Modular link dimensioning and cost in two-layer network

1
Modular link dimensioning and cost in two-layer
network

• Jian Li
• EL736 Final Project
• Polytechnic University

2
Overview

• Modular links
• Formulations
• A simulated two-layer network with different link
  modules.
• Find the minimize cost
• Result data and comparison
• Conclusion

3
Linear link model

• Various types of flow variables continuous,
  binary, and integral
• Link capacity equal to link load minimal
  capacity
• The cost of the link the link capacity times an
  unit cost efficient ?eye

4
Modular links

• A common feature in communication network.
• North-American pulse-code modulation (PCM) system
  modularity of M24 voice circuits
• European PCM system modularity of M30 trunks
• VC-4 SDH network modularity of 63 PCM primary
  groups

5
Formulation

• Links with universal modular size
• Links with multiple modular sizes
• Links with incremental modules

6
Two-layer network topology and demands
7
Two-layer dimensioning with modular links

• constants
• hd volume of demand d, in demand volume units,
  DVUs
• dedp 1 if link e of upper layer belongs to path
  p realizing demand d 0, otherwise M size of the
  link capacity module in upper layer
• ?e cost of one DVU of link e of upper layer
• ?geq 1 if link g of lower layer belongs to path
  q realizing link e of upper layer 0, otherwise
• N size of link capacity module in lower layer
• ?g cost of one DVUs of link g of lower layer
• variables
• xdp (non-negative continuous) flow allocated to
  path p realizing volume of demand d
• ye (non-negative integral) M-module capacity of
  upper layer link e
• zeq (non-negative integral) flow allocated to
  path q realizing capacity of link e
• ug (non-negative integral) N-module capacity of
  lower layer link g

8
Cont.

• objective
• minimize F ?e ?e M ye ?g ?g N ug
• constraints
• ?p xdp hd, d 1, 2, . . . ,D
• ?d?p dedp xdp M ye, e 1, 2, . . . ,E
• ?q zeq ye, e 1, 2, . . . ,E
• M ?e ?q ?geq zeq N ug, g 1, 2, . . . ,G.

9
Data
Upper layer modular size, M Lower layer modular size, N Lower layer modular size, N Lower layer modular size, N Lower layer modular size, N Lower layer modular size, N Lower layer modular size, N Lower layer modular size, N Lower layer modular size, N
Upper layer modular size, M 1 3 5 7 11 13 23 31
1 8075 8090 8099 8113 8153 8182 8188 8296
3 8127 8127 8155 8153 8179 8227 8275 8323
5 8170 8189 8170 8214 8255 8267 8285 8445
7 8211 8223 8230 8211 8274 8316 8358 8453
11 8283 8297 8311 8359 8283 8377 8476 8534
13 8294 8321 8343 8353 8428 8294 8506 8542
23 8533 8564 8568 8631 8650 8667 8533 8878
10
Result
11
Conclusion

• Increases of modular size in either upper or
  lower layer lead the cost solutions further away
  from optimal
• Get worse when the link capacity module, M is
  much larger than the flow unit