Queues in series via interacting particle systems
Mathematics of Operations Research
Balancing performance and flexibility with hardware support for network architectures
ACM Transactions on Computer Systems (TOCS)
Scalability of fork/join queueing networks with blocking
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Sharpness, a tight condition for throughput scalability
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
On throughput in linear wireless networks
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Sharpness: A Tight Condition for Scalability
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
On throughput in stochastic linear loss networks
ACM SIGMETRICS Performance Evaluation Review
Semi-Markov-Based Approach for the Analysis of Open Tandem Networks with Blocking and Truncation
International Journal of Applied Mathematics and Computer Science
On the costs and benefits of stochasticity in stream processing
Proceedings of the 47th Design Automation Conference
Tandem queues with subexponential service times and finite buffers
Queueing Systems: Theory and Applications
Large number of queues in tandem: Scaling properties under back-pressure algorithm
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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Systems consisting of many queues in series have been considered by Glynn and Whitt (1991) and Baccelli, Borovkov and Mairesse (2000). We extend their results to apply to situations where the queues have finite capacity and so various types of “blocking” can occur. The models correspond to max-plus type recursions, of simple form but in infinitely many dimensions; they are related to “percolation” problems of finding paths of maximum weight through a 2-dimensional lattice with random weights at the vertices. Topics treated include: laws of large numbers for the speed of customers progressing through the system; stationary behaviour for systems with external arrival processes; a functional central limit theorem describing the behaviour of the “front of the wave” progressing through a system which starts empty; stochastic orderings for waiting times of customers at successive queues. Several open problems are noted.