Analysis of a Multiservice and an Elastic Traffic Model on a CDMA link

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

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

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 Rs • Eb/Norequirements 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. 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. 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, LNRT is reserved • use of whatever capacity is left-over from RT traffic (number of calls with max rate) (max number of RT calls)

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. QuasiBirthDeath Analysis • Departure rate of NRT calls: • QBD process with • for level • HSDPA: Homogeneous QBD process • PS: Non-homogeneous QBD process (LDQBD)

10. Numerical Results

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=πQ0e- πQ2e>0, the LDQBD process is also not ergodic

12. Proof sketch • Denote the 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 • Then is not ergodic, from which we can establish that the original LDQBD is not ergodic

13. Elastic Traffic Model

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

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

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

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. 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. 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. Examples • Poisson arrivals, 2 classes, separate limits M1, M2, common limit M(M<M1+M2) • Engset-like system, 2 classes, source populations M1, M2, separate limits S1, S2.

22. Graphs Blocking probabilities in a 2-class, Engset-like system with separate constraints (S1=10, S2=5, M1=15, M2=8). Total load ρ=1000 Blocking probabilities in a 2-class, Engset-like system with a common constraint (S=20, M1=15, M2=8) Total load ρ=1000

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