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Performance Modeling of Stochastic Capacity Networks

Performance Modeling of Stochastic Capacity Networks. Carey Williamson iCORE Chair Department of Computer Science University of Calgary. Introduction. There exist many practical systems in which the system capacity varies unpredictably with time

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Performance Modeling of Stochastic Capacity Networks

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  1. Performance Modeling ofStochastic Capacity Networks Carey Williamson iCORE Chair Department of Computer ScienceUniversity of Calgary CanQueue September 15, 2006

  2. Introduction • There exist many practical systems in which the system capacity varies unpredictably with time • These systems are complicated to model and understand • Main focus of this talk: • Stochastic capacity networks • Lots of modeling issues and questions • A few answers (mostly from simulation) CanQueue September 15, 2006

  3. Queueing systems Loss systems Some Examples • Safeway checkout line • Variable-rate servers • Load-dependent servers • Grid computing center • Priority-based reservation networks • Wireless Local Area Networks (WLANs) • Wireless media streaming scenarios • Handoffs in mobile cellular networks • “Soft capacity” cellular networks CanQueue September 15, 2006

  4. Queueing systems Loss systems Some Examples • Safeway checkout line • Variable-rate servers • Load-dependent servers • Grid computing center • Priority-based reservation networks • Wireless Local Area Networks (WLANs) • Wireless media streaming scenarios • Handoffs in mobile cellular networks • “Soft capacity” cellular networks CanQueue September 15, 2006

  5. Grid Computing Example • Jobs of random sizes arrive at random times to central dispatcher, and are then sent to one of M possible computing nodes • If a computing node fails, then all jobs that are currently in progress on that node are irretrievably lost • Performance impacts: • Lost work needs to be redone • Increased queue delay for waiting jobs CanQueue September 15, 2006

  6. Wireless LAN (WLAN) Example • An IEEE 802.11b WLAN (“WiFi”) supports four different physical transmission rates: • 1 Mbps, 2 Mbps, 5.5 Mbps, 11 Mbps • Stations can dynamically switch between these rates on a per-frame basis depending on signal strength and perceived channel error rate • Performance impacts: • The presence of one low-rate station actually degrades throughput for all WLAN users [Pilosof et al. IEEE INFOCOM 2003] CanQueue September 15, 2006

  7. Cellular Network Terminology Forward Reverse MS BSC PSDN BS CanQueue September 15, 2006

  8. Cellular Handoff Example • Mobile phones communicate via a cellular base station (BS) • Movement of active users beyond the coverage area of current BS necessitates handoff to another BS • If no resources available, drop call • Possible strategies: • Guard channels (static or dynamic) • Power control, “soft handoff”, etc. CanQueue September 15, 2006

  9. New Calls (Poisson) Handoff Calls To neighbour cells Handoff Traffic in a Base Station Channel Pool with total C channels Call completion (exponential distribution) (blocking possible) C-g (dropping possible) g Handoff Calls (non-Poisson) From neighbour cells Guard channels (static scheme) Cell Site [Dharmaraja et al. 2003] CanQueue September 15, 2006

  10. New Calls (Poisson) Handoff Calls To neighbour cells Handoff Traffic in a Base Station Channel Pool with total C channels Call completion (exponential distribution) (blocking possible) C-g (dropping possible!) (dropping possible) g Handoff Calls (non-Poisson) From neighbour cells Guard channels (dynamic scheme) Cell Site CanQueue September 15, 2006

  11. “Soft Capacity” Example • Problem originally motivated by research project with TELUS Mobility • Q: How many users at a time can be supported by one BS? - CLW • A: “It depends” - MW • CDMA cellular systems are typically interference-limited rather than channel limited (i.e., time varying) • Intra-cell and inter-cell interference CanQueue September 15, 2006

  12. Soft Capacity: “Cell Breathing” The effective service area expands and contracts according to the number of active users! CanQueue September 15, 2006

  13. Observation and Motivation • Networks with time-varying capacity tend to exhibit higher call blocking rates and higher outage (dropping) probabilities than regular networks • Investigating performance in such systems requires consideration of the traffic process as well as the capacity variation process (and interactions between these two processes) CanQueue September 15, 2006

  14. Research Questions • What are the performance characteristics observed in stochastic capacity networks? • How sensitive are the results to the parameters of the stochastic capacity variation process? • Can one develop an “effective capacity” model for such networks? CanQueue September 15, 2006

  15. Background: Erlang Blocking Formula • The Erlang B formula expresses the relationship between call blocking, offered load, and the number of channels in a circuit-based network CanQueue September 15, 2006

  16. Circuit-Switched Network Model Capacity for C Calls CanQueue September 15, 2006

  17. Blocking state Markov Chain Model State 0 State 1 State N • Call arrival process: Poisson • Call holding time distribution: Exponential CanQueue September 15, 2006

  18. 2% Erlang B Results CanQueue September 15, 2006

  19. Erlang B Model Summary Offered Load Blocking Probability p Capacity C CanQueue September 15, 2006

  20. Our Goal: Effective Capacity Model Offered Load Blocking Probability p Dropping Policy Equivalent Capacity Dropping Probability d CanQueue September 15, 2006

  21. Modeling Methodology Overview Traffic Model Analytic Approach System Model Capacity Model Simulation Approach CanQueue September 15, 2006

  22. Traffic Model State 0 State 1 State N • Arrival process: Poisson, Self-similar • Holding time: Exponential, Pareto CanQueue September 15, 2006

  23. Fixed Capacity C = 10 Stochastic Capacity Fixed Capacity C = 5 Fixed Capacity C = 4 t Traffic and Capacity Example Traffic Occupancy Process (Counting Process) Traffic Arrival and Departure Process (Point Process) CanQueue September 15, 2006

  24. Stochastic Capacity Example CanQueue September 15, 2006

  25. Stochastic Capacity Terminology “High variance” “Low variance” CanQueue September 15, 2006

  26. Stochastic Capacity Terminology “High frequency” “Low frequency” CanQueue September 15, 2006

  27. Stochastic Capacity Terminology “Correlated” “Uncorrelated” CanQueue September 15, 2006

  28. Stochastic Capacity Model High value H Medium value • Value process {Ci} • Timing process {ti} L Low value CanQueue September 15, 2006

  29. High value H State 0 State 1 State N Medium value L Low value Effective Capacity + • Effects of Capacity Value process • Effects of Capacity Timing process • Effect of Correlations • Interactions between Traffic and Capacity CanQueue September 15, 2006

  30. Dropping Transitions Blocking States Full Model Structure Traffic Process Capacity Variation CanQueue September 15, 2006

  31. Parameters in Simulations CanQueue September 15, 2006

  32. Results and Observations (Preview) • Factors that matter: • Mean of capacity value process • Variance of capacity value process • Correlation of capacity value process • Frequency of capacity timing process • Choice of call dropping policy used • Relative time scales of joint processes • Factors that don’t matter: • Distribution for capacity timing process CanQueue September 15, 2006

  33. Effect of Capacity Value Mean Small capacity C = 30 (100% load) Medium capacity C = 40 (75% load) Large capacity C = 50 (60% load) CanQueue September 15, 2006

  34. Effect of Capacity Value Variance High variance (75% load) Medium variance (75% load) Low variance (75% load) CanQueue September 15, 2006

  35. Effect of Capacity Correlation Uncorrelated Correlated CanQueue September 15, 2006

  36. Effect of Capacity Timing Process CanQueue September 15, 2006

  37. Effect of Call Dropping Policy (1 of 2) CanQueue September 15, 2006

  38. Effect of Call Dropping Policy (2 of 2) CanQueue September 15, 2006

  39. Effect of Relative Time Scale R = E[call arrivals/capacity change] CanQueue September 15, 2006

  40. Results and Observations (Recap) • Factors that matter: • Mean of capacity value process • Variance of capacity value process • Correlation of capacity value process • Frequency of capacity timing process • Choice of call dropping policy used • Relative time scales of joint processes • Factors that don’t matter: • Distribution for capacity timing process CanQueue September 15, 2006

  41. Summary and Conclusion • Studied call-level performance in a network with stochastic capacity variation • Shows influences from the properties of the stochastic capacity variation process • Shows that mean and variance of capacity process have the largest impact, as do the correlation structure and timing • Shows impact of interactions between traffic and capacity processes • One step closer to our goal, but the hard part is still ahead! CanQueue September 15, 2006

  42. Our Goal: Effective Capacity Model Offered Load Blocking Probability p Dropping Policy Equivalent Capacity Dropping Probability d CanQueue September 15, 2006

  43. References • H. Sun and C. Williamson, “Simulation Evaluation of Call Dropping Policies for Stochastic Capacity Networks”, Proceedings of SCS SPECTS 2005, Philadelphia, PA, pp. 327-336, July 2005. • H. Sun and C. Williamson, “On Effective Capacity in Time-Varying Wireless Networks”, Proceedings of SCS SPECTS 2006, Calgary, AB, July 2006. • H. Sun, Q. Wu, and C. Williamson, “Impact of Stochastic Traffic Characteristics on Effective Capacity in CDMA Networks”, to appear, Proceedings of P2MNet, Tampa, FL, Nov. 2006. • H. Sun and C. Williamson, “On the Role of Call Dropping Controls in Stochastic Capacity Networks”, submitted for publication, 2006. CanQueue September 15, 2006

  44. Related Work • S. Dharmaraja, K. Trivedi, and D. Logothetis, “Performance Modelling of Wireless Networks with Generally Distributed Hand-off Interarrival Times”, Computer Communications, Vol. 26, No. 15, pp. 1747-1755, 2003. • V. Gupta, M. Harchol-Balter, A. Scheller-Wolf, and U. Yechiali, “Fundamental Characteristics of Queues with Fluctuating Load”, Proceedings of ACM SIGMETRICS 2006, St. Malo, France, June 2006. • G. Haring, R. Marie, R. Puigjaner, and K. Trivedi, “Loss Formulae and Optimization for Cellular Networks”, IEEE Transactions on Vehicular Technology, Vol. 50, No. 3, pp. 664-673, 2001. • B. Haverkort, R. Marie, R. Gerardo, and K. Trivedi, Performability Modeling: Techniques and Tools, 2001. CanQueue September 15, 2006

  45. Thanks! • Questions? • Credits: • Hongxia Sun • Jingxiang Luo • Qian Wu • S. Dharmaraja • For more information: • Email carey@cpsc.ucalgary.ca • http://www.cpsc.ucalgary.ca/~carey CanQueue September 15, 2006

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