A burst assignment problem for satellite-switched time-division multiple access networks is generalized to distinguish traffic requirements of earth stations in a network. This distinction leads to shorter transmission time in general. The satellite provides coverage for u uplink spotbeams and v downlink spotbeams with prescribed limits on the maximum number of available carriers in each spotbeam, subject to a total of K carriers in use at any one time. Earth stations are equipped for simultaneous transmission on and reception of multiple carriers. If u + v is O(K), the number of switching modes required is O(K-2) and a transmission-time optimal schedule can be found in O(K-4) time. Technology considerations are discussed.

102. Tham, Yiu-Kwok

Generalized satellite beam-switching modes1997In: IEICE transactions on communications, ISSN 0916-8516, E-ISSN 1745-1345, Vol. E80-B(10), p. 1523-1528Article in journal (Refereed)

Abstract [en]

Satellite beam-switching problems are studied where there are m up-link beams, n down-link beams and multiple carriers per beam. By augmenting a traffic matrix with an extra row and column, it is possible to find a sequence of switching modes ((0, 1)-matrices with generally multiple unit entries in each row and column) that realize optimal transmission time. Switching modes generated are shown to be linearly independent. The number of switching modes required for an m x n matrix is bounded by (m - 1)(n - 1) + 1. For an augmented (m + 1) x (n + 1) matrix, the bound is then mn + 1. The bounds on the number of switching modes and the computational complexity for a number of related satellite transmission scheduling problems are lowered. In simplified form, the results (particularly the linear independence of permutation matrices generated) apply to algorithmic decomposition of doubly stochastic matrices into convex combinations of permutation matrices.

The asymmetrical multiconnection three-stage rearrangeable Clos network is considered, where, in general, many-to-many connections are allowed between input and output terminals. The problem of routing the connections over the switches is efficiently solved. The computational complexity is improved from O(mf(3)) to O(f(4)) using a network flow model for the routing problem, where f is the number of first-stage switches and m is the number of second-stage switches; the number of third-stage switches is assumed to be of the same order as f. Note that the O(f(4)) complexity is independent of the number of second-stage switches. Using an appropriate data structure, the computational complexity of an edge-coloring approach to the routing problem is lowered from O(mK(2)) to O(m(f(2) + K log K)), where K is the aggregate capacity of the interconnecting links between all first-stage switches and a second-stage switch; the aggregate capacity of the interconnecting links between a second-stage switch and all third-stage switches is assumed to be of the same order as K. This makes the edge-coloring approach competitive for small values of m and K. (C) 1998 John Wiley & Sons, Inc.

Virtual paths facilitate the rapid movement of end-to-end traffic streams in an ATM network by keeping processing at intermediate nodes en route to the minimum. There may exist, however, some virtual paths in an ATM network with low volumes of traffic on them. Balancing between efficient utilization of transmission resources en route and keeping intermediate switching to the minimum, lightly loaded virtual paths are decomposed into at most two logical hops, which require only one intermediate switching for an end-to-end traffic stream. The decomposition procedure and data structure for efficient implementation are described. For a twenty-node network with between three and four hundred virtual paths, experimental results show that the average number of lightly loaded virtual paths that cannot be decomposed by our procedure is about 6.5. Work in progress and future work lie in simulating network performance and investigating improved network dimensioning techniques for direct and two-hop routes in ATM networks.

The paper deals with inclusion relations between s(p) and H-s(p). Here s(p) is the set of all a is an element ofJ such that the Weyl operator a(w) (x, D) is a Schatten-von Neumann operator on L-2 to the order p is an element of [1, infinity], and H-s(p) is the Sobolev space of distributions with s derivatives in L-p. At the same time we compute the trace norm for a(w) (x, D), when a is an arbitrary Gauss function.