Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1
- Author
- Dieter Claeys (UGent) , Joris Walraevens (UGent) , Koenraad Laevens (UGent) and Herwig Bruneel (UGent)
- Organization
- Abstract
- In this paper, we compute the probability generating functions (PGF's) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be obtained from these PGF's, through which we study and compare both systems. We pay special attention to the influence of the distribution of the arrival batch sizes. The main observation is that the difference between the two policies depends highly on this distribution. Another conclusion is that the results are considerably different as compared to Bernoulli (single) arrivals, which are frequently considered in the literature. This demonstrates the necessity of modeling the arrivals as batches.
- Keywords
- QUEUES, VACATIONS, WAITING TIME, BULK SERVICE, RULE, Batch service, Batch arrivals, Immediate versus full-batch service policy, Customer delay
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-838327
- MLA
- Claeys, Dieter, et al. “Delay Analysis of Two Batch-Service Queueing Models with Batch Arrivals: Geo(X)/Geo(c)/1.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, vol. 8, no. 3, 2010, pp. 255–69, doi:10.1007/s10288-009-0111-2.
- APA
- Claeys, D., Walraevens, J., Laevens, K., & Bruneel, H. (2010). Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, 8(3), 255–269. https://doi.org/10.1007/s10288-009-0111-2
- Chicago author-date
- Claeys, Dieter, Joris Walraevens, Koenraad Laevens, and Herwig Bruneel. 2010. “Delay Analysis of Two Batch-Service Queueing Models with Batch Arrivals: Geo(X)/Geo(c)/1.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 8 (3): 255–69. https://doi.org/10.1007/s10288-009-0111-2.
- Chicago author-date (all authors)
- Claeys, Dieter, Joris Walraevens, Koenraad Laevens, and Herwig Bruneel. 2010. “Delay Analysis of Two Batch-Service Queueing Models with Batch Arrivals: Geo(X)/Geo(c)/1.” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 8 (3): 255–269. doi:10.1007/s10288-009-0111-2.
- Vancouver
- 1.Claeys D, Walraevens J, Laevens K, Bruneel H. Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1. 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH. 2010;8(3):255–69.
- IEEE
- [1]D. Claeys, J. Walraevens, K. Laevens, and H. Bruneel, “Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1,” 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, vol. 8, no. 3, pp. 255–269, 2010.
@article{838327,
abstract = {{In this paper, we compute the probability generating functions (PGF's) of the customer delay for two batch-service queueing models with batch arrivals. In the first model, the available server starts a new service whenever the system is not empty (without waiting to fill the capacity), while the server waits until he can serve at full capacity in the second model. Moments can then be obtained from these PGF's, through which we study and compare both systems. We pay special attention to the influence of the distribution of the arrival batch sizes. The main observation is that the difference between the two policies depends highly on this distribution. Another conclusion is that the results are considerably different as compared to Bernoulli (single) arrivals, which are frequently considered in the literature. This demonstrates the necessity of modeling the arrivals as batches.}},
author = {{Claeys, Dieter and Walraevens, Joris and Laevens, Koenraad and Bruneel, Herwig}},
issn = {{1619-4500}},
journal = {{4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH}},
keywords = {{QUEUES,VACATIONS,WAITING TIME,BULK SERVICE,RULE,Batch service,Batch arrivals,Immediate versus full-batch service policy,Customer delay}},
language = {{eng}},
number = {{3}},
pages = {{255--269}},
title = {{Delay analysis of two batch-service queueing models with batch arrivals: Geo(X)/Geo(c)/1}},
url = {{http://doi.org/10.1007/s10288-009-0111-2}},
volume = {{8}},
year = {{2010}},
}
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