Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism

G.J.J.A.N. Houtum, van; I.J.B.F. Adan; J. Wessels; W.H.M. Zijm

doi:10.1007/3-540-29057-5_12

Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism

G.J.J.A.N. Houtum, van, I.J.B.F. Adan, J. Wessels, W.H.M. Zijm

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Abstract

In this paper we study a production system consisting of a group of parallel machines producing multiple job types. Each machine has its own queue and it can process a restricted set of job types only. On arrival a job joins the shortest queue among all queues capable of serving that job. Under the assumption of Poisson arrivals and identical exponential processing times we derive upper and lower bounds for the mean waiting time. These bounds are obtained from so-called flexible bound models, and they provide a powerful tool to efficiently determine the mean waiting time. The bounds are used to study how the mean waiting time depends on the amount of overlap (i.e. common job types) between the machines.

Original language	English
Title of host publication	Stochastic Modeling of Manufacturing Systems
Editors	G. Liberopoulos, C.T. Papadopoulos, B. Tan, J. MacGregor Smith, S.B. Gershwin
Place of Publication	Berlin
Publisher	Springer
Pages	289-305
ISBN (Print)	3-540-26579-1
DOIs	https://doi.org/10.1007/3-540-29057-5_12
Publication status	Published - 2006

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Houtum, van, G. J. J. A. N., Adan, I. J. B. F., Wessels, J., & Zijm, W. H. M. (2006). Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism. In G. Liberopoulos, C. T. Papadopoulos, B. Tan, J. MacGregor Smith, & S. B. Gershwin (Eds.), Stochastic Modeling of Manufacturing Systems (pp. 289-305). Springer. https://doi.org/10.1007/3-540-29057-5_12

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abstract = "In this paper we study a production system consisting of a group of parallel machines producing multiple job types. Each machine has its own queue and it can process a restricted set of job types only. On arrival a job joins the shortest queue among all queues capable of serving that job. Under the assumption of Poisson arrivals and identical exponential processing times we derive upper and lower bounds for the mean waiting time. These bounds are obtained from so-called flexible bound models, and they provide a powerful tool to efficiently determine the mean waiting time. The bounds are used to study how the mean waiting time depends on the amount of overlap (i.e. common job types) between the machines.",

author = "{Houtum, van}, G.J.J.A.N. and I.J.B.F. Adan and J. Wessels and W.H.M. Zijm",

year = "2006",

doi = "10.1007/3-540-29057-5_12",

language = "English",

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pages = "289--305",

editor = "G. Liberopoulos and C.T. Papadopoulos and B. Tan and {MacGregor Smith}, J. and S.B. Gershwin",

booktitle = "Stochastic Modeling of Manufacturing Systems",

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address = "Germany",

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Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism. / Houtum, van, G.J.J.A.N.; Adan, I.J.B.F.; Wessels, J. et al.

Stochastic Modeling of Manufacturing Systems. ed. / G. Liberopoulos; C.T. Papadopoulos; B. Tan; J. MacGregor Smith; S.B. Gershwin. Berlin : Springer, 2006. p. 289-305.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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AB - In this paper we study a production system consisting of a group of parallel machines producing multiple job types. Each machine has its own queue and it can process a restricted set of job types only. On arrival a job joins the shortest queue among all queues capable of serving that job. Under the assumption of Poisson arrivals and identical exponential processing times we derive upper and lower bounds for the mean waiting time. These bounds are obtained from so-called flexible bound models, and they provide a powerful tool to efficiently determine the mean waiting time. The bounds are used to study how the mean waiting time depends on the amount of overlap (i.e. common job types) between the machines.

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Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism

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