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Network topology and payment system resilience - first results

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					 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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Description: 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.