Packet‐switched network design with constraints on the circuit discreteness

Abstract

AbstractThe packet‐switched network design problem can be formulated as a capacity and flow assignment problem (CFAP). The CFAP of an elementary network consisting of one tandem switch (TS) and n local switches (LSs) has been analyzed, and economical configurations shown in previous papers. This paper extends the study to include cases in which there are constraints on circuit discreteness. A large‐scale network usually employs a hierarchical structure with elementary networks used as structural units. In addition, the most economical structure of an elementary network in a hierarchical network is ascertained.The first assumption is that circuit speed is restricted to a predetermined discrete number (multiple of unit speed), and either one or no circuit can be installed per link. When the elementary network represents the entire small‐scaled network, economical regions of star, mesh and combined star/mesh are complicated. This is because effective traffic packing to a discrete capacity circuit sometimes yields more economical network configurations. When the elementary network is a structural unit in a large‐scale network, star occupies most of the economical region because a tandem circuit is always installed for carrying external traffic. The second assumption is that circuit speed is fixed. If a number of circuits can take real numbers, combined star/mesh is always the minimum cost topology in which internal traffic is assigned to the direct circuit, and external traffic through a tandem switch is assigned to the tandem circuit. When the number of circuits is a natural number, it is more economical in some cases to assign some part of the traffic to a tandem circuit because of the integrity of the number of circuits.