Eline De Cuypere

Performance evaluation of a kitting process

Nowadays, customers request more variation in a companys 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 study a kitting process with two parts as a continuous-time Markovian queueing model. Using sparse matrix techniques to solve this model, we assess the impact of kitting interruptions, bursty part arrivals and the kitting time distribution on the behaviour of the part buffers.

A Maclaurin-series expansion approach to multiple paired queues

Motivated by kitting processes in assembly systems, we consider a Markovian queueing system with K paired finite-capacity 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.

A queueing model of an energy harvesting sensor node with data buffering

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.

Opinion propagation in bounded medium-sized populations

Abstract We study the dynamics of opinion propagation in a medium-sized population with low population turnover. Opinion spreading is modelled by a Markovian non-standard Susceptible–Infected–Recovered (SIR) epidemic model with stochastic arrivals, departures, infections and recoveries. The system performance is evaluated by two complementary approaches: a numerical but approximate solution approach which relies on Maclaurin-series expansions of the stationary solution of the Markov process and a fluid limit approach. Both methods are evaluated numerically. Moreover, convergence to the fluid limit is proved, and explicit expressions for the fixed points of the differential equations are obtained for the case of linearly increasing infection and arrival rates.

Optimal Inventory Management in a Fluctuating Market

In the highly competitive environment in which companies operate today, it is crucial that the supporting processes such as inventory management are as efficient as possible. In particular, a trade-off between inventory costs and service levels needs to be assessed. In this paper, we determine an optimal batch ordering policy accounting for both demand and market price fluctuations such that the long-term discounted cost is minimised. This means that future costs are reduced by a constant factor as we need to take inflation and other factors into account. To this end, the inventory system is modelled as a Markovian queueing system with finite capacity in a random environment. Assuming phase-type distributed lead times, Markovian demand and price fluctuations, the optimal ordering strategy is determined by a Markov decision process (MDP) approach. To illustrate our results, we analyse the ordering policy under several price fluctuation scenarios by some numerical examples.

A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times

We propose an efficient numerical scheme for the evaluation of large-scale Markov processes that have a generator matrix that reduces to a triangular matrix when a certain rate is sent to zero. The methodology at hand is motivated by coupled queueing systems. Such systems are a natural abstraction for kitting processes in assembly systems and consist of multiple parallel buffers. The buffers are coupled in the sense that departures from the different buffers are synchronised and that there is no service if any of the buffers is empty. As multiple customer buffers are involved, the Markovian description of the system obviously suffers from the state-space explosion problem. To cope with this problem, a numerical algorithm is presented which calculates the coefficients of the Maclaurin-series expansion of the steadystate probability vector. While the series expansion is a regular perturbation problem for the coupled queueing system with exponential service times, it is a singular perturbation problem if the service times are phase-type distributed. Some numerical examples show that the series expansion technique combined with a simple heuristic provides high numerical accuracy.