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22
A closed form solution for mapping general distributions to minimal ph distributions
 In International Conference on Performance Tools – TOOLS 2003
, 2003
"... Approximating general distributions by phasetype (PH) distributions is a popular technique in stochastic analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution, G, to a PH distribution, whi ..."
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Approximating general distributions by phasetype (PH) distributions is a popular technique in stochastic analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution, G, to a PH distribution, which matches the first three moments of G. Efficiency of our algorithm hinges on narrowing the search space to a particular subset of the PH distributions, which we refer to as EC distributions. The class of EC distributions has a small number of parameters, and we provide closedform solutions for these. Our solution applies to any distribution whose first three moments can be matched by a PH distribution. Also, our resulting EC distribution requires a nearly minimal number of phases, within one of the minimal number of phases required by any acyclic PH distribution. Key words: PH distribution, moment matching, closed form, normalized moment PACS: 1
Queueing models for appointmentdriven systems o
"... Queueing models for appointmentdriven systems ..."
An advanced queueing model to analyze appointmentdriven service systems
 Computers and Operations Research
, 2009
"... Abstract Many service systems are appointmentdriven. In such systems, customers make an appointment and join an external queue (also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility and receives service. Important measures of interest include ..."
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Abstract Many service systems are appointmentdriven. In such systems, customers make an appointment and join an external queue (also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility and receives service. Important measures of interest include the size of the waiting list as well as the time spent in the waiting list. We develop a model to assess these performance measures. The model may be used to support strategic decisions concerning server capacity (e.g. how often should a server be online, how many customers should be served during each service session,...). The model is a vacation model that uses efficient algorithms and matrix analytical techniques to obtain waiting list performance measures.
A Markov model for measuring service levels in nonstationary G(t)/G(t)/s(t) + G(t) queues
"... A Markov model for measuring service levels in nonstationary ..."
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A Markov model for measuring service levels in nonstationary
The optimal allocation of server time slots over different classes of patients
 European Journal of Operational Research
, 2012
"... Abstract We present a model for assigning server time slots to different classes of patients. The objective is to minimize the total expected weighted waiting time of a patient (where different patient classes may be assigned different weights). A bulk service queueing model is used to obtain the ..."
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Abstract We present a model for assigning server time slots to different classes of patients. The objective is to minimize the total expected weighted waiting time of a patient (where different patient classes may be assigned different weights). A bulk service queueing model is used to obtain the expected waiting time of a patient of a particular class, given a feasible allocation of service time slots. Using the output of the bulk service queueing models as the input of an optimization procedure, the optimal allocation scheme may be identified. For problems with a large number of patient classes and/or a large number of feasible allocation schemes, a stepwise heuristic is developed. A common example of such a system is the allocation of operating room time slots over different medical disciplines in a hospital.
Performance Evaluation of Scheduling Policies in Symmetric Multiprocessing Environments
"... Abstract—The shift of hardware architecture towards parallel execution led to a broad usage of multicore processors in desktop systems and in server systems. The benefit of additional processor cores for software performance depends on the software’s parallelism as well as the operating system sch ..."
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Abstract—The shift of hardware architecture towards parallel execution led to a broad usage of multicore processors in desktop systems and in server systems. The benefit of additional processor cores for software performance depends on the software’s parallelism as well as the operating system scheduler’s capabilities. Especially, the load on the available processors (or cores) strongly influences response times and throughput of software applications. Hence, a sophisticated understanding of the mutual influence of software behaviour and operating system schedulers is essential for accurate performance evaluations. Multicore systems pose new challenges for performance analysis and developers of operating systems. For example, an optimal scheduling policy for multiserver systems, such as shortest remaining processing time (SRPT) for singleserver systems, is not yet known in queueing theory. In this paper, we present a detailed experimental evaluation of general purpose operating system (GPOS) schedulers in symmetric multiprocessing (SMP) environments. In particular, we are interested in the influence of multiprocessor load balancing on software performance. Additionally, the evaluation includes effects of GPOS schedulers that can also occur in singleprocessor environments, such as I/Oboundedness of tasks and different prioritisation strategies. The results presented in this paper provide the basis for the future development of more accurate performance models of today’s software systems. I.
Adapting Hidden Markov Models for Online Learning
"... Abstract In modern computer systems, the intermittent behaviour of infrequent, additional loads affects performance. Often, representative traces of storage disks or remote servers can be scarce and obtaining real data is sometimes expensive. Therefore, stochastic models, through simulation and pro ..."
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Abstract In modern computer systems, the intermittent behaviour of infrequent, additional loads affects performance. Often, representative traces of storage disks or remote servers can be scarce and obtaining real data is sometimes expensive. Therefore, stochastic models, through simulation and profiling, provide cheaper, effective solutions, where input model parameters are obtained. A typical example is the Markovmodulated Poisson process (MMPP), which can have its time index discretised to form a hidden Markov model (HMM). These models have been successful in capturing bursty behaviour and cyclic patterns of I/O operations and Internet traffic, using underlying properties of the discrete (or continuous) Markov chain. However, learning on such models can be cumbersome in terms of complexity through retraining on data sets. Thus, we provide an online learning HMM (OnlineHMM), which is composed of two existing variations of HMMs: first, a sliding HMM using a moving average technique to update its parameters "onthefly" and, secondly, a multiinput HMM capable of training on multiple discrete traces simultaneously. The OnlineHMM reduces data processing times significantly and thence synthetic workloads become computationally more cost effective. We measure the accuracy of reproducing representative traces through comparisons of moments and autocorrelation on original data points and HMMgenerated synthetic traces. We present, analytically, the training steps saved through the OnlineHMM's adapted BaumWelch algorithm and obtain, through simulation, mean waiting times of a queueing model. Finally, we conclude our work and offer model extensions for the future.
ISSN 18744850A Survey on Performance Analysis of Warehouse Carousel Systems
, 2008
"... This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousels, give an overview of related problems in this ar ..."
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This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousels, give an overview of related problems in this area, and present an extensive literature review. Emphasis has been given on future research directions in this area.