The Extended Connection-Dependent Threshold Model for

Elastic and Adaptive Traffic

V. Vassilakis, I. Moscholios and M. Logothetis

Wire Communications Laboratory,Department of Electrical & Computer Engineering,

University of Patras,265 04 Patras, Greece.

E-mail: vasilak@wcl.ee.upatras.gr

I. Introduction

II. Review of the Erlang Multi-rate Loss ModelA) Model DescriptionB) Call Blocking Probability & Link Utilization

III. The Extended Connection-Dependent Threshold Model A) Model Description B) Call Blocking Probability & Link Utilization

IV. Evaluation – Numerical Examples

V. Conclusion

Outline

Performance Measures

Stream(real-time video)

Call Blocking Probability

Link Utilization

Types of Traffic

Elastic(file transfer)

Introduction

Adaptive(adaptive video)

Example:Two services: b1=1 and b2=2System state: j

Erlang Multi-rate Loss Model

Link bandwidth capacity and calls bandwidth requirements are expressed in bandwidth units (b.u.)For example 1b.u. = 64 Kbps

Number of occupied b.u.

j =1

j = 1 3

j = 3 2

q( j): probability of state j

Blocking stateof 1st service

Blocking statesof 2nd service

State Transition Diagram fortwo services: b1=1 and b2=2

Erlang Multi-rate Loss Model

λκ : arrival rate (Poisson process)

μκ : service rate

Yκ( j): mean number of calls

1

1 for 0

1ˆ ˆ( ) ( ) for 1,...,

0 otherwise

K

kk kk =

j

q j = q j - b j Cα bj

0

ˆ( )( )

ˆ( )

C

j=

q jq j

q j

1( )

k

C

kj = C - b +

B = q j

State Probability

Call Blocking Probability Link Utilization

1( )

C

j = U = j q j

Erlang Multi-rate Loss Model

Extended Connection-Dependent Threshold Model

Bandwidth Allocation

Example: transmission link: C=5, T=7 in-service calls: b1=1, b2=2 arriving call: b3=3

Call Admission Control

Virtual Capacity : Used for Call Admission Control

j : system state ( 0 ≤ j ≤ T )Number of occupied resources assuming that

all in-service calls receive maximum bandwidth

Extended Connection-Dependent Threshold Model

Jk1 thresholds of kth service

bκ0 > bκ1 bandwidth requirements

μκ0 > μκ1 service rate (elastic calls)

μκ0 = μκ1 service rate (adaptive calls)

Example: An arriving video call to an ISDN node requests for 384 Kbps or, if the node is congested, 128 Kbps.

Extended Connection-Dependent Threshold Model

State Transition Diagram for a service with: one threshold: Jk1 two bandwidth requirements: bk0=2, bk1=1

In states j > C :

bandwidth reduction by r( j)=C/j for all calls

service rate reduction by r( j)=C/j for elastic calls

no service rate reduction for adaptive calls

State Probability

0

0

1 for 0

1ˆ ( )

ˆ ( )1

ˆ ( ) for 1,...,

0 othe

( )min( )

( )

rwise

k

le

k

la

l l l

l l l

S

kK l

k k kk

k k kk

=

S

kK l =

j

α b q j - b

q j =

α b

δ jC, j

δ j q j j

T- b j

0

ˆ( )( )

ˆ( )

T

j=

q jq j

q j

1( )

Sk k

T

Tk

j= -bB = q j

Call Blocking Probability Link Utilization

1 1) ( )(

T

j =

C

+j C=C q jU = j q j

Extended Connection-Dependent Threshold Model

Evaluation – Numerical Examples

We compare Analytical to Simulation results

1st service-class 2nd service-class

Link Utilization vs Traffic-load

Call Blocking Probability vs Traffic-load

We propose a new model the E-CDTM for the analysis of a single-link multi-rate loss system with two types of traffic, elastic and adaptive.

We present recurrent formulas for the calculation of state probabilities and determine the Call Blocking Probability and Link Utilization

The accuracy of the proposed calculations is verified by simulation results

Conclusion

Extended Connection-Dependent Threshold Model

Assumptions

The recurrent calculation of the state probabilities is based on: – local balance between adjacent states. – migration approximation: calls accepted in the system with other than the maximum bandwidth requirement are negligible within a space, called

migration space and related to the variable δk0( j). – upward approximation: calls accepted in the system with their maximum bandwidth are negligible within a space, called upward space and related to

the variable δkl( j) for l=1,…, Sk

0 0 0 1

1 when 1 and 0

( ) 1 when and 0

0 otherwise

lk

k k k k

j T l, b =

δ j = j J + b b >

11 when and 0

( )0 otherwise

l l l- l ll

k k k k kk

J + b j > J + b b >δ j =