Optimal allocation of buffers and customers in a two-node cyclic network with multiple servers
Pages 19 - 24
Abstract
Suppose there are a fixed number of waiting positions which need to be allocated between two nodes in a closed, two-node, cyclic, queueing network with multiple servers in order to maximize throughput. We determine the optimal allocation under quite general assumptions about the service times. For example, under production blocking, the optimal allocation is to split the waiting positions as equally as possible between the two nodes without regard to the number of servers at each node. We also determine the optimal number of customers circulating in the network, which depends on both the total number of servers in the system and how the waiting spaces are allocated between the two servers.
References
[1]
I.F. Akyildiz, General closed queueing networks with blocking, in: P.J. Courtois, Latouche (Eds.), Performance '87; Elsevier, North-Holland, Amsterdam, 1988, pp. 283-303.
[2]
P.P. Bocharov, On two-node queueing networks with finite capacity, Proceedings of the First International Workshop on Queueing Networks with Blocking, North Carolina State University, USA, 1988, pp. 239-257.
[3]
Boxma, O.J., The cyclic queue with one general and one exponential server. Adv. Appl. Probab. v15. 857-873.
[4]
Bozer, Y.A. and White, J.A., A generalized design and performance analysis model for end-of-aisle order-picking systems. IIE Trans. v28. 271-280.
[5]
Gaver, D.P. and Shelder, G.S., Processor utilization in multiprogramming systems via diffusion approximation. Oper. Res. v21. 569-576.
[6]
Gelenbe, E., On approximate computer system models. J. Assoc. Comput. Mach. v22. 261-269.
[7]
Monotonicity in generalized semi-Markov processes. Math. Oper. Res. v17. 1-21.
[8]
Glasserman, P. and Yao, D.D., . 1994. Wiley, New York.
[9]
Glasserman, P. and Yao, D.D., Structured buffer-allocation problems. Discrete Event Dyn. Systems: Theory Appl. v6. 9-41.
[10]
Gordon, W.J. and Newell, G.F., Cyclic queueing system with restricted length queues. Oper. Res. v15. 266-277.
[11]
The steady-state queueing time distribution for the M/G/1 finite capacity queue. Manager. Sci. v21. 501-506.
[12]
Onvural, R.O. and Perros, H.G., On equivalencies of blocking mechanisms in queueing networks with blocking. Oper. Res. Lett. v5. 293-298.
[13]
B.C. Park, E.H. Frazelle, J.A. White, Buffer sizing models for end-of-aisle order picking systems, IIE Trans. 31 (1999) 31-38.
[14]
Rajan, R. and Agrawal, R., Cyclic networks with general blocking and starvation. Queueing Systems Theory Appl. v15. 99-136.
[15]
Sauer, C.H. and Chandy, K.M., Approximate analysis of central server models. IBM J. Res. Develop. v19. 301-313.
[16]
Optimal server allocations in a system of multi-server stations. Manager. Sci. v33. 1173-1180.
[17]
Shanthikumar, J.G. and Yao, D.D., Monotonicity and concavity properties in cyclic queueing networks with finite buffers. In: Perros, H.G., Altiok, T. (Eds.), Queueing Networks with Blocking, Elsevier, North-Holland, Amsterdam. pp. 325-344.
[18]
Comparing multi-server queues with finite waiting rooms, I: same number of servers. Adv. Appl. Probab. v11. 439-447.
[19]
Sparaggis, P.D. and Gong, W., Optimal buffer allocation in a two-stage queueing system. J. Appl. Probab. v30. 478-482.
- Optimal allocation of buffers and customers in a two-node cyclic network with multiple servers
Recommendations
On the optimal assignment of servers in a two stations tandem queue with no intermediate waiting room
A tandem queueing system with two stations and no intermediate storage between them, is considered. The paper studies the optimal assignment of the slower and the faster servers to the two stations in order to stochastically minimize the departure times ...
A Large Closed Queueing Network Containing Two Types of Node and Multiple Customer Classes: One Bottleneck Station
The paper studies a closed queueing network containing two types of node. The first type (server station) is an infinite server queueing system, and the second type (client station) is a single server queueing system with autonomous service, i.e. every ...
Optimal Dynamic Assignment of Customers to Heterogeneous Servers in Parallel
The system under consideration comprises two classes of customers to be served by two stations, with parallel servers in each station. While class-1 customers can only receive service from station 1, class-2 customers can be served by either station. ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Copyright © Elsevier Science B.V. © 2002.
Publisher
Elsevier Science Publishers B. V.
Netherlands
Publication History
Published: 01 February 2002
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 27 Feb 2025