Queue length and occupancy in discrete-time cyclic networks with several types of nodes

Authors:
Victor Pestien;S. Ramakrishnan
Affiliations:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124-4250, USA E-mail: &lcub/pestien&semi/ramakris&rcub/@cs.miami.edu;Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124-4250, USA E-mail: &lcub/pestien&semi/ramakris&rcub/@cs.miami.edu
Venue:
Queueing Systems: Theory and Applications
Year:
1999

Citing 2
Cited 2

The Time for a Round Trip in a Cycle of Exponential Queues

Journal of the ACM (JACM)
The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues

Journal of the ACM (JACM)

Monotonicity and Asymptotic Queue-Length Distribution in Discrete-Time Networks

Queueing Systems: Theory and Applications
Throughput limits from the asymptotic profile of cyclic networks with state-dependent service rates

Queueing Systems: Theory and Applications

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Abstract

For a discrete-time, closed, cyclic queueing network, where the nodes have independent, geometric service times, the equilibrium rate of local progress is determined. Faster nodes are shown to have a capacity depending only on the service probabilities. A family of such networks, each with the same number of types of nodes, is analyzed. If the number of nodes approaches infinity, and if the ratio of jobs to nodes has a positive limit and each node type has an asymptotic density, then for a given node type, the limits of the proportion of occupied nodes and the expected queue length are calculated. These values depend on the service parameter and on the asymptotic rate of local progress. The faster nodes can attain their capacity only when the limiting density of nodes of slowest type is zero.