On transient queue-size distribution in a single-machine production system with breakdowns

Wojciech M. Kempa; Iwona Paprocka; Krzysztof Kalinowski; Cezary Grabowik

doi:10.4028/www.scientific.net/AMR.1036.505

On transient queue-size distribution in a single-machine production system with breakdowns

Katedra Metod Matematycznych w Technice i Informatyce (RMS/RMS3)
Katedra Automatyzacji Procesów Technologicznych i Zintegrowanych Systemów Wytwarzania (RMT/RMT2)

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Abstrakt

An operation of a single-machine manufacturing system is modeled by an unreliable finite-buffer M/M /1/ N -type queuing system with Poisson arrivals, in which service times, failure-free times and times of repairs are totally independent and exponentially distributed random variables. Applying the idea of embedded Markov chain and the formula of total probability a system of integral equations for the transient conditional queue-size distributions of jobs present in the system at fixed time t is built. The solution of the corresponding system written for Laplace transforms is obtained in a compact form using the potential technique.

Język oryginału	angielski
Tytuł publikacji goszczącej	Modern Technologies in Industrial Engineering II
Redaktorzy	Alexander Mikhaylov, Dumitru Nedelcu, Alexei Toca, Andrzej Wrobel, Constantin Carausu, Emil Oanta
Wydawca	Trans Tech Publications Ltd.
Strony	505-510
Liczba stron	6
ISBN (elektroniczny)	9783038352556
Identyfikatory DOI	https://doi.org/10.4028/www.scientific.net/AMR.1036.505
Status publikacji	Opublikowano - 2014

Seria publikacji

Nazwa	Advanced Materials Research
Tom	1036
ISSN (drukowany)	1022-6680
ISSN (elektroniczny)	1662-8985

Cele SDG ONZ

Ten wynik przyczynia się do realizacji następujących celów zrównoważonego rozwoju

Cel 9 Przemysł, innowacje i infrastruktura

Obszary tematyczne ASJC Scopus

Inżynieria ogólna

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Cytowanie

Kempa, W. M., Paprocka, I., Kalinowski, K., & Grabowik, C. (2014). On transient queue-size distribution in a single-machine production system with breakdowns. W A. Mikhaylov, D. Nedelcu, A. Toca, A. Wrobel, C. Carausu, & E. Oanta (Red.), Modern Technologies in Industrial Engineering II (str. 505-510). (Advanced Materials Research; Tom 1036). Trans Tech Publications Ltd.. https://doi.org/10.4028/www.scientific.net/AMR.1036.505

Kempa, Wojciech M. ; Paprocka, Iwona ; Kalinowski, Krzysztof i in. / On transient queue-size distribution in a single-machine production system with breakdowns. Modern Technologies in Industrial Engineering II. redaktor / Alexander Mikhaylov ; Dumitru Nedelcu ; Alexei Toca ; Andrzej Wrobel ; Constantin Carausu ; Emil Oanta. Trans Tech Publications Ltd., 2014. str. 505-510 (Advanced Materials Research).

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title = "On transient queue-size distribution in a single-machine production system with breakdowns",

abstract = "An operation of a single-machine manufacturing system is modeled by an unreliable finite-buffer M/M /1/ N -type queuing system with Poisson arrivals, in which service times, failure-free times and times of repairs are totally independent and exponentially distributed random variables. Applying the idea of embedded Markov chain and the formula of total probability a system of integral equations for the transient conditional queue-size distributions of jobs present in the system at fixed time t is built. The solution of the corresponding system written for Laplace transforms is obtained in a compact form using the potential technique.",

keywords = "Finite-buffer queue, Machine breakdown, Markov moment, Queue-size distribution, Total probability formula",

author = "Kempa, \{Wojciech M.\} and Iwona Paprocka and Krzysztof Kalinowski and Cezary Grabowik",

note = "Publisher Copyright: {\textcopyright} (2014) Trans Tech Publications, Switzerland.",

year = "2014",

doi = "10.4028/www.scientific.net/AMR.1036.505",

language = "English",

series = "Advanced Materials Research",

publisher = "Trans Tech Publications Ltd.",

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booktitle = "Modern Technologies in Industrial Engineering II",

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}

Kempa, WM , Paprocka, I , Kalinowski, K & Grabowik, C 2014, On transient queue-size distribution in a single-machine production system with breakdowns. w A Mikhaylov, D Nedelcu, A Toca, A Wrobel, C Carausu & E Oanta (red), Modern Technologies in Industrial Engineering II. Advanced Materials Research, tom 1036, Trans Tech Publications Ltd., str. 505-510. https://doi.org/10.4028/www.scientific.net/AMR.1036.505

On transient queue-size distribution in a single-machine production system with breakdowns. / Kempa, Wojciech M.; Paprocka, Iwona ; Kalinowski, Krzysztof i in.
Modern Technologies in Industrial Engineering II. red. / Alexander Mikhaylov; Dumitru Nedelcu; Alexei Toca; Andrzej Wrobel; Constantin Carausu; Emil Oanta. Trans Tech Publications Ltd., 2014. str. 505-510 (Advanced Materials Research; Tom 1036).

Wyniki badań: Rozdział w książce/raport/materiał konferencyjny › Wkład w konferencję › recenzja

TY - GEN

T1 - On transient queue-size distribution in a single-machine production system with breakdowns

AU - Kempa, Wojciech M.

AU - Paprocka, Iwona

AU - Kalinowski, Krzysztof

AU - Grabowik, Cezary

N1 - Publisher Copyright: © (2014) Trans Tech Publications, Switzerland.

PY - 2014

Y1 - 2014

N2 - An operation of a single-machine manufacturing system is modeled by an unreliable finite-buffer M/M /1/ N -type queuing system with Poisson arrivals, in which service times, failure-free times and times of repairs are totally independent and exponentially distributed random variables. Applying the idea of embedded Markov chain and the formula of total probability a system of integral equations for the transient conditional queue-size distributions of jobs present in the system at fixed time t is built. The solution of the corresponding system written for Laplace transforms is obtained in a compact form using the potential technique.

AB - An operation of a single-machine manufacturing system is modeled by an unreliable finite-buffer M/M /1/ N -type queuing system with Poisson arrivals, in which service times, failure-free times and times of repairs are totally independent and exponentially distributed random variables. Applying the idea of embedded Markov chain and the formula of total probability a system of integral equations for the transient conditional queue-size distributions of jobs present in the system at fixed time t is built. The solution of the corresponding system written for Laplace transforms is obtained in a compact form using the potential technique.

KW - Finite-buffer queue

KW - Machine breakdown

KW - Markov moment

KW - Queue-size distribution

KW - Total probability formula

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DO - 10.4028/www.scientific.net/AMR.1036.505

M3 - Conference contribution

AN - SCOPUS:84922363434

T3 - Advanced Materials Research

SP - 505

EP - 510

BT - Modern Technologies in Industrial Engineering II

A2 - Mikhaylov, Alexander

A2 - Nedelcu, Dumitru

A2 - Toca, Alexei

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A2 - Carausu, Constantin

A2 - Oanta, Emil

PB - Trans Tech Publications Ltd.

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Kempa WM , Paprocka I , Kalinowski K , Grabowik C. On transient queue-size distribution in a single-machine production system with breakdowns. W Mikhaylov A, Nedelcu D, Toca A, Wrobel A, Carausu C, Oanta E, redaktorzy, Modern Technologies in Industrial Engineering II. Trans Tech Publications Ltd. 2014. str. 505-510. (Advanced Materials Research). doi: 10.4028/www.scientific.net/AMR.1036.505

On transient queue-size distribution in a single-machine production system with breakdowns

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Cele SDG ONZ

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