Remarks to the paper "Control system for reducing energy consumption in backbone computer network" from "Concurrency and Computation: Practice and Experience" journal

The paper [1] considers a backbone computer network formed by routers labeled with r = 1, . . . , R, line cards labeled with c = 1, . . . , C, communication ports labeled with p = 1, . . . , P and directed links labeled with e = 1, . . . , E. The hierarchical representation of a router is assumed, i.e., each router is equipped with a number of line cards and each card contains a number of communication ports. All network components can operate in different energy states. Two ports connected by the same link e are in the same state k = 1, . . . ,K , which at the expense of the power consumption ξek allows for the transmission throughput Mek. Wc and Tr are fixed power cost components associated to utilizing, respectively, a card c and a router r. All demands imposed on the network are labeled with d = 1, . . . , D and characterized by the source node sd, the destination node td and a given volume Vd, ensuring end-to-end Quality of Service (QoS). The topology of the network is described by four matrices of binary indicators: lcp, grc, aep, bep, whether, respectively: port p belongs to the card c, card c belongs to the router r, link e is outgoing from the port p and link e is incoming to the port p. The decision variables are two vectors of binary indicators xc, zr whether the card c or the router r is used for data transmission and two incidence matrices with elements: yek whether the link e is in the state k and ued whether the demand d uses the link e.