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          Institute: MPI für Mathematik     Collection: Export Zagier     Display Documents

ID: 744962.0, MPI für Mathematik / Export Zagier
On the capacity of disjointly shared networks
Authors:Lagarias, J.C.; Odlyzko, A.M.; Zagier, Don B.
Date of Publication (YYYY-MM-DD):1985
Title of Journal:Computer Networks and Isdn Systems
Start Page:275
End Page:285
Review Status:Internal review
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:Summary: Multi-access broadcast channels have the property that only one user can successfully transmit on the channel at a time. We consider a hypothetical channel called a disjointly shared channel in which more than one user pair can communicate simultaneously over physically disjoint parts of the channel. We consider the question of how much extra capacity such a channel has over that of a broadcast channel, as measured by the number of user pairs on the channel. The amount of extra capacity depends on the topology of the channel and the distribution of offered traffic. We analyze the problem for a particular disjointly shared channel having n users whose topology consists of k disjoint parallel cables. For an offered traffic pattern equally weighting each pair of users the capacity increases by at most a factor of three over that of k disjoint multi-access broadcast channels, i.e. on average at most 3k pairs of users will be communicating. For a specific offered traffic pattern which heavily weights connections between users close to each other the capacity is approximately α\\sb kn for a constant α\\sb k depending on the number of cables k, and it is shown that 1/4≤ α\\sb klt;1/2 with α\\sb k increasing to 1/2 as k→ ∞. The analysis for the second traffic pattern leads to a permutation enumeration problem which is solved using generating functions, continued fractions and Hermite polynomials.
External Publication Status:published
Document Type:Article
Communicated by:nn
Affiliations:MPI für Mathematik
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