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