Motivated by kitting processes in assembly systems, we consider a Markovian queueing system with K paired finitecapacity buffers. Pairing means that departures from the buffers are synchronised and that service is interrupted if any of the buffers is empty. To cope with the inherent state-space explosion problem, we propose an approximate numerical algorithm which calculates the first L coefficients of the Maclaurin series expansion of the steady-state probability vector in O(KLM ) operations, M being the size of the state space.

Abstract. Nowadays, customers request more variation in a company's product assortment leading to an increased amount of parts moving around on the shop floor. To cope with this tendency, a kitting process can be implemented. As it gathers the necessary parts into a container prior to assembly, kitting enables a more cost-efficient and qualitative production. However, the performance of this preparation technique in an assembly process has merely been investigated. Therefore, we studied a kitting process with two parts as a continuous-time Markovian queueing model. Using sparse matrix techniques to solve our queueing model, we assessed the impact of kitting interruptions, bursty part arrivals and phase-type distributed kitting times on the behaviour of the part buffers. Consequently, this paper studies part buffer behaviour under realistic assumptions in order to evaluate the performance of kitting operations in a production environment.

Battery lifetime is a key impediment to long-lasting low power sensor nodes and networks thereof. Energy harvesting -conversion of ambient energy into electrical energy -has emerged as a viable alternative to battery power. Indeed, the harvested energy mitigates the dependency on battery power and can be used to transmit data. However, unfair data delivery delay and energy expenditure among sensors remain important issues for such networks. We study performance of sensor networks with mobile sinks: a mobile sink moves towards the transmission range of the different static sensor nodes to collect their data. We propose and analyse a Markovian queueing system to study the impact of uncertainty in energy harvesting, energy expenditure, data acquisition and data transmission. In particular, the energy harvesting sensor node is described by a system with two queues, one queue corresponding to the battery and the other to the data buffer. We illustrate our approach by numerical examples which show that energy harvesting correlation considerably affects performance measures like the mean data delay and the effective data collection rate.

We present a comprehensive numerical approach with reasonably light complexity in terms of implementation and computation for assessing the performance of hybrid make-to-stock (MTS)/make-to-order (MTO) systems. In such hybrid systems, semi-finished products are produced up front and stored in a decoupling inventory. When an order arrives, the products are completed and possibly customised. We study this system in a stochastic setting: demand and production are modelled by random processes. In particular, our model includes two coupled Markovian queues: one queue represents the decoupling inventory and the other the order backlog. These queues are coupled as order processing can only occur when both queues are non-empty. We rely on matrix analytic techniques to study the performance of the MTO/MTS system under non-restrictive stochastic assumptions. In particular, we allow for arrival correlation and non-exponential setup and MTS and MTO processing times, while the hybrid MTS/MTO system is managed by an (s,S)-type threshold policy that governs switching from MTO to MTS and back. By some numerical examples, we assess the impact of inventory control, irregular order arrivals, setup and order processing times on inventory levels and lead times.

Nowadays, customers request more variation in a company’s product assortment leading to an increased amount of parts moving around on the shop floor. To cope with this tendency, a kitting process can be implemented. Kitting is the operation of collecting the necessary parts for a given end product in a specific container, called a kit, prior to arriving at an assembly unit. As kitting performance is critical to the overall cost and performance of the manufacturing system, this paper analyses a two-part kitting process as a Markovian model. In particular, kitting is studied as a paired queue, thereby accounting for stochastic part arrivals, and kit assembly times. Using sparse matrix techniques, we assess the impact of kitting interruptions, bursty part arrivals and phase-type distributed kit assembly times on the behaviour of the part buffers. Finally, a cost-profit analysis of kitting processes is conducted and an approximation for a two-part kitting process is established.