A new Paradigm for Traffic Engineering of

1
A new Paradigm for Traffic Engineering
of Multi-Service Networks Villy Bæk Iversen COM
?DTU, Technical University of Denmark
2
Classical Loss systems Single-rate
Erlang-B formula Engset ( Pascal) formula are
known to be insensitive to the service time
distribution. Engset formula is also insensitive
to the idle time distribution. Successfully
applied during 90 years.
3
Classical delay systems single rate
Erlang-C formula and Palm machine/repair model
are only valid for exponential service
times. Palms model is insensitive to idle time
distribution. If we assume Processor Sharing PS
(Flow model), (Generalized Processor Sharing
GPS for multiple servers), then both models
become insensitive to the service time
distribution. We get same mean performance values
as for the classical models with exponential
service times. GPS all calls same bandwidth
requirement.
4
Multi-rate Loss systems

• Multi-rate loss systems well-known models
• BPP multi-rate traffic models.
• Insensitivity as for classical single-rate
  models.
• Algorithms
• Convolution algorithm (1987) (also for
  networks).
• Generalized state algorithm (for links only).
• Individual performance measures for each stream.

5
Hybrid model

• How to combine the two insensitive models
• Underload Multi-rate loss model
• Overload Generalized Processor Sharing
• How to get optimal utilization? Require
• reversibility to maintain insensitivity and
• keep capacity used at maximum.
• Construct reversible state transition diagram.

6
Reversible scheduling
Product form lost, but reversibility
insensitivity kept Allocated resources between
max-min scheduling and proportional
scheduling. Normal load more resources to
broadband streams, Overload in the limit same
capacity to every stream. May limit number of
streams of any type.
7
Numerical evaluation

• Exploit reversibility and find each individual
  state
• Very simple effective algorithm

8
Generalizations
Stable algorithm by normalizing probabilities
after each new global state. Find individual
performance for each traffic stream.

• By truncating state space final buffer for
• Each traffic stream and/or
• All traffic streams.
• Applicable to networks of nodes (open closed).
• Includes all classical loss/delay models

9
Miscellaneous aspects
Earlier used a lot of simulations to investigate
these strategies. Insensitivity By using
constant service times the variance is minimized.

• Multi-layer model
• Connection level Lost connections cleared
• Packet level Lost packets held

10
Algorithm
Special case Algorithm for loss systems
11
BPP Traffic model
n number ofchannels N number of traffic
streams Each traffic stream characterized by Ai
mean offered traffic Zi peakedness di bandwidth
Binomial/Pascal parameters S number of
sources ? offered traffic per idle source
12
Delbroucks algorithm 1983
This is equivalent, but more complex Kaufman
Roberts (Fortet Grandjean) is a special case (Z
1)
13
Recursive formula

• Start with x 0 channels
• Let p(0)1
• Let xx1
• Calculate pi(x) and p(x) (need only di previous
  terms)
• Renormalize by dividing di previous terms by
  1p(x)
• Special case recursions for Erlang and Engset
  formulæ

14
Algorithm properties
The algorithm is numerically accurate for
increasing x The memory requirements
are Number of operations is We get
individual performance measures
15
Performance measures
E Time congestion Proportion of time the system
is congested C Traffic congestion Proportion of
offered traffic blocked Offered traffic
carried traffic when capacity is infinite B Call
congestion Proportion of call attempts blocked
16
Individual performance measures
Ei Time congestion is obtained from last di
global states Ci Traffic congestion is obtained
from offered traffic Ai and carried traffic yi
where
Bi Call congestion is always
17
Title in AGaramond 24 pt bold
18
Title in AGaramond 24 pt bold
19
Title in AGaramond 24 pt bold
20
Title in AGaramond 24 pt bold
21
Conclusions Further work

• Fast accurate stable algorithm
• Very low memory requirements
• Generalizations to
• Arrival blocking (state bandwidth dependent)
• Departure blocking (GPS generalized PS)
• MinMax allocation per stream (trunk
  reservation)
• End-to-end blocking in circuit switched networks
• End-to-end delay in packet switched networks
• Teletraffic engineering Handbook
• http//www.com.dtu.dk/education/34340/material/tel
  enook.pdf