server multi-core open queueing networks..

Open Queueing Networks

Systems often have two or more stages and a customer must go several stages before finalizing their service. The systems can be arranged in series or in network. Chapter 5 is dedicated specifically to the performance analysis of systems that have several stages both in series and those that have network arrangement; the theorems of Burke and Jackson are presented; the calculations of the flow and variability in a network and of the measures of performance (cycle time and work in process) are also exposed. Several codes are proposed in Scilab Language to perform calculations automatically. The chapter ends with a section devoted to identifying and analyzing the bottleneck in a system from a cost approach.