Design and management of Noncooperative Communication Networks Ariel Orda Dept. of Electrical Engineering Technion – Israel Institute of Technology

Ariel Orda, Dept. of EE, Technion2 Queuing systems (early work) [Leeman, 1964] It is a bit surprising that in a capitalist economy, applied queuing theory limits itself to recommendations of administrative measures for the reduction of queues. One might have expected to observe such an approach in a planned economy but not in an economy in which prices and markets play so large a role. [Kleinrock, 1967] Optimum Bribing for Queue Position [Naor, 1969] Queue imposes admission fee, customers join/balk. Individual decision deviates from socially preferred one. Implicit investigation of equilibrium behavior. [Adiri & Yechiali, 1974] Optimal Priority-Purchasing and Pricing Decisions in Queues

Ariel Orda, Dept. of EE, Technion3 Transportation networks (early work) Highly individualized Each driver makes their own route choices [Wardrop, 1952] Equilibrium principle: the journey time on all routes actually used are equal, and less than those … on any unused route. System Optimum principle: The average journey time is minimum. 1 st principle analogous to Nash ’ s Equilibrium [1950]: A flow pattern is a Nash equilibrium if no individual decision maker on the network can change to a less costly route. [Beckmann, McGuire, and Winsten, 1956] Existence and uniqueness of Wardrop (Nash) equilibrium through transformation [Dafermos and Sparrow, 1969,1971] Equilibration algorithms Tolls that guarantee that the user-optimized and system-optimized solutions coincide.

Ariel Orda, Dept. of EE, Technion4 Early motivation in communication networks System-wide optimization demands coordination/cooperation among components. Impractical in large-scale networks: Large size  prohibitive delays. Many components  lot of information. Variability/dynamics  frequent global changes. Heterogeneity of users  different goals. No single administration (internetworking).

Ariel Orda, Dept. of EE, Technion5 Early motivation in communication networks (cont.) Alternative Approach: Decentralized control decisions by network components (users). Each user optimizes its performance. Research methodology: Game Theory. Network operating points: Nash equilibria.

Ariel Orda, Dept. of EE, Technion6 More recent motivation in communication networks Deregulation and privatization  competitive behavior among telecom operators. Intelligence pushed to the edges of the network  possibility for intelligent yet selfish decisions. Ad hoc networks: “ hosts ” are also “ nodes/routers ”. Increased interest due to the Internet boom.

Ariel Orda, Dept. of EE, Technion7 “Architecting Noncooperative Networks” Motivation: Noncooperative equilibria are inefficient and lead to suboptimal network performance. Goal: Given the noncooperative character of network control, devise design and management rules, so that the overall network performance is improved.  Architect the operating points (Nash equilibria) so that they exhibit certain desirable properties. Methodology: Provisioning phase: network resource configuration. Run time phase: control part of the traffic, employ pricing mechanisms. a tility functions: just monotonic in the link flows. Parallel links: Nash equilibrium exists but is not unique. Dynamic convergence by best-reply moves from any initial profile. General-topology networks: Bottleneck-type cost functions: above results extended. Additive cost functions: Nash equilibrium need not exist.

Ariel Orda, Dept. of EE, Technion8 Motivation – the Braess Paradox The Braess Paradox [Braess, 1969]: Increasing capacity leads to performance degradation of all users. Observed in networks of various kinds: transportation networks [Dafermos & Nagurney, 1984] electrical circuits [Cohen & Horwitz, 1991] mechanical networks of strings and springs, hydraulic systems queuing networks (infinite population) [Cohen & Kelly, 1990] distributed computation systems [Glance & Hogg, 1995] telecommunication networks (finite population) [Korilis, Lazar & Orda, 1995; Cohen & Jeffries, 1997]

Ariel Orda, Dept. of EE, Technion9 The Braess Paradox (cont.)