- Email: [email protected]
A decentralized closed-loop solution to the routing problem in networks
A decentralized closed-loop solution to the routing problem in networks
H.Aicardi, G.Casalino, F.Davoli, R.Hinciardi, R.Zoppoli Dipartimento di Informatica, Sistemistica e Telematica Universita' di Genova, Via Opera Pia 11 A, 16145 Genova, Italy
Several approaches have been attempted in the literature dealing with the problem of designing a routing protocol in a packet-switched computer communication network. However, most of the literature considers the problem only from a static optimization viewpoint, that is, it aims at determining routing policies where deCISIons are preordered and are not functions of the current state of the network. On the other hand, a control theoretic viewpoint would imply the determination of routing decisions at each control instant on the basis of a state feedback law (dynamic routing), and would be more responsive to variations in the network state. The first significant results in this direction are gIven by Moss and Segall, who Introduced a state space model and developed a closedloop optimal policy. The main characteristics of this approach are the following: i) a continuous-time linear time-invariant model of the network; ii) the practical lack of consideration of stochastic events; iii) the centralized nature of the solution. The third point represents a serIOUS drawback for the practical implementation in a data network, requiring control information about the network state to traverse the network at a velocity much higher than that of proper message information. A decentralized control strategy, where the routing decisions are determined, at each instant, on the baSIS of local information at each node (with a moderate information exchange among nodes). seems to bP more attractive in this respect. Th~ approach of this paper defInes a decentralized control problem. On the baSIS of suitable assumptIons on exchange mechanism among the varIOUS deCISIon makers nodes the Information structure of the team is found
stochastic team the InformatIon located at the to be partIally
nested; this fact allows the reduction of the dynamic team problem to a static one. The optimal control strategies are determined in a tabular form vi a the sol utI on of a 1 i near integer programming probI em, whose complexity increases with the control hOClzon . Some poSSIbilities are explored in order to reduce the computational complexity of the whole procedure: i) applicatIon of a receding horizon control scheme; ii) "partial" SOlutIon of the integer programming probIell\; iii) analYSIS of the conditions under whIch the optimal solution of the lInear relaxed problem can be shown to be itself Integer .
255
H.Aicardi, G.Casalino, F.Davoli, R.Hinciardi, R.Zoppoli Dipartimento di Informatica, Sistemistica e Telematica Universita' di Genova, Via Opera Pia 11 A, 16145 Genova, Italy
Several approaches have been attempted in the literature dealing with the problem of designing a routing protocol in a packet-switched computer communication network. However, most of the literature considers the problem only from a static optimization viewpoint, that is, it aims at determining routing policies where deCISIons are preordered and are not functions of the current state of the network. On the other hand, a control theoretic viewpoint would imply the determination of routing decisions at each control instant on the basis of a state feedback law (dynamic routing), and would be more responsive to variations in the network state. The first significant results in this direction are gIven by Moss and Segall, who Introduced a state space model and developed a closedloop optimal policy. The main characteristics of this approach are the following: i) a continuous-time linear time-invariant model of the network; ii) the practical lack of consideration of stochastic events; iii) the centralized nature of the solution. The third point represents a serIOUS drawback for the practical implementation in a data network, requiring control information about the network state to traverse the network at a velocity much higher than that of proper message information. A decentralized control strategy, where the routing decisions are determined, at each instant, on the baSIS of local information at each node (with a moderate information exchange among nodes). seems to bP more attractive in this respect. Th~ approach of this paper defInes a decentralized control problem. On the baSIS of suitable assumptIons on exchange mechanism among the varIOUS deCISIon makers nodes the Information structure of the team is found
stochastic team the InformatIon located at the to be partIally
nested; this fact allows the reduction of the dynamic team problem to a static one. The optimal control strategies are determined in a tabular form vi a the sol utI on of a 1 i near integer programming probI em, whose complexity increases with the control hOClzon . Some poSSIbilities are explored in order to reduce the computational complexity of the whole procedure: i) applicatIon of a receding horizon control scheme; ii) "partial" SOlutIon of the integer programming probIell\; iii) analYSIS of the conditions under whIch the optimal solution of the lInear relaxed problem can be shown to be itself Integer .
255