A single server queue with mixed types of interruptions
Acta Informatica
Approximate Analysis of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Computers
Acyclic fork-join queuing networks
Journal of the ACM (JACM)
On the execution of parallel programs on multiprocessor systems—a queuing theory approach
Journal of the ACM (JACM)
Equivalence relations in queueing models of fork/join networks with blocking
Performance Evaluation - Queueing networks with finite capacity queues
Manufacturing flow line systems: a review of models and analytical results
Queueing Systems: Theory and Applications - Special issue on queueing models of manufacturing systems
Concepts and Notations for Concurrent Programming
ACM Computing Surveys (CSUR)
Communicating sequential processes
Communications of the ACM
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
Performance Analysis of Stochastic Timed Petri Nets Using Linear Programming Approach
IEEE Transactions on Software Engineering
A model of periodic acknowledgement
Performance Evaluation
Scalability of fork/join queueing networks with blocking
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Mathematical programming models of closed tandem queueing networks
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Queueing networks with blocking: analysis, solution algorithms and properties
Network performance engineering
IEEE/ACM Transactions on Networking (TON)
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In this paper, we study quantitative as well as qualitative properties of Fork-Join Queuing Networks with Blocking (FJQN/Bs). Specifically, we prove results regarding the equivalence of the behavior of a FJQN/B and that of its duals and a strongly connected marked graph. In addition, we obtain general conditions that must be satisfied by the service times to guarantee the existence of a long-term throughput and its independence on the initial configuration. We also establish conditions under which the reverse of a FJQN/B has the same throughput as the original network. By combining the equivalence result for duals and the reversibility result, we establish a symmetry property for the throughput of a FJQN/B. Last, we establish that the throughput is a concave function of the buffer sizes and the initial marking, provided that the service times are mutually independent random variables belonging to the class of PERT distributions that includes the Erlang distributions. This last result coupled with the symmetry property can be used to identify the initial configuration that maximizes the long-term throughput in closed series-parallel networks.