An Application of the Birth and Death Process to the Provision of Spare Machines

Taylor, Jimoh; Jackson, Rebecca L.

doi:10.1057/jors.1954.22

Cited by 46 publications

(10 citation statements)

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“…This work includes papers aimed more towards managers explaining the virtues of queue modelling in various contexts; for example, Taylor and Jackson (1954) on the provision of spare machines in the context of the airline industry; and the creation of queueing tables to overcome the practical difficulties of using some of the queueing theory results, for example, Cromie and Chaudhry (1976).…”

Section: Improving Accessibility Of Models and Resultsmentioning

confidence: 99%

Reflections on queue modelling from the last 50 years

Worthington

2009

Journal of the Operational Research Society

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Queueing theory continues to be one of the most researched areas of operational research, and has generated numerous review papers over the years. The phrase 'queue modelling' is used in the title to indicate a more practical emphasis. This paper uses work taken predominantly from the last 50 years of pages of the Operational Research Quarterly and the Journal of the Operational Research Society to offer a commentary on attempts of operational researchers to tackle real queueing problems, and on research foci past and future. A new discipline of 'queue modelling' is proposed, drawing upon the combined strengths of analytic and simulation approaches with the responsibility to derive meaningful insights for managers.

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Section: Improving Accessibility Of Models and Resultsmentioning

confidence: 99%

Reflections on queue modelling from the last 50 years

Worthington

2009

Journal of the Operational Research Society

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“…The ORQ had reached its fifth year, and the first article that attempted to extend the theoretical aspects of OR was published (Taylor and Jackson 1954). There were attempts to try to define the subject, but no agreed form of words emerged.…”

Section: Or Club and Or Society: The First Fifteen Yearsmentioning

confidence: 99%

War and Peace: The First 25 Years of or in Great Britain

Haley

2002

Operations Research

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This paper identifies a number of events and circumstances, which contributed in Great Britain during the period 1938–1963 to the development and adoption of OR outside the military and defence concerns. I show how the OR club formed a focus for industrial activity and the development of the subject. The early growth in education and training provision will also be traced to indicate its influence on the direction of OR and its acceptance as an academic discipline.

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“…Each failed machine receives time slice of permanent as well as additional removable repairmen and recovers from the faults after receiving several quantum of repair time depending on the severity of the faults/damage. Taylor and Jackson (1954) introduced the standby provisioning in machine repair system by incorporating the use of cold standbys in a machine repair system. In the past years, a lot of researches have been done on the repairable machining system with standbys by many renowned queue theoreticians (cf.…”

Section: Introductionmentioning

confidence: 99%

A time-shared machine repair problem with mixed spares under N-policy

Jain

Shekhar

Shukla³

2016

J Ind Eng Int

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The present investigation deals with a machine repair problem consisting of cold and warm standby machines. The machines are subject to breakdown and are repaired by the permanent repairman operating under N-policy. There is provision of one additional removable repairman who is called upon when the work load of failed machines crosses a certain threshold level and is removed as soon as the work load again ceases to that level. Both repairmen recover the failed machines by following the time sharing concept which means that the repairmen share their repair job simultaneously among all the failed machines that have joined the system for repair. Markovian model has been developed by considering the queue dependent rates and solved analytically using the recursive technique. Various performance indices are derived which are further used to obtain the cost function. By taking illustration, numerical simulation and sensitivity analysis have been provided.

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An Application of the Birth and Death Process to the Provision of Spare Machines

Cited by 46 publications

References 1 publication

Reflections on queue modelling from the last 50 years

Reflections on queue modelling from the last 50 years

War and Peace: The First 25 Years of or in Great Britain

A time-shared machine repair problem with mixed spares under N-policy

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