Large deviations of an infinite-server system with a linearly scaled background process

This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ¿i¿i by a factor NN and the transition rates ¿ij¿ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where NN tends to 88). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening. Keywords: Queues; Infinite-server systems; Markov modulation; Large deviation

Performance evaluation of a decoupling inventory for hybrid push-pull systems

Nowadays, companies that oer product variety while maintaining short lead times and competitive quality and cost, gain a competitive edge over their competitors. Therefore, hybrid push-pull systems allow for efficiently balancing lead times and production costs. Raw materials are `pushed' into the semi-finished good warehouse and customers `pull' products by placing orders. As performance of the decoupling stock is critical to the overall performance of the manufacturing system, we define and analyse a Markovian queueing model with two buers, thereby accounting for both the decoupling stock as well as for possible backlog of orders. In particular, our study assesses the eect of variability in the production process and the ordering process on the performance of the decoupling stock

Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit

This article studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates (i) by a factor N and the rates (ij) of the background process by N1+E (for some E>0), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that N tends to . In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean

Performance analysis of a decoupling stock in a make-to-order system

In a Make-to-Order system, products are only manufactured when orders are placed. As this may lead to overly long delivery times, a stock of semi-finished products can be installed to reduce production time: the so-called decoupling stock. As performance of the decoupling stock is critical to the overall performance and cost of the production system, we propose and analyse a Markovian model of the decoupling stock. In particular, we focus on a queueing model with two buffers, thereby accounting for both the decoupling stock as well as for possible backlog of orders. By means of numerical examples, we then quantify the impact of production inefficiency on delivery times and overall cost

Analysis of Markov-modulated infinite-server queues in the central-limit regime

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on the state of the background process. The main contribution concerns the derivation of central limit theorems for the number of customers in the system at time $t\ge 0$, in the asymptotic regime in which the arrival rates $\lambda_i$ are scaled by a factor $N$, and the transition rates $q_{ij}$ by a factor $N^\alpha$, with $\alpha \in \mathbb R^+$. The specific value of $\alpha$ has a crucial impact on the result: (i) for $\alpha>1$ the system essentially behaves as an M/M/$\infty$ queue, and in the central limit theorem the centered process has to be normalized by $\sqrt{N}$; (ii) for $\alpha<1$, the centered process has to be normalized by $N^{{1-}\alpha/2}$, with the deviation matrix appearing in the expression for the variance

Stochastic modelling of energy harvesting for low power sensor nodes

Battery lifetime is a key impediment to long-lasting low power sensor nodes. Energy or power harvesting mitigates the ependency on battery power, by converting ambient energy into electrical energy. This energy can then be used by the device for data collection and transmission. This paper proposes and analyses a queueing model to assess performance of such an energy harvesting sensor node. Accounting for energy harvesting, data collection and data transmission opportunities, the sensor node is modelled as a paired queueing system. The system has two queues, one representing accumulated energy and the other being the data queue. By means of some numerical examples, we investigate the energy-information trade-off

A two-queue model for optimising the value of information in energy-harvesting sensor networks

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Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved