Simple bounds for queueing systems with breakdowns

Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes

Simple and insensitive bounds for a grading and an overflow model

Simple and intuitively obvious lower and upper bounds are suggested for a specific grading and an overflow model. The bounds are based on product-type modifications and are insensitive. Numerical support indicates a potential usefulness for quick engineering purposes

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are (i) classical circuit switch telephone networks (loss networks) and (ii) present-day wireless mobile networks. Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it does not have one in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hypercubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to (1) upper bounds for loss probabilities and \ud (2) analytic error bounds for the accuracy of the approximation for various performance measures.\ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud (1)• pure loss networks as under (2)• GSM networks with fixed channel allocation as under.\ud The results are of practical interest for computational simplifications and, particularly, to guarantee that blocking probabilities do not exceed a given threshold such as for network dimensioning

Preface

This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner.  The handbook is organized into five parts: Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow subnetworks to be aggregated into single nodes to reduce computational burden. Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the proces generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures. Part 3 presents diffusion and fluid results. It specifically looks at  the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic. Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks. Part 5 enlightens selected applications as loss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest. The book shows that the intertwined progress of theory and practice  will remain to be most intriguing and will continue to be the basis of further developments in queueing networks

To pool or not to pool in hospitals: a theoretical and practical comparison for a radiotherapy outpatient department

This paper examines whether urgent and regular patients waiting for a consultation at a radiotherapy outpatient department should be pooled or not. Both queuing theory and discrete event simulation were applied to a realistic case study. The theoretical approach shows that pooling is not always beneficial with regard to the waiting times of urgent patients. Furthermore, the practical approach indicates that the separation of queues may require less capacity to meet the waiting time performance target for urgent as well as regular patients. The results seem to be of general interest for hospital

Guest editorial to the first international workshop on performability modelling of computer and communication systems

The papers in this issue of Performance Evaluation all deal with performability modelling of computer and communication systems. This was the topic of the First International Workshop on Performability Modelling of Computer and Communication Systems (PMCCS-1), held 7-8 February 1991, at the University of Twente, Enschede, the Netherlands

Optimization of charging strategies for electric vehicles in PowerMatcher-driven smart energy grids

A crucial challenge in future smart energy grids is the large-scale coordination of distributed energy demand and generation. The well-known PowerMatcher is a promising approach that integrates demand and supply exibility in the operation of the electricity system through dynamic pricing and a hierarchical bidding coordination scheme. However, as the PowerMatcher focuses on short-term coordination of demand and supply, it cannot fully exploit the exibility of e.g. electric vehicles over longer periods of time. In this paper, we propose an extension of the PowerMatcher comprising a planning module, which provides coordinated predictions of demand/price over longer times as input to the users for determining their short-term bids. The optimal short-term bidding strategy minimizing a user's costs is then formulated as a Stochastic Dynamic Programming (SDP) problem. We derive an analytic solution for this SDP problem leading to a simple short-term bidding strategy. Numerical results using real-world data show a substantial performance improvement compared to the standard PowerMatcher, without significant additional complexity

Met het oog op wachttijd

Zonder een goed functionerend hoornvlies, hierna genoemd cornea, kunnen de ogen hun taak niet goed uitvoeren. Iets meer dan 100 jaar geleden, in 1905, werd de eerstes uccesvolle transplantatie van een cornea van een overleden donor uitgevoerd in Tsjechië, door oogarts Zirm. Mede door de ontwikkeling van operatiemicroscopen, extra dun hechtdraad en het gebruik van antibiotica worden vandaag de dag in Nederland ongeveer 900 corneatransplantaties per jaar uitgevoerd. In Nederland is de Nederlandse transplantatie Stichting (NTS) verantwoordelijk voor het toewijzen van cornea’s aan patiënten (Bokhorst et al., 2007).\ud De gemiddelde wachttijd voor een cornea in Nederland is ongeveer een half jaar, ofwel 175 dagen. (Zie figuur 1) De door de NTS en oogartsen meest genoemde oorzaken zijn een tekort aan operatiecapaciteit en cornea’s en de fluctuatie in zowel vraag als aanbod van cornea’s. Ons eerste doel was te onderzoeken in welke mate deze zaken de wachttijd beïnvloeden. Een tweede doel was mogelijke verbeteringen aan te dragen