Mean value analysis of mixed, multiple class BCMP networks with load dependent service stations

Abstract In this paper we describe a mean value analysis algorithm to solve product form queueing network models of the Baskett, Chandy, Muntz, and Palacios type (BCMP) [5]. These networks can accommodate multiple job classes and load dependent service stations. The networks can be closed (i.e., jobs neither enter nor leave the network), open (i.e., jobs can enter and leave the network), or mixed (i.e., closed with respect to some job classes and open with respect to others). Two major aspects of this paper are: 1. (1)to present a unified approach to the solution of this class of BCMP queueing networks [5], and 2. (2)to thereby extend and consolidate the results of the work of several authors (Balbo, Bruell and Schwetman (1977), Bruell and Balbo (1980), Chandy and Sauer (1980), Krzesinki, Teunissen and Kritzinger (1981), Resier and Kobayashi (1975), Reiser and Lavenberg (1980), Reiser (1981), Sauer (1983), Schwetman (1980), Tucci and MacNair (1982) and Zahorjan and Wong (1981)). The paper concludes by collecting together all the results into an explicit algorithm, MVALDMX (for mean value analysis load dependent mixed) that is a generalization of the original MVA algorithm of Reiser and Lavenberg (1978, 1980).

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

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

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

[4]  Eugene Wong,et al.  The solution of separable queueing network models using mean value analysis , 1981, SIGMETRICS '81.

[5]  Gianfranco Balbo,et al.  Computational algorithms for closed queueing networks , 1980 .

[6]  Isi Mitrani,et al.  The Distribution of Queuing Network States at Input and Output Instants , 1979, JACM.

[7]  Peter J. Denning,et al.  Operational Treatment of Queue Distribution and Mean Value Analysis , 1979 .

[8]  Steven C. Bruell,et al.  On the Load Balancing Bus Accessing Scheme , 1983, IEEE Transactions on Computers.

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

[10]  Herb Schwetman,et al.  Customer Classes and Closed Network Models-A Solution Technique , 1977, IFIP Congress.

[11]  S. C. Bruell,et al.  On single and multiple job class queueing network models of computer systems. , 1978 .

[12]  Martin Reiser,et al.  Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks , 1981, Perform. Evaluation.

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

[14]  Leonard Kleinrock,et al.  Queueing Systems - Vol. 1: Theory , 1975 .

[15]  Herb Schwetman,et al.  Implementing the Mean Value Algorithm for the Solution of Queueing Network Models , 1980 .

[16]  Charles H. Sauer,et al.  Computational algorithms for state-dependent queueing networks , 1983, TOCS.

[17]  Johnny Wai-Nang Wong,et al.  Queueing network models for computer systems. , 1975 .

[18]  Stephen S. Lavenberg,et al.  Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers , 1980, Journal of Applied Probability.

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

[20]  Jeffrey P. Buzen,et al.  Queueing Network Models of Multiprogramming , 1971, Outstanding Dissertations in the Computer Sciences.

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

[22]  W. J. Gordon,et al.  Closed Queuing Systems with Exponential Servers , 1967, Oper. Res..

[23]  L. Schrage,et al.  Queueing systems, Vol. I: Theory , 1977, Proceedings of the IEEE.

[24]  Jeffrey R. Spirn.  Queuing Networks with Random Selection for Service , 1979, IEEE Transactions on Software Engineering.