Chair of Computer Networks and Computer Communications
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Publication database

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2014

Journal articles:

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Tien V. Do, Patrick Wuechner, Tamas Berczes, Janos Sztrik and Hermann De Meer
A New Finite-source Queueing Model for Mobile Cellular Networks Applying Spectrum Renting
Asia Pacific Journal of Operational Research (APJOR), 31(2):1440004:1-19
2014

Keywords: Mobile cellular networks; Retrial queues; Finite-source; Impatience; Spectrum renting; Discount factor

Tags: MOSEL2, Socionical, EINS_NoE

Abstract: This paper proposes a retrial queueing model with the finite number of sources to evaluate the performance of spectrum renting in mobile cellular networks. The model incorporates necessary ingredients such as the finite number of subscribers, their impatience and a queue for the outbound service. To consider the specific feature of spectrum renting and the current mobile cellular technology, a variable number of servers that are switched on and off in groups is introduced. We present a novel way to take into account the renting fee, which can be used to fine-tune the operation of the spectrum renting procedure. Numerical results show that it is still profitable to initiate a spectrum renting request at high loads, even if no discount is offered by the frequency bands? owners.

Note: (c) World Scientific Publishing Co. & Operational Research Society of Singapore

2011

Conference and workshop papers:

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Patrick Wuechner, Janos Sztrik and Hermann De Meer
Modeling Wireless Sensor Networks Using Finite-Source Retrial Queues with Unreliable Orbit
Proc. of the Workshop on Performance Evaluation of Computer and Communication Systems (PERFORM 2010) Volume 6821 of Lecture Notes in Computer Science (LNCS) , page 73--86.
Publisher: Springer-Verlag,
2011

Keywords: Performance evaluation; Unreliable finite-source retrial queue; Wireless sensor network; Energy efficiency; Self-organization

Tags: DFG_MathMod, AutoI, ResumeNet, EuroNF, EuroNF_PADU, MOSEL2

Abstract: Motivated by the need for performance models suitable for modeling and evaluation of wireless sensor networks, we introduce a retrial queueing system with a finite number of homogeneous sources, unreliable servers, orbital search, and unreliable orbit. All random variables involved in model construction are assumed to be independent and exponentially distributed. Providing a generalized stochastic Petri net model of the system, steady-state analysis of the underlying continuous-time Markov chain is performed and steady-state performance measures are computed by the help of the MOSEL-2 tool. The main novelty of this investigation is the introduction of an unreliable orbit and its application to wireless sensor networks. Numerical examples are derived to show the influence of sleep/awake time ratio, message dropping, and message blocking on the senor nodes' performance.

Note: The original publication is available at www.springerlink.com

2010

Conference and workshop papers:

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Patrick Wuechner, Janos Sztrik and Hermann De Meer
Finite-Source Retrial Queues with Applications
Proc. of the 8th Int'l Conf. on Applied Informatics Volume 2 , page 275--285.
2010

Keywords: Retrial queueing systems; Finite number of sources; Orbital search; Performance tool; Performance measures; Hypoexponential distribution; Generalized exponential distribution

Tags: EuroNF, Socionical, ResumeNet, DFG_MathMod

Abstract: We consider a single-server retrial queueing system with a finite number of homogeneous sources generating requests after a random time. The service of an arriving customer finding the server idle starts immediately; otherwise the request enters into an orbit from where the calls are repeated after a random time. Upon completion of a service, with a certain probability the server searches for an orbiting customer. We assume the search time to be negligible. While modeling generation, retrial, and service times by their first two moments, we are interested in steady-state performance measures. The novelty of the investigation is the discussion of the second moment's effect on the performance of finite-source retrial queues with orbital search. The MOSEL-2 tool is used to formulate and solve the problem resulting in various illustrative numerical examples showing the effect of the moments and the search probability on the mean response time of the requests.

2009

Journal articles:

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Patrick Wuechner, Janos Sztrik and Hermann De Meer
Finite-source M/M/S retrial queue with search for balking and impatient customers from the orbit
Computer Networks (ComNet), 53(8):1264--1273
2009

Keywords: Performance modeling; Finite-source retrial queues; Orbital search; Balking customers; Impatient customers; MOSEL-2

Tags: AutoI, DFG_MathMod, EuroNF, ResumeNet, MOSEL2

Abstract: The present paper deals with a generalization of the homogeneous multi-server finite-source retrial queue with search for customers in the orbit. The novelty of the investigation is the introduction of balking and impatience for requests who arrive at the service facility with a limited capacity and FIFO queue. Arriving customers may balk, i.e., they either join the queue or go to the orbit. Moreover, the requests are impatient and abandon the buffer after a random time and enter the orbit, too. In case of an empty buffer, each server searches for a customer in the orbit after finishing service. All random variables involved in the model construction are supposed to be exponentially distributed and independent of each other. The primary aim of this analysis is to show the effect of balking, impatience, and buffer size on the steady-state performance measures. Concentrating on the mean response time, several numerical examples are investigated by the help of the MOSEL-2 tool used for creating the model and calculating the stationary characteristics.

Note: Performance of Computer Networks: Special Issue in Memory of Dr. Gunter Bolch.

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Patrick Wuechner, Janos Sztrik and Hermann De Meer
Investigating the mean response time in finite-source retrial queues using the algorithm by Gaver, Jacobs, and Latouche
Annales Mathematicae et Informaticae (AMI), 36:143--160
2009
ISSN: 1787-5021 (Print); 1787-6117 (Online)

Keywords: Performance evaluation; Finite-source retrial queues; Closed-form solutions; Orbital search; Block-structured Markov chain; MOSEL-2

Tags: AutoI, DFG_MathMod, EuroNF, ResumeNet, MOSEL2

Abstract: In this paper, we discuss the maximum of the mean response time that appears in finite-source retrial queues with orbital search when the arrival rate is varied. We show that explicit closed-form equations of the mean response time can be derived by exploiting the block-structure of the finite Markov chain underlying the model and using an efficient computational algorithm proposedby Gaver, Jacobs, and Latouche. However, we also show that already for the discussed relatively simple model, the resulting equation is rather complex which hampers further evaluation.

2008

Journal articles:

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Matthias Hollick, Hermann De Meer, Jens B. Schmitt and Patrick Wuechner
Modeling of Self-Organizing Systems (Guest Editorial)
Praxis der Informationsverarbeitung und Kommunikation (PIK), 31(1):2--3
2008
ISSN: 0930-5157

Tags: DFG_MathMod, EuroNF, EuroFGI, EuroFGI_MMSOS

Abstract: In the last decade, we witnessed the unparalleled success of communication networks such as the Internet or wireless mobile communication networks. The unprecedented scale of the aforementioned networks does not mark the end of the growth, but the emergence of wireless sensor networks and the ,,Internet of Things" are going to further add to the complexity of today's communication networks. For providers and network operators to be able to plan, build, and maintain next generation networks, it is necessary to push the envelope of traditional means to control the network. From a user's perspective, the organic growth of autonomously operated (community) networks and of application-level overlay networks presents further challenges.

Note: Editorial

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Patrick Wuechner, Janos Sztrik and Hermann De Meer
The Impact of Retrials on the Performance of Self-Organizing Systems
Praxis der Informationsverarbeitung und Kommunikation (PIK), 31(1):29--33
2008
ISSN: 0930-5157

Tags: AutoI, DFG_MathMod, EuroFGI, EuroFGI_MMSOS, EuroNF, ResumeNet, MOSEL2

Abstract: This article describes the application of the theory of retrial queues in capturing certain aspects of self-organizing behavior that arises, for example, in Peer-to-Peer networks. It can be shown that retrials have a fair effect on the performance of such self-organizing systems, and thus, should be taken into account adequately during the design and evaluation of these systems. Moreover, it can be shown that there is a notable difference between finite-source and infinite-source retrial queueing models. The main goal of this paper is to show the practical applicability of retrial queues and some of their varieties.

Conference and workshop papers:

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Patrick Wuechner, Janos Sztrik and Hermann De Meer
Homogeneous Finite-Source Retrial Queues with Search of Customers from the Orbit
Proc. of the 14th GI/ITG Conf. on Measurement, Modelling and Evaluation of Computer and Communication Systems (MMB 2008) , page 109--124.
Publisher: VDE Verlag,
2008
ISBN: 978-3-8007-3090-2

Keywords: Retrial queueing systems; Finite number of sources; Orbital search; Performance tool; Performance measures

Tags: DFG_MathMod, EuroNF, MOSEL2

Abstract: We consider a retrial queueing system with a finite number of homogeneous sources of calls and a single server. Each source generates a request after an exponentially distributed time. An arriving customer finding the server idle enters into service immediately; otherwise the customer enters into an orbit. The service times are supposed to be exponentially distributed random variables. An orbiting customer competes for service, the inter-retrial times are exponentially distributed. Upon completion of a service, with a certain probability the server searches for an orbiting customer. Assuming the search time to be negligible, the source, service, and retrial times to be independent random variables, we perform the steady-state analysis of the model computing various steady-state performance measures and illustrative numerical examples are presented. The novelty of the investigation is the introduction of orbital search by the server for customers in finite-source retrial queues. The MOSEL-2 tool is used to formulate and solve the problem.

2007

Conference and workshop papers:

pdf
Patrick Wuechner, Hermann De Meer, Gunter Bolch, Janos Roszik and Janos Sztrik
Modeling Finite-Source Retrial Queueing Systems with Unreliable Heterogeneous Servers and Different Service Policies Using MOSEL
In Khalid Al-Begain, Armin Heindl and Miklos Telek, editor, Proc. of the 14th Int'l Conf. on Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2007) , page 75--80.
2007
ISBN: 0-9553018-4-X (Print); 0-9553018-3-1 (CD)

Keywords: Performance and Reliability Evaluation; Retrial Queuing System Model; Unreliable Heterogeneous Servers

Tags: DFG_MathMod, EuroFGI, MOSEL2

Abstract: This paper deals with the performance analysis of multiple server retrial queueing systems with a finite number of homogeneous sources of calls, where the heterogeneous servers are subject to random breakdowns and repairs. The requests are serviced according to Random Selection and Fastest Free Server disciplines. The novelty of this investigation is the introduction of different service rates and different service policies together with the unreliability of the servers, which has essential influence on the performance of the system, and thus, it plays an important role in practical modeling of computer and communication systems. All random variables involved in the model construction are assumed to be exponentially distributed and independent of each other. The main steady-state performability measures are derived, and several numerical calculations are carried out by the help of the MOSEL tool (Modeling, Specification and Evaluation Language) under different service disciplines. The numerical results are graphically displayed to illustrate the effect of failure rates on the mean response time and on the overall system utilization.

pdf
Patrick Wuechner, Janos Sztrik and Hermann De Meer
Structured Markov Chains Arising from Homogeneous Finite-Source Retrial Queues with Orbital Search
In Dario Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche and Peter Taylor, editor, Proc. of the Dagstuhl Seminar on Numerical Methods for Structured Markov Chains Volume 07461 of Dagstuhl Seminar Proceedings
Publisher: Schloss Dagstuhl, Leibniz-Zentrum fuer Informatik GmbH, Dagstuhl, Germany
2007

Tags: DFG_MathMod, EuroFGI, EuroFGI_MMSOS, MOSEL2

Abstract: We consider retrial queueing systems with a finite number of homogeneous sources of calls, a single reliable server, and the search for orbiting customers by the server after job completion. During this investigation, the infinitesimal generator of the underlying (finite) continuous-time Markov chain takes a (level-dependent) QBD-like form. After solving for the steady state probabilities using the MOSEL-2 tool, the results show a surprising maximum of the mean response time. This maximum was already discovered by other researchers dealing with finite-source retrial queues. However, to our best knowledge, no thorough investigation was done yet why this maximum exists and in which way it depends on the system parameters. In the talk, after introducing the backgrounds of finite-source retrial queues with orbital search, a generalized stochastic Petri net is used to derive the underlying continuous-time Markov chain and its generator. Finally, using the seminar, we can hopefully bring forward discussions how to make more general statements on the parameter-dependent behavior of the response time's maximum.

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