A tree-structured mean value analysis algorithm

In a recent paper, Lam and Lien described an algorithm called tree-convolution that can reduce the space and computation time required for evaluating sparse multiclass, product-form queueing networks. In this paper, we develop an exact algorithm based on mean value analysis (MVA) that is the counterpart of the tree-convolution algorithm. The order of reduction in storage and computation achieved by our new Tree-MVA algorithm compared to the standard MVA algorithm is the same order of reduction obtained by the tree-convolution algorithm over that of the standard convolution algorithm. Our Tree-MVA algorithm preserves the inherent simplicity of MVA based algorithms.

[1]  K. Mani Chandy,et al.  Computational algorithms for product form queueing networks , 1980 .

[2]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[3]  Luke Y.-C. Lien,et al.  A tree convolution algorithm for the solution of queueing networks , 1983, CACM.

[4]  K. Mani Chandy,et al.  Parametric Analysis of Queuing Networks , 1975, IBM J. Res. Dev..

[5]  Hisashi Kobayashi,et al.  Queuing Networks with Multiple Closed Chains: Theory and Computational Algorithms , 1975, IBM J. Res. Dev..

[6]  J. Little.  A Proof for the Queuing Formula: L = λW , 1961 .

[7]  K. Mani Chandy,et al.  Computer Systems Performance Modeling , 1981 .

[8]  Gianfranco Balbo,et al.  Computational aspects of aggregation in multiple class queueing networks , 1983, Perform. Evaluation.

[9]  Jeffrey P. Buzen,et al.  Computational algorithms for closed queueing networks with exponential servers , 1973, Commun. ACM.

[10]  Simon S. Lam,et al.  Dynamic Scaling and Growth Behavior of Queuing Network Normalization Constants , 1982, JACM.

[11]  John Zahorjan,et al.  The approximate solution of large queueing network models , 1980 .

[12]  S. C. Bruell,et al.  Mean value analysis of mixed, multiple class BCMP networks with load dependent service stations , 1984, Perform. Evaluation.

[13]  Charles H. Sauer,et al.  The Tree MVA Algorithm , 1985, Perform. Evaluation.

[14]  Stephen S. Lavenberg,et al.  Mean-Value Analysis of Closed Multichain Queuing Networks , 1980, JACM.