Paper Info
Title
On the capacity of disjointly shared networks
Abstract
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 αkn for a constant αk depending on the number of cables k, and it is shown that 14 ≤ αk < 12 with αk increading to 12 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.
Year
DOI
Venue
1986
10.1016/0169-7552(85)90070-4
Computer Networks
Keywords
Field
DocType
disjointly shared network,ethernet,hermite polynomials
Generating function,Weighting,Airfield traffic pattern,Disjoint sets,Computer science,Permutation,Communication channel,Hermite polynomials,Computer network,Ethernet
Journal
Volume
Issue
ISSN
10
5
0169-7552
Citations 
PageRank 
References 
4
0.98
1
Authors
3
Name
Order
Citations
PageRank
J. C. Lagarias1563235.61
A. M. Odlyzko2414183.74
D. B. Zagier340.98