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ABSTRACT: To characterise and forecast daily patient arrivals into an accident and emergency (A&E) department based on previous arrivals data.
Arrivals between 1 April 2002 and 31 March 2007 to a busy case study A&E department were allocated to one of two arrival streams (walk-in or ambulance) by mode of arrival and then aggregated by day. Using the first 4 years of patient arrival data as a "training" set, a structural time series (ST) model was fitted to characterise each arrival stream. These models were used to forecast walk-in and ambulance arrivals for 1-7 days ahead and then compared with the observed arrivals given by the remaining 1 year of "unseen" data.
Walk-in arrivals exhibited a strong 7-day (weekly) seasonality, with ambulance arrivals showing a distinct but much weaker 7-day seasonality. The model forecasts for walk-in arrivals showed reasonable predictive power (r = 0.6205). However, the ambulance arrivals were harder to characterise (r = 0.2951).
The two separate arrival streams exhibit different statistical characteristics and so require separate time series models. It was only possible to accurately characterise and forecast walk-in arrivals; however, these model forecasts will still assist hospital managers at the case study hospital to best use the resources available and anticipate periods of high demand since walk-in arrivals account for the majority of arrivals into the A&E department.
Emergency Medicine Journal 05/2009; 26(4):241-4. · 1.44 Impact Factor
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ABSTRACT: We present and validate an enhanced analytical queueing network model of zoned RAID. The model focuses on RAID levels 01 and 5, and yields the distribution of I/O request response time. Whereas our previous work could only support arrival streams of I/O requests of the same type, the model presented here supports heterogeneous streams with a mixture of read and write requests. This improved realism is made possible through multiclass extentions to our existing model. When combined with priority queueing, this development also enables more accurate modelling of the way subtasks of RAID 5 write requests are scheduled. In all cases we derive analytical results for calculating not only the mean but also higher moments and the full distribution of I/O request response time. We validate our model against measurements from a real RAID system.
Modeling, Analysis and Simulation of Computers and Telecommunication Systems, 2008. MASCOTS 2008. IEEE International Symposium on; 10/2008
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ABSTRACT: The Laguerre method for the numerical inversion of Laplace transforms is a well known approach to the approximation of probability density functions (PDFs) and cumulative distribution functions (CDFs) of first passage times in Markov chains. Results are presented that relate the Laguerre generating functions and Laguerre coefficients of a PDF with those of the corresponding complementary CDF. This enables the ability to compute the PDF or CDF from the Laplace transform of either at the cost of computing only one set of Laguerre coefficients.
Electronics Letters 02/2008; · 0.96 Impact Factor
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ABSTRACT: Performance trees are a recently-proposed mechanism for the specification of performance properties and measures. They represent an attractive alternative to stochastic logics, since they support traditional stochastic model checking queries, while also allowing for the direct extraction of a wide range of quantitative measures. In this paper we illustrate differences in expressiveness between performance trees and continuous stochastic logic (CSL), and present quantitative semantics showing the mathematical basis underlying performance tree operators. As a running example, we demonstrate performance query specification with performance trees on a stochastic Petri net model of a healthcare system.
Quantitative Evaluation of Systems, 2007. QEST 2007. Fourth International Conference on the; 10/2007
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ABSTRACT: A model inspired by a scenario found in Grid-based scheduling systems is considered. Scheduling is performed remotely without access to up-to-date resource availability and usage information. This system is modelled as a collection of queues where servers break down and are subsequently repaired. There is a delay before the scheduler learns of failures, and requests may continue to arrive into a resource queue for some time after active service has ceased. The queues are considered to be persistent under failure. However, these queues have finite capacity; therefore there is the possibility that queues become full, causing job-loss. Stochastic process algebra and stochastic probes are used to analyse this model to find steady-state measures and passage time distributions. The effect of the duration of any delay on information propagation on the system response time and job loss is investigated and evaluated numerically.
IEE Proceedings - Software 11/2004; · 0.40 Impact Factor
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ABSTRACT: PEPA is a popular stochastic process algebra and a powerful formalism for describing performance models of communication and computer systems. We augment the current state-of-the-art in the analysis of PEPA models by presenting a tool set that cannot only perform steady-state and transient analysis, but also response time analysis. Response time densities and quantiles are important performance metrics which are used to specify service level agreements (SLAs) and benchmarks. HYDRA is a tool specialising in response time analysis of large Markov systems based on stochastic Petri nets. By using the imperial PEPA compiler (ipc), we can generate a HYDRA model from a PEPA model and obtain steady-state, transient and response time measures based on the original PEPA description.
Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings. First International Conference on the; 10/2004
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ABSTRACT: In this paper we present a coarse-grained parallel multi-level algorithm for the k-way hypergraph partitioning problem. The algorithm significantly improves on our previous work in terms of run time and scalability behaviour by improving processor utilisation, reducing synchronisation overhead and avoiding disk contention. The new algorithm is also generally applicable and no longer requires a particular structure of the input hypergraph to achieve a good partition quality. We present results which show that the algorithm has good scalability properties on very large hypergraphs with Θ(10<sup>7</sup>) vertices and consistently outperforms the approximate partitions produced by a state-of-the-art parallel graph partitioning tool in terms of partition quality, by up to 27%.
Parallel and Distributed Computing, 2004. Third International Symposium on/Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks, 2004. Third International Workshop on; 08/2004
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ABSTRACT: A technique for defining and extracting passage-time densities from high-level stochastic process algebra models is presented. Our high-level formalism is PEPA, a popular Markovian process algebra for expressing compositional performance models. We introduce ipc, a tool which can process PEPA-specified passage-time densities and models by compiling the PEPA model and passage specification into the DNAmaca formalism. DNAmaca is an established modelling language for the low-level specification of very large Markov and semiMarkov chains. We provide performance results for ipc/DNAmaca and comparisons with another tool which supports PEPA, PRISM. Finally, we generate passage-time densities and quantiles for a case study of a high-availability Web server.
Modeling, Analysis and Simulation of Computer Telecommunications Systems, 2003. MASCOTS 2003. 11th IEEE/ACM International Symposium on; 11/2003
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Petri Nets and Performance Models, 2003. Proceedings. 10th International Workshop on; 10/2003
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ABSTRACT: Semi-Markov processes (SMPs) are expressive tools for modelling concurrent systems; they are a generalisation of Markov processes that allow for arbitrarily distributed sojourn times. The paper presents an iterative technique for passage time and transient analysis of large structurally unrestricted semi-Markov processes. Our method is based on the calculation and subsequent numerical inversion of Laplace transforms and is amenable to a highly scalable distributed implementation. Results for a distributed voting system model with up to 1.1 million states are presented and compared against simulation.
Parallel and Distributed Processing Symposium, 2003. Proceedings. International; 05/2003
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ABSTRACT: A distributed lock manager (DLM) provides distributed applications
with a convenient means of synchronising their accesses to shared
resources. The authors present a performance study of three different
implementation strategies for a DLM, considering both the layout of the
lock database (centralised or distributed) and the strategy used to
assign lock masters (static or dynamic). For each implementation
strategy, accurate analytical models of communication cost, resource
utilisation and lock request response time are developed. The models
highlight bottlenecks in the system and show clearly for what mixes of
incoming lock request types it is best to use static or dynamic lock
master positioning. The analytical formulae are validated against a
detailed event-driven simulation which uses realistic hardware
parameters. This validation reveals a good agreement between analytical
and simulation results, particularly with respect to communication cost,
node and CPU utilisation, system capacity and the response time trend
IEE Proceedings - Computers and Digital Techniques 08/2001;
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ABSTRACT: High-level semi-Markov modelling paradigms such as semi-Markov stochastic Petri nets and process algebras are used to capture realistic performance models of computer and communication systems but often have the drawback of generating huge underlying semi-Markov processes. Extraction of performance measures such as steady-state probabilities and passage-time distributions therefore relies on sparse matrixâvector operations involving very large transition matrices. Previous studies have shown that exact state-by-state aggregation of semi-Markov processes can be applied to reduce the number of states. This can, however, lead to a dramatic increase in matrix density caused by the creation of additional transitions between remaining states. Our paper addresses this issue by presenting the concept of state space partitioning for aggregation. We present a new deterministic partitioning method which we term barrier partitioning. We show that barrier partitioning is capable of splitting very large semi-Markov models into a number of partitions such that first passage-time analysis can be performed more quickly and using up to 99% less memory than existing algorithms.
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ABSTRACT: The precision of location tracking technology has improved greatly over the last few decades. We aim to show that by tracking the locations of individuals in a closed environment, it is now possible to record the nature and frequency of interactions between them. Further, that it is possible to use such data to predict the way in which an infection will spread throughout such a population, given parameters such as transmission and recovery rates. We accordingly present a software package that is capable of recording and then replaying location data provided by a high-precision location tracking system. The software then employs a combination of SIR modelling and the epidemiological technique of contact tracing in order to predict the spread of an infection. We use this software to conduct a number of experiments using a sample data set, and compare the SIR graphs generated from these to similar graphs generated using the traditional SIR differential equations.
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ABSTRACT: Useful analytical models of storage system performance must support the characteristics exhibited by real I/O workloads. Two essential features are the ability to cater for bursty arrival streams and to support a given distribution of I/O request size. This paper develops and applies the theory of bulk arrivals in queueing networks to support these phenom-ena in models of I/O request response time in zoned disks and RAID systems, with a specific focus on RAID levels 01 and 5. We represent a single disk as an M X /G/1 queue, and a RAID system as a fork-join queueing network of M X /G/1 queues. We find the response time distribution for a ran-domly placed request within a random bulk arrival. We also use the fact that the response time of a random request with size sampled from some distribution will be the same as that of an entire batch whose size has the same distribution. In both cases, we validate our models against measurements from a zoned disk drive and a RAID platform.
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ABSTRACT: We develop an approximate generating function analysis (AGFA) technique which approximates the Laplace transform of the probability density function of customer response time in networks of queues with class-based priorities. From the approximated Laplace transform, we derive the first two moments of customer response time. This technique is applied to a model of a large hospital's Accident and Emergency department for which we obtain the mean and standard deviation of total patient service time. We experiment with different patient-handling priority schemes and compare the AGFA moments with the results from a discrete event simulation.
