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Topology is the term borrowed from geometry. Network topology is a network shape, or its physical connectivity. Constitutes the topology of the network there are many. Network topology is the interconnection with the transmission media, the physical layout of equipment, that is, in what way to network computers and other devices connected. Topology given network servers, workstations, network configuration and the inter-connection, the structure of its main star structure, ring structure, bus structure, the distributed structure, tree structure, network structure, honeycomb structure.
Bank of Finland Simulation Seminar and Workshop 23 August 2006 Network topology and payment system resilience - first results Kimmo Soramäki1 Walt Beyeler2 Morten L. Bech3 Robert J. Glass2 1 Helsinki Univ. of Technology / European Central Bank 2 3 Sandia National Laboratories Federal Reserve Bank of New York The views expressed in this presentation are those of the authors and do not necessarily reflect the views of their respective institutions 2 Research problem and approach • How does the topology of the payment network affect its resilience? • Devise a simple model to test the impact of topology: 1. stochastic instruction arrival process 2. “prototypical” topologies of interbank relationships 3. simple reflexive bank behavior, and 4. single disrupted bank 3 1. Stochastic instruction arrival process • Each bank has a given level of customer deposits (Di) • Each unit of deposits has the same probability of been transformed into a payment instruction • where λi is the initial rate • When a bank receives a payment its deposits increase -> the instructions arrival increases • When a bank sends a payment its deposits decrease -> the instructions arrival decreases 4 2. “Prototypical” topologies of interbank relationships Homogeneous deposit distribution 400 banks, 8*400 links lattice complete random Heterogeneous deposit distribution random scale-free 5 2.1 Network statistics average Degree average path degree range length lattice 8 8 6.7 random 8 8 3.1 – homogeneous complete 399 399 1 random 8 1 – 19 3.1 – heterogeneous scale-free 8 1 – 225 2.6 6 2.2 Real networks… Fedwire has a scale-free network topology i.e. it has a power law degree distribution, where Source: The Topology of Interbank Payment Flows http://www.newyorkfed.org/research/staff_reports/sr243.pdf 7 3. Simple reflexive bank behavior Central bank Payment system 4 Payment account 5 Payment account is debited is credited Bi Bj 6 Depositor account 3 Payment is settled is credited or queued Qi Bi > 0 Di Dj Qj > 0 Qj 2 Depositor account Bank i Bank i 7 Queued payment, is debited if any, is released 1 Agent instructs bank to send a payment Productive Agent Productive Agent 8 Example: queues in a lattice network, 4. Single disrupted bank 10,000 nodes, low liquidity before: • An “operational incident” • Other banks are not aware: the bank can receive, but cannot send payments • The single bank acts as a liquidity sink. Eventually all liquidity is at the failing bank after: and no payments can be settled • We examine the liquidity absorption rate and system throughput in the time period until all liquidity is at the failing bank 9 Steady state performance steady state Low liquidity queues queue High liquidity time time Steady state performance is varies under the alternative network topologies 10 Queues in steady state High average path length, uniform degree distribution 125,000 Shorter average path length, 100,000 higher degree heterogeneity Shorter average path length 75,000 queues Shortest average path length 50,000 25,000 0 1 10 100 10,000 1,000,000 1,000 100,000 total liquidity 11 Queues in steady state: scale free network 250,000 Highest degree heterogeneity 200,000 150,000 queues -> higher degree heterogeneity and a longer 100,000 average path length increase the level of queues in the steady state 50,000 0 1 10 100 1,000 10,000 1,000,000 100,000 total liquidity 12 Liquidity absorption rate The amount of liquidity absorbed by the failing bank by each instruction arriving to the system 13 Liquidity absorption rate 0.50% Higher degree heterogeneity, 0.40% larger failing bank liq. absorption rate 0.30% Shortest average path length 0.20% Shorter average path length High average path length, 0.10% uniform degree distribution 0.00% 10 100 1,000 10,000 100,000 1,000,000 liquidity 14 Liquidity absorption rate: scale free network 5.00% 4.00% Highest degree heterogeneity, largest failing bank liq. absorption rate 3.00% Higher degree heterogeneity/ 2.00% larger failing bank and a shorter average path length increase the speed of liquidity absorption 1.00% 0.00% 10 100 1,000 100,000 1,000,000 10,000 liquidity 15 Throughput The fraction of arriving instructions that the bank can settle in a given time interval (the remaining being queued) 16 Throughput 100% High average path length, uniform degree distribution 75% throughput Shortest average path length Shorter average path length 50% Higher degree heterogeneity, larger failing bank 25% 1,000,000 1,000 10,000 10 100 100,000 liquidity 17 Throughput: scale-free network Throughput decreases with 100% increased degree heterogeneity and the 80% removal of larger banks throughput 60% 40% 20% Highest degree heterogeneity, largest failing bank 0% 10 100 1,000 10,000 100,000 1,000,000 liquidity 18 Summary • First investigation into the impact of topology in “payment system” type of network dynamics • Topology matters – both for normal performance and – for performance under stress – efficient topologies are not necessarily less resilient • Next steps – Investigate alternative times for other banks’ knowledge of failure and failure resumption times – Impact of the existence of a market? – Perturbations in market? – Build behavior for banks
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