RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks

RECAL, a Recursion by Chain Algorithm for computing the mean performance measures of product-form multiple-chain closed queuing networks, is presented. It is based on a new recursive expression that relates the normalization constant of a network with r closed routing chains to those of a set of networks having (r - 1) chains. It relies on the artifice of breaking down each chain into constituent subchains that each have a population of one. The time and space requirements of the algorithm are shown to be polynomial in the number of chains. When the network contains many routing chains, the proposed algorithm is substantially more efficient than the convolution or mean value analysis algorithms. The algorithm, therefore, extends the range of queuing networks that can be analyzed efficiently by exact means.

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

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

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

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

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

[6]  K. Mani Chandy,et al.  Linearizer: a heuristic algorithm for queueing network models of computing systems , 1982, CACM.

[7]  Stephen S. Lavenberg,et al.  Computer Performance Modeling Handbook , 1983, Int. CMG Conference.

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

[9]  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.

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

[11]  A. E. Conway,et al.  A New Method For Computing The Normalization Constant Of Multiple-Chain Queueing Networks , 1986 .

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

[13]  Debasis Mitra,et al.  Asymptotic Expansions and Integral Representations of Moments of Queue Lengths in Closed Markovian Networks , 1984, JACM.

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

[15]  J. McKenna,et al.  Integral representations and asymptotic expansions for closed Markovian queueing networks: Normal usage , 1982, The Bell System Technical Journal.

[16]  Simon S. Lam,et al.  Queueing network models of packet switching networks part 2: Networks with population size constraints , 1982, Perform. Evaluation.

[17]  Journal of the Association for Computing Machinery , 1961, Nature.

[18]  Douglas Malcolm Neuse.  Approximate analysis of large and general queueing networks , 1982 .

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