Revisiting the notion of Origin-Destination Traffic Matrix of the Hosts that are attached to a Switched Local Area Network

Abstract

There is a widely held notion in the literature that there is an origin-destination traffic matrix for all the hosts (end nodes) that are attached to any switched local area network. This is usually in relation to the need to calculate the end-to-end (or maximum end-to-end) delays between all the end nodes that are attached to the network, for the sole purpose of using these delays values to design upper-bounded delay switched local area networks, in efforts at solving the delay problems of this class of networks. In this paper, we show that this notion of origin-destination traffic matrix for all the hosts that are attached to a switched local area network does not seem to be correct.

Switched Local Area network bit-carrying capacity determination

“…Fig. 1 has been drawn with attached hosts excluded from the drawing; this is in accordance with the fact that, the number of end-to-end delays in a switched LAN is only dependent on the number of switches in the LAN as was shown in [6]. It is noted, also, that, a router is a switching device, which, in the context of the switched LAN, will be taken as one of the switches.…”

“…It was shown in [6] that the end-to-end delays of any switched LAN should not be enumerated with respect to the user hosts that are attached to the LAN, but that, the enumeration should be carried out with respect to the nodes (switches) of which the LAN is composed. How to carry out this enumeration was shown in [7]; while in [8], a generic maximum delay model of a packet switch, which, can be used to calculate all the maximum end-to-end delays of any switched LAN was reported.…”

“…(6) Or, M × λ = C. Obviously, the capacity of the network is the sum of the capacities of all the origin-destination paths of which the network consists. Denote the capacity of a switched LAN with n switches by C n , then, C n =C 11 +C 12 + +C 1n +C 21 + +C 2n + +C n−11 + +C n−1n +C n1 + +C nn−1 +C nn ( 7 ) Assume that a hypothetical switched LAN has 3 switches; Eq.…”