Abstract
Arrivals in traffic streams with different characteristics can experience drastically different delays when offered to a common server. Such is particularly the case in computer communication networks because of the differences between data traffic types, such as batch and interactive. To analyze mean delays for this problem, an approximate approach is presented for the superposition of independent renewal processes offered to an exponential server.
The solution for the ΣGIi/M/1 queue is reduced to the solution of individual GI/M/1 queues. The approach is based on two approximations, one of which is suggested by heavy traffic limit theory. For 2 input streams, numerical results indicate that the approximation is accurate in heavy traffic and that it underestimates at lower loads. It is surprisingly accurate in some cases of lower loads. The extension to more than 2 streams is also discussed.
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© 1982 Birkhäuser Boston, Inc.
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Holtzman, J.M. (1982). Mean Delays of Individual Streams into a Queue: The ΣGIi/M/1 Queue. In: Disney, R.L., Ott, T.J. (eds) Applied Probability-Computer Science: The Interface Volume 1. Progress in Computer Science, vol 2. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5791-2_18
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DOI: https://doi.org/10.1007/978-1-4612-5791-2_18
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-5793-6
Online ISBN: 978-1-4612-5791-2
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