The Extended Connection-Dependent Threshold Model for Elastic and Adaptive Traffic

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. Outline • 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

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

4. j = 13 j = 32 Erlang Multi-rate Loss Model Link bandwidth capacity andcalls bandwidth requirements are expressed in bandwidth units (b.u.)For example 1b.u. = 64 Kbps Example:Two services:b1=1andb2=2System state:j Number of occupied b.u. j =1

5. Erlang Multi-rate Loss Model Blocking statesof 2nd service State Transition Diagramfortwo services:b1=1andb2=2 Blocking stateof 1st service • λκ: arrivalrate (Poisson process) • μκ: servicerate • Yκ( j): mean number of calls q( j):probability of state j

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

7. Extended Connection-Dependent Threshold Model Example: transmission link: C=5, T=7 in-service calls: b1=1, b2=2 arriving call: b3=3 Virtual Capacity : Used for Call Admission Control Number of occupied resources assuming that all in-service calls receive maximum bandwidth • j : system state ( 0 ≤ j ≤ T ) Call Admission Control Bandwidth Allocation

8. Extended Connection-Dependent Threshold Model • Jk1thresholds of kth service • bκ0 > bκ1bandwidth 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.

9. Extended Connection-Dependent Threshold Model • State Transition Diagramfor a service with: • one threshold: Jk1 • two bandwidth requirements: bk0=2, bk1=1 • In statesj > C : • bandwidth reduction by r( j)=C/jfor all calls • service rate reduction by r( j)=C/j for elastic calls • no service rate reduction for adaptive calls

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

11. 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

12. Conclusion • 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

13. Thank You !

15. Extended Connection-Dependent Threshold Model Assumptions The recurrent calculation of the state probabilities isbased 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