1. Analysis of a Multiservice and an Elastic Traffic Model on a CDMA link Ioannis Koukoutsidis Post-Doctoral Fellow, INRIA Projet MAESTRO

2. 2 Traffic Demand in a Multiservice Network Real-time traffic: strict QoS requirements  duration, bit rate (conversational traffic: audio, video, streaming traffic) Performance metric: blocking probability Non real-time traffic: Elastic  transmission rate is freely adjusted (documents, web pages, downloadable audio/video) Performance metric: transfer time

3. 3 Traffic Analysis of CDMA networks Evaluation of capacity is more difficult than FDMA, TDMA or wireline networks - interference-limited capacity - different problem and parameters in uplink, downlink - traffic and transmission power strongly coupled through power control Need to consider various services and classes of traffic (variable bit rates, traffic characteristics)

4. 4 Modeling Capacity and Throughput on a CDMA Link : energy per bit to noise density : processing gain Uplink: Capacity is expressed as a function of the number of users the CDMA cell can theoretically sustain without the total power going to infinity : ratio of intercell to intracell interference

5. 5 Downlink: : ratio of received intercell to intracell power : fraction of received own cell power experienced as intracell interference due to multipath fading Notes Δ(s) is an increasing function of R s E b /N o requirements are higher on the downlink DL: power used up for SCH and CCH channels  DL is the bottleneck, even on a symmetric link (despite the use of orthogonal signaling on the downlink!)

6. 6 Objectives of Analysis Solution of a multiservice model with RT and NRT calls Integration of RT and NRT with “interactive use of resources” use of QBD process theory for numerical solution resource sharing trade-offs, admission control policies Solution of an elastic traffic model with only NRT calls Processor-sharing for NRT traffic application of a GPS model access-control policies

7. 7 Multiservice traffic model RT traffic has priority over the system resources GoS control: more RT calls with degraded transmission rates NRT traffic employs processor sharing a portion of the total capacity, L NRT is reserved use of whatever capacity is left-over from RT traffic (number of calls with max rate) (max number of RT calls)

8. 8 Two models for NRT capacity usage HSDPA, HSUPA: High-speed downlink (uplink) packet access (WCDMA) total capacity assigned to a single mobile for a very short time Total throughput (downlink) Processor-sharing (standard CDMA) capacity used simultaneously by the number of mobiles present Total throughput (downlink)

9. 9 Q uasi B irth D eath Analysis Departure rate of NRT calls: QBD process with for level HSDPA: Homogeneous QBD process PS: Non-homogeneous QBD process (LDQBD)

10. 10 Numerical Results

11. 11 Ergodicity of the LDQBD process For a homogeneous QBD process, a necessary and sufficient ergodicity condition is What is an ergodicity condition in the LDQBD case? We observe that the total throughput reaches a limit in both the UL and DL cases, i.e. the sub-matrices of the LDQBD process converge to level-independent submatrices Theorem: If the homogeneous QBD process is ergodic, the LDQBD process also is. Conversely, if the homogeneous QBD is not ergodic with positive expected drift, d=πQ 0 e- πQ 2 e>0, the LDQBD process is also not ergodic

12. 12 Proof sketch Denotethe LDQBD and QBD processes respectively It holds that Then we can show that, from which the forward part of the proof follows In the reverse part, we show that there exists a modified QBD process which is not ergodic and for which holds Thenis not ergodic, from which we can establish that the original LDQBD is not ergodic

13. 13 Elastic Traffic Model

14. 14 Generalized Processor Sharing (GPS) The GPS model, defined and studied by Cohen (1979), applies here:

15. 15 Poisson arrivals model - K different groups of flows - (arrival process) k ~ Poisson (λ k ), service requirement - with mean - - Mean transfer times can be derived by Little’s law

16. 16 Theorem P1: The stochastic process of the number of flows in the system is ergodic if and only if Theorem P2: The mean sojourn time of a flow whose service requirement is deterministic, c, is given by: where E[T] is the mean sojourn time in a corresponding single class system with the same total load and maximum number of admitted flows (in loss systems) and with mean service requirement E[σ]

17. 17 Engset-like model Both service rate reduction and blocking finite population of M k sources for each class k, total max. no. of flows S for

18. 18 Theorems Theorem E1: The blocking probability of a class-m source is given by Theorem E2: The sojourn time of a class-m source is given by

19. 19 Proof (E2): Consider the countable state space of the system, S. In a processor-sharing system that is ergodic, the arrival rate must equal the departure rate, since flows are not queued. Then it suffices to show that is the departure rate of class-m flows, defined as: This is straightforward if we consider the regenerative process structure of Cohen (extended to K classes, viz. that the process is regenerative), since then the time average equals the mean of the limiting distribution.

20. 20 Insensitivity and truncation properties Insensitivity properties apply to all GPS examined models In loss systems, truncation principle applies  We can prove insensitivity by an easier and more general method (Burman’s restricted flow equations, Schassberger’s method of clocks) Truncation principle then follows since the associated Markov process of the system is reversible  Extend results to other access models (dedicated access, fully shared access, or other strategies in between)

21. 21 Examples Poisson arrivals, 2 classes, separate limits M 1, M 2, common limit M (M<M 1 +M 2 ) Engset-like system, 2 classes, source populations M 1, M 2, separate limits S 1, S 2.

22. 22 Graphs Blocking probabilities in a 2-class, Engset-like system with a common constraint (S=20, M 1 =15, M 2 =8) Total load ρ=1000 Blocking probabilities in a 2-class, Engset-like system with separate constraints (S 1 =10, S 2 =5, M 1 =15, M 2 =8). Total load ρ=1000

23. 23 Other Research Directions Capacity model compare with Shannon’s capacity include spatial density of mobiles Combine different access techniques (e.g. CDMA and WiFi) study resource sharing and scheduling techniques for different traffic models