Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
A Generalized Queueing Discipline for Product Form Network Solutions
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
A Characterization of Product-Form Queuing Networks
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Mean Value Analysis fo Queueing Networks - A New Look at an Old Problem
Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems: Performance of Computer Systems
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Interconnection networks with heterogeneous activity or finite buffers: beyond Jackson's theorem
Proceedings of the 11th communications and networking simulation symposium
Multiprocessor networks with small buffers: theory and simulation
SpringSim '09 Proceedings of the 2009 Spring Simulation Multiconference
Latency and saturation in networks with finite buffers
Proceedings of the 14th Communications and Networking Symposium
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A multiprocessor networks modeled as a ring and as a 2- dimensional toroidal square lattice of nodes are considered. Each node has 2 or, respectively, 4 output buffers of infinite capacity and a local processor that generates messages with probability λ per clock cycle per output port. Once a buffer is not empty, the corresponding output port sends out exactly one message every clock cycle. We derive explicit analytical expressions for the queue length distribution, the average number of messages in buffers, and the latency (average delay). It is shown that the network experiences a phase transition from equilibrium to the saturation regime, and the critical exponent is equal to 1. The critical network load is found and shown to be inversely proportional to the distance between the source and destination. Empirical results obtained by extensive simulations demonstrate an excellent agreement with theoretical predictions and validate the assumption of independent queues.