Martin Epp

A discrete-time queueing network approach to performance evaluation of autonomous vehicle storage and retrieval systems

In this paper, we present a method for performance evaluation of autonomous vehicle storage and retrieval systems (AVS/RSs) with tier-captive single-aisle vehicles. A discrete-time open queueing network approach is applied. The data obtained from the evaluation of the lift and vehicle movements can be used directly as input for the general discrete service time distributions of the queueing network. Furthermore, the approach allows for the computation of the retrieval transaction time distribution as well as of the distribution of the number of transactions waiting to be stored. Consequently, not only expected values and variances but also quantiles of the performance measures can be obtained. Comparison to discrete-event simulation quantifies approximation errors resulting from the decomposition approach in the discrete-time domain. Moreover, the errors obtained by the discrete-time approach are compared to the errors obtained using a continuous-time open queueing network approach. Finally, it will be outlined how the model can be used for designing AVS/RSs according to given system requirements, such as storage capacity, throughput, height and length of the system as well as the 95% quantile of the retrieval transaction time.

Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times

This paper is motivated by the performance evaluation of circulating vertical conveyor systems (CVCSs). CVCSs are bulk queues of transportation type. These material handling systems feature generally distributed inter-arrival times, which can be longer than the bulk service time. This leads to interdependencies between the number of arrivals in consecutive service intervals and the number of loads in the queue. We propose a new discrete-time approach for the steady-state analysis of such bulk service queues of transportation type with general arrival and service processes and finite server and limited queue capacities. The approach is based on a finite Markov chain that generates complete probability distributions for the key performance measures, including the queue length, waiting time and departing batch size. The proposed approach is exact in the cases of discrete-time slots, e.g. as in communication systems. We investigate the discretisation error that arises if the approach is used as an approximation for the continuous time using a numerical comparison to a discrete-event simulation. Moreover, we examine the impact of arrival stream variability on the system performance and compare the positive effects of a higher frequency of server visits with the effects arising from larger pickup capacities.

An Exact Model to Determine the Lead-Time Distribution of Perishable Goods in a Kanban-Controlled Production System = [Ein exaktes modell zur bestimmung der durchlaufzeitverteilung von umge-bungsempfindlichen gütern in einem kanban-gesteuerten produktionssystem]

In many production and logistics systems the lead-time distribution of the transported products and goods plays a major role for what concerns the system performances. In particular, when the sojourn time in a part of the supply chain exceeds the target range, some quality and rework costs may arise, for example in case of perishable goods. This paper presents an analytical model to exactly determine the lead-time distribution in closed loop systems and to compute the correspondent costs by means of discrete-time Markov chains.