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# Asymptotic throughput

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### Asymptotic throughput

The asymptotic throughput (less formal asymptotic bandwidth) for a packet-mode communication network is the value of the maximum throughput function, when the incoming network load approaches infinity, either due to a message size as it approaches infinity,[1] or the number of data sources is very large. As other bit rates and data bandwidths, the asymptotic throughput is measured in bits per second (bit/s), very seldom bytes per second (B/s), where 1 B/s is 8 bit/s. Decimal prefixes are used, meaning that 1 Mbit/s is 1000000 bit/s.

Asymptotic throughput is usually estimated by sending or simulating a very large message (sequence of data packets) through the network, using a greedy source and no flow control mechanism (i.e. UDP rather than TCP), and measuring the network path throughput in the destination node. Traffic load between other sources may reduce this maximum network path throughput. Alternatively, a large number of sources and sinks may be modeled, with or without flow control, and the aggregate maximum network throughput measured (the sum of traffic reaching its destinations). In a network simulation model with infinite packet queues, the asymptotic throughput occurs when the latency (the packet queuing time) goes to infinity, while if the packet queues are limited, or the network is a multi-drop network with many sources, and collisions may occur, the packet-dropping rate approaches 100%.

A well known application of asymptotic throughput is in modeling point-to-point communication where (following Hockney) message latency T(N) is modeled as a function of message length N as T(N) = (M + N)/A where A is the asymptotic bandwdith and M is the half-peak length.[2]

As well as its use in general network modeling, asymptotic throughput is used in modeling performance on massively parallel computer systems, where system operation is highly dependent on communication overhead, as well as processor performance.[3] In these applications, asymptotic throughput is used in Xu and Hwang model (more general than Hockney's approach) which includes the number of processors, so that both the latency and the asymptotic throughput are functions of the number of processors.[4]

## References

1. ^ Modeling Message Passing Overhead by C.Y Chou et al. in Advances in Grid and Pervasive Computing: First International Conference, GPC 2006 edited by Yeh-Ching Chung and JosÃ© E. Moreira ISBN 3540338098 pages 299-307
2. ^ Recent Advances in Parallel Virtual Machine and Message Passing Interface by Jack Dongarra, Emilio Luque and Tomas Margalef 1999 ISBN 3540665498 page 134
3. ^ M. Resch et al. A comparison of MPI performance on different MPPsin Recent Advances in Parallel Virtual Machine and Message Passing Interface, Lecture Notes in Computer Science, 1997, Volume 1332/1997, 25-32
4. ^ High-Performance Computing and Networking edited by Peter Sloot, Marian Bubak and Bob Hertzberge 1998 ISBN 3540644431 page 935
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