1. 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

2. I.Introduction II.Review of the Erlang Multi-rate Loss Model A) Model Description B) 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

3. Performance Measures Stream (real-time video) Call Blocking Probability Link Utilization Types of Traffic Elastic (file transfer) Introduction Adaptive (adaptive video)

4. Example: Two services: b 1 =1 and b 2 =2 System 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

5. q( j): probability of state j Blocking state of 1 st service Blocking states of 2 nd service State Transition Diagram for two services: b 1 =1 and b 2 =2 Erlang Multi-rate Loss Model  λ κ : arrival rate (Poisson process)  μ κ : service rate  Y κ ( j ): mean number of calls

6. State Probability Call Blocking ProbabilityLink Utilization Erlang Multi-rate Loss Model

7. Extended Connection-Dependent Threshold Model Bandwidth Allocation Example: transmission link: C=5, T=7 in-service calls: b 1 =1, b 2 =2 arriving call: b 3 =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

8. Extended Connection-Dependent Threshold Model  J k 1 thresholds of k th service  b κ 0 > b κ 1 bandwidth requirements  μ κ 0 > μ κ 1 service rate (elastic calls)  μ κ 0 = μ κ 1 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.

9. Extended Connection-Dependent Threshold Model State Transition Diagram for a service with:  one threshold: J k 1  two bandwidth requirements: b k 0 =2, b k 1 =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

10. State Probability Call Blocking Probability Link Utilization Extended Connection-Dependent Threshold Model

11. Evaluation – Numerical Examples We compare Analytical to Simulation results 1 st service-class2 nd service-class Link Utilization vs Traffic-load Call Blocking Probability vs Traffic-load

12.  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

15. 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 δ k 0 ( 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 δ k l ( j) for l=1,…, S k