A Study of Bandwidth-sharing Mechanisms in Connection-oriented Networks

1. A Study of Bandwidth-sharing Mechanisms in Connection-oriented Networks Ph.D. Dissertation presented by Xiangfei Zhu Department of Computer Science University of Virginia Feb 19, 2008

2. Outline • Quick overview • Hypothesis and Metrics • Contributions and Publications • Motivation • Proposed mechanisms • BA-n • BA-First • VBDS • Immediate-request • Related work • Summary Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

3. Hypothesis • Well-designed algorithms employing immediate-request and book-ahead bandwidth-sharing mechanisms will lead to efficient utilization of modern high-speedconnection-oriented networks Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

4. Metrics • Service provider-oriented metrics • Utilization • Always possible to achieve high utilization if there are no user-oriented performance requirements • User-oriented metrics • Call blocking probability: book-ahead mechanisms for session-type requests • Delay: book-ahead mechanisms for data-type requests • Combined metrics • Session type: express call blocking probability as a function of utilization • Data type: express mean transfer delay as a function of utilization Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

5. Key contributions • Two book-ahead mechanisms for session-type requests • Analytical and simulation models for these two schemes • Models can be used as tools to test design choices and parameter values • A book-ahead mechanism for data-type requests • Overcomes a disadvantage of using circuit-switched networks for file transfers(when compared to packet switching) • Design and deployment of a wide-area, high-speed, optical dynamic circuit network • Demonstrated the readiness of off-the-shelf switches for actual service offerings • Measurements of actual end-to-end call setup delays and per-switch processing delays • Useful to other researchers for modeling purposes Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

6. Publications • X. Zhu and M. Veeraraghavan, " Analysis and Design of Book-ahead Bandwidth-Sharing Mechanisms," accepted by the IEEE Transactions on Communications (TCOM). • X. Zhu, M. E. McGinley, T. Li, and M. Veeraraghavan, "An Analytical Model for a Book-ahead Bandwidth Scheduler," Proc. of IEEE Global Telecommunications Conference (Globecom) 2007, Washington, DC, Nov. 2007. • X. Zhu, X. Zheng, and M. Veeraraghava, "Experiences in implementing an experimental wide-area GMPLS network,"IEEE Journal on Selected Areas in Communications (JSAC), vol. 25, pp. 82-92, Apr. 2007. • X. Zhu, X. Zheng, M. Veeraraghavan, Z. Li, Q. Song, I. Habib, and N. S. V. Rao, “Implementation of a GMPLS-based network with end host initiated signaling,” in Proc. Of IEEE International Conference on Communications (ICC) 2006, Istanbul, Turkey, Jun. 2006. Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

7. Why the renewed interest in connection-oriented networks? • Internet – connectionless packet-switching • Pros: efficient (high utilization) • Cons: low quality of service (bandwidth, delay, jitter, etc. ) • Resurgence of interests in connection-oriented networks: • Top-down driver: large-team scientific projects require predictable high-speed network services • Bottom-up driver: advances in optical circuit-switching technologies • Various connection-oriented testbeds are being deployed around the world • NSF Experimental Infrastructure Network (EIN) program • ESnet4 (US), CA*net4 (Canada), UKLight (UK), SURFnet (Netherlands), JGN2 (Japan) • Internet2 Dynamic Circuit network Terascale Supernova Initiative (TSI)http://www.phy.ornl.gov/tsi/ Large Hadron Collider (LHC)http://www.phys.ufl.edu/~matchev/LHCJC/lhc.html Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

8. Internet2 deployment of Dynamic Circuit network Backbone picture reprinted from http://www.internet2.edu/pubs/networkmap.pdf IP Network Dynamic Circuit Network Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

9. Why revisit the topic of bandwidth sharing in connection-oriented networks? Immediate request Leased lines • Existing mechanisms • Immediate-request (IR) mode: used in the telephone network • Leased-line mode: used in high-speed connection-oriented networks, such as SONET and WDM • Can these mechanisms be used in connection-oriented networks in new context (high-speed + new apps)? • IR mode: cannot achieve high utilization with low call blocking probability when channel density is low • Channel density in the telephone network is on the order of 100 or more • Channel density in high-speed testbeds is on the order of 10 • Leased-line mode: poor temporal sharing, expensive and inefficient • Cannot be used because the number of universities involved in these projects is large Better service quality Better utilization New bandwidth-sharing mechanisms are needed! Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

10. What mechanisms exist for sharing resources in other contexts? • Reservation systems • Reservation phase before resource usage • e.g., book flight tickets, make medical appointments, etc. • Queueing systems • On-demand service • e.g., bank teller, grocery store checkout, etc. • Two types of queueing system based on waiting space • Bufferless queueing – no waiting space • e.g., street parking • Buffered queueing – has waiting space • e.g., bank teller, grocery store checkout Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

11. H3 H4 H5 H2 H1 X3 X1 X2 H6 H7 H8 Are these mechanisms suitable for bandwidth sharing? • Reservation systems • Yes, book-ahead mode • Queueing systems • Bufferless queueing – Yes, immediate-request call-blocking mode • Buffered queueing – No idle idle Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

12. Two types of book-ahead systems • Classification based on request type • Session-type requests • Specify desired bandwidth and duration • e.g., remote visualization and remote instrument control • Data-type requests • Specify size of data to be transferred • e.g., file transfers • File size known at the sending end Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

13. Proposed mechanisms Bandwidth Sharing in high-speed connection-oriented networks Book-ahead Immediate-request high per-channel rate Low-to-moderate per-channel rate • Deployed a testbed • Implemented software • Measured call-setup delays BA-n/BA-First VBDS (Varying-Bandwidth Delayed Start) session-type requests data-type requests • Simulation model • Comparison with packet switching Published in JSAC BA-n BA-First Published in ICC Users specify a set of call-initiation time options Users accept any call-initiation time • Analytical model • Simulation model • Comparison with IR • Analytical model • Simulation model • Comparison with IR Published in TCOM Published in Globecom Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

14. Channel available for H timeslots starting at any one of the n call-initiation times? Yes, accept request No, reject request Analytical model for the BA-n scheme A call specifies: - Bandwidth: 1 channel - Holding time: H timeslots - Set of n call-initiation times: {s1, s2,…, sn} • Assumptions: • Call arrival process is Poisson scheduler m channels X X Switch2 Switch1 Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

15. Discrete-time Markov Chain model (x1, x2, …xK) m: link capacity in channels K: reservation window in timeslots • System state: vector X with K components (x1, x2, …xK) • xi: number of reserved channels in the ith interval • 0≤xi ≤ m • Challenges • Non-homogeneous system • Transition rates at time interval boundaries are infinite, but finite at other times • Mixed system • Call arrival process: continuous • Call holding time: discrete • A user can reserve any timeslots in the reservation window • Key insights • Embedded DTMC at time interval boundaries • Discretize time into very “small” timeslots to use geometric distribution to approximate (exponential) call interarrival time distribution • Timeslots should be small enough to make the probability of more than 1 call arriving in a timeslot negligible • Any call arrival rate can be downgraded to a small call arrival rate by changing the time unit • e.g., 36 call/hour -> 0.01 call/second Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

16. Simulation model • Limitation of the analytical model – does not scale with m • Recall that the state space is defined as • Size of the state space: (m+1)K • Simulation model • Support larger values of m • Relax assumptions used in the analytical model • Call-initiation time options: uniform distribution → bell-shaped distribution • Per-call bandwidth: single channel → multi channels • Path length: single link → multi links Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

17. Model validation and verification • “Three aspects of model validation • Assumptions • Input parameter values and distributions • Output values and conclusions” [Jain91] • Model validation • Our models are for an initial design and implementation of BA systems • Therefore, no real-world measurements • Model validation technique – peer/expert reviews • Real system measurements “available” for input parameters • Example: • Real-system measurements for telephony applications - Poisson call arrival process • Same pattern likely in video-conference calls • Model verification • Compare analytical model results with simulation model results • “Three validation techniques • Expert intuition • Real system measurements • Theoretical results” [Jain91] “Qualitative validation has to be used when adequate acceptable real world data do not exist to permit quantitative validation and is based mainly on SME (Subject Matter Expert) and peer view” [Pace02] [Jain91] R. Jain, The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling, New York, Wiley-Interscience, 1991. [Pace02] D. K. Pace and J. Sheehan, “Subject matter expert (SME)/peer use in m&s v&v,” in Proc. of the Foundations, Lauarel, MD, Oct. 2002. Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

18. Key results from the BA-n study • BA-n scheme outperforms IR scheme when per-channel rate is high • e.g., when m=10 • With the IR mode, high utilization achievable but at a cost • 23% call blocking probability at 80% utilization • 46% call blocking probability at 90% utilization • With the BA-3 mode, high utilization achievable with low call blocking probability • 0.1% call blocking probability at 80% utilization • 2% call blocking probability at 90% utilization • Reservation window size (K) dependence on call holding time (H) • K/H does not need to be large • e.g., when m=10, to achieve90% utilization with 2% call blocking probability, K=4H. • Multi-link scenario • BA-n scheme outperforms IR • Fairness achieved with “trunk reservation” • Between long-path and short-path calls Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

19. Roadmap Bandwidth Sharing in high-speed connection-oriented networks Book-ahead Immediate-request high per-channel rate Low-to-moderate per-channel rate • Deployed a testbed • Implemented software • Measured call-setup delays BA-n/BA-First VBDS session-type requests data-type requests • Simulation model • Comparison with packet switching Published in JSAC BA-n BA-First Published in ICC calls specify a set of call-initiation time options calls accept any call-initiation time • Analytical model • Simulation model • Comparison with IR • Analytical model • Simulation model • Comparison with IR Published in TCOM Published in Globecom Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

20. Is a channel available in the entire reservation window? Yes, accept request No, reject request Analytical model for the BA-First scheme A call specifies: - Bandwidth: 1 channel - Holding time: H timeslots - Set of n call-initiation times: {s1, s2,…, sn} - Any call-initiation time • Assumptions: • Call arrival process is Poisson 1 timeslot scheduler m channels X X Switch2 Switch1 Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

21. System state Call arrivals • Use “bins” to represent reservation intervals • If the ith bin is not full, all bins after it must be empty • The system state is expressed as a 2-tuple (i, n) • i – index of the first bin that is not full • n – number of reserved channels in the ith bin • A special case is (K, m), which denotes the state in which all bins are full Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

22. CTMC Call arrivals Call arrivals • The state of the system changes in two cases • A call arrives: • e.g., (i, n)->(i, n+1) if n<m-1; (i, n)->(i+1, 0) if n=m-1 and i<K • A time-interval boundary is encountered • e.g., (i, n)->(i-1, n) if i>1 • The model is a CTMC but it is non-homogeneous • The system behavior at the timer-interval boundaries is different from its behavior at other times • There is an embedded time-homogeneous DTMC if we only look at the system at the time-interval boundaries Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

23. Embedded DTMC j Call arrivals Call arrivals q • The transition probability can be calculated by counting the number of calls (denoted by a) that arrived in the past time interval, and calculating the probability that a calls arrive in a interval • A: number of call arrivals in the current interval • FA(a) is the Cumulative Distribution Function of A • GA(a) is the Probability Mass Function of A • The transition probability from state (i, n) to state (j, q) is • 1-FA(mK-1) if i=1 & (j,q)=(K,m), i.e., mK or more calls arrived • GA(m(j-1)+q) if i=1 & (j,q)≠(K,m), i.e., m(j-1)+q calls arrived • 1-FA(m(K-i+1)+m-n-1) if i≠1 & (j,q)=(K,m), i.e., m(K-i+1)+m-n or more calls arrived • GA(m(j-i+1)+q-n) if i≠1 & (j,q)≠(K,m), i.e., m(j-i+1)+q-n calls arrived Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

24. Performance metrics Call arrivals integral part fractional part • Call blocking probability • Link utilization • Mean scheduling delay - two parts • Integral part: number of intervals before scheduled service interval • Fractional part: delay within the arrival interval Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

25. Use of the model - Test design choices and parameter values • IR v.s. BA schemes • Example • To achieve a 90% utilization with a call blocking probability less than 10% • BA-First schemes are needed when m<59 • To achieve a 90% utilization with a call blocking probabilityless than 20% • BA-First schemes are needed when m<32 Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

26. Parameters:1) link capacity in channels, m = 2 or 8 2) reservation window size, K = 2, 4, 8, or 16 To run a system at 100% offered load with a 4% or less call blocking probability If m=2, K should be 8 time units If m=8, the number is only 4 time units Is larger value of K always better? If m=8, call blocking probability and utilization plots for K=4, 8 and 16 overlap But mean scheduling delay increases significantly as K increases Use of the model - Select an appropriate reservation window size Increasing reservation window size beyond a certain level is actually detrimental to system performance! Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

27. 1/2 Use of the model - An approximate solution for M/D/m/p system • Solutions exist for M/D/1, M/D/m (approximation) systems • No existing solution forM/D/m/p system • BA-First model (m, K) ≈ M/D/m/m(K+1) queuing model at moderate-to-high loads • Why? • Call-arrival process: both Poisson • Call holding time: both deterministic • Reservation window is effectively “waiting space” fractional part Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

28. We modeled the BA-First mechanism using a non-homogeneous CTMC We extracted an embedded DTMC and solved it for steady-state probabilities We obtained solutions for metrics such as call blocking probability, link utilization, and mean scheduling delay We demonstrated the use of the model as a design tool for book-ahead systems We demonstrated the use of the model as a solution for M/D/m/p queueing system at moderate-to-high loads Key results from the BA-First study Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

29. Roadmap Bandwidth Sharing in high-speed connection-oriented networks Book-ahead Immediate-request high per-channel rate Low-to-moderate per-channel rate • Deployed a testbed • Implemented software • Measured call-setup delays BA-n/BA-First VBDS session-type requests data-type requests • Simulation model • Comparison with packet switching Published in JSAC BA-n BA-First Published in ICC calls specify a set of call-initiation time options calls accept any call-initiation time • Analytical model • Simulation model • Comparison with IR • Analytical model • Simulation model • Comparison with IR Published in TCOM Published in Globecom Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

30. Book-ahead scheme for data-type requests • Data-type requests: specify size of data to be transferred • Drawback of using circuits for file transfers • With fixed-bandwidth allocation, file transfers cannot take advantage of bandwidth freed by the completion of other transfers • Fixed-Bandwidth Delayed Start (FBDS) • Fixed-bandwidth allocation with rate set to maximum rate • Varying-Bandwidth Delayed Start (VBDS) • Assign different bandwidth levels for different time ranges File transfer request =(File Size, Maximum rate, [Requested start time]) Can be provided by file server Limited by various constraints at end hosts, such as disk-access speed Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

31. VBDS • Idea of VBDS • Upon receiving a reservation request, VBDS scheduler returns a Time-Range-Channel (TRC) vector {(Bk, Ek, Ck, k=1,2,…)} • Bk: start time of the kth time range • Ek: end time of the kth time range • Ck: set of channels allocated to the transfer in the kth time range • Scheduler maintains channel-availability function γ(t) • Cost of VBDS • Switches need to be reprogrammed multiple times within a transfer • Switch programming time is considered in the analysis • Switches need to maintain channel availability function • Reduce the number of changes in channel-availability function • Discretize time Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

32. VBDS example Channel availability γ(t) 4 3 2 1 Time 0 10 20 30 40 50 60 70 80 … ∞ • Assumptions: • 4-channel link with per-channel rate 10Gbps • Unit of time discretization: 100ms • Switch programming time: 1 unit • A file transfer request specifies (5GB, 20Gbps, 50) • (50, 60, {4}) – 1.125GB • (60, 70, {2, 4}) – 2.375GB • (70, 75, {2, 4}) – 1.5GB (File Size, Maximum rate, Requested start time) Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

33. Numeric results • Compare VBDS, FBDS, and Packet switching (PS) Average throughput Normalized Delay Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

34. Key results from the VBDS study • Circuit-switched network with VBDS achieves similar performance as packet-switched networks for moderate-to-large files • Significant: at high speeds, circuit switching cost << packet switching cost • VBDS favors large files when compared to packet switching • Packet switching: newly arriving transfers “cut in” • VBDS: Not so. Allocated bandwidth remains dedicated to ongoing transfers • We do not recommend using circuit-switched network for small files • Scheduling and circuit setup overheads • Cost • Circuit switching: setup overhead (unsuitable for small files) • Packet switching: congestion control algorithm (lower throughput for moderate-to-large files) Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

35. Roadmap Bandwidth Sharing in high-speed connection-oriented networks Book-ahead Immediate-request high per-channel rate Low-to-moderate per-channel rate • Deployed a testbed • Implemented software • Measured call-setup delays BA-n/BA-First VBDS session-type requests data-type requests • Simulation model • Comparison with packet switching Published in JSAC BA-n BA-First Published in ICC calls specify a set of call-initiation time options calls accept any call-initiation time • Analytical model • Simulation model • Comparison with IR • Analytical model • Simulation model • Comparison with IR Published in TCOM Published in Globecom Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

36. Immediate-request bandwidth sharing • Deployed a wide-area experimental network with immediate-request mode of bandwidth sharing - CHEETAH • State-of-the-art in 2004 • Control-plane protocols are standardized by IETF - GMPLS protocol suite • Vendors have implemented these protocols in high-speed optical circuit switches • No deployed network uses these functions • No signaling protocol client for end hosts to enable the creation of end-to-end high-speed circuits Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

37. OC192 card ControlCard GbE/10GbEcard H H H OC192 card ControlCard GbE/10GbEcard H H CHEETAH network • Switches: Sycamore SN16000 Intelligent Optical switch • Robust implementation of GMPLS control-plane protocols • Support standardized Ethernet-SONET mapping Oak Ridge, TN Raleigh, NC SN16000 To Cray X1 SN16000 zelda4 zelda5 OC192 card ControlCard GbE/10GbEcard wukong H Atlanta, GA OC-192 OC-192 SN16000 zelda1 zelda2 zelda3 • End hosts: general-purpose Linux PCs with two NICs and CHEETAH end-host software Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

38. IR mode of sharing in CHEETAH • Designed and implemented an end-host software package based on the GMPLS architecture • Stand-alone circuit request tools • Integrated into applications such as Squid (an open-source web proxy software) • Ran experiments of IR mode call setups and releases • Measured end-to-end circuit setup delays and per-switch signaling message processing delays • Measurements useful to other researchers for modeling purposes • Demonstrated the readiness of off-the-shelf switches for actual service offerings Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

39. Related work • Research papers on book-ahead bandwidth sharing • Most of these papers use simulations • None of them considers book-ahead calls with multiple acceptable options • Our results show that a book-ahead mechanism that specifies only one call-initiation time may perform worse than an immediate-request mechanism • File transfers • List scheduling: all proposed algorithms use fixed allocations • Bin packing: cannot break a block into pieces to fit into bins • TCP improvements: determine fair share for a flow faster and more accurately, while we determine share for a flow during setup • Optical connection-oriented testbeds • e.g.: ESnet4, NSF DRAGON, CA*net4, UKLight, JGN2, etc. • Focus: implementation & inter-domain usage • Our work: mixed study of IR and BA; theoretical modeling + implementation Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

40. Summary • High-speed connection-oriented networks should support a combination of bandwidth-sharing services For reservations that specify desired bandwidth and duration For reservations that specify file size (large file transfers) For serving as “wires” between switches to create networks that offer other services For video telephony, transfers of moderate-sized files New services: BA-n/BA-First VBDS Leased lines Immediaterequest Existing services: IP services Better service quality Greater sharing Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

41. Future work • Routing issue in reservation phase • Currently assume a linear topology in multi-link scenarios • Multiple route options should be exploited • Distributed implementation • Necessary for inter-domain scheduling • Service providers do not share network topology information with each other • Validate models against real measurements • A long-term future work item after deployment & user base build-up Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

42. Questions from Form G111

43. Questions from Form G111 - Defining the problem • In the context of new optical circuit-switched technologies and new application requirements, what bandwidth-sharing mechanisms can lead to efficient utilization of modern high-speed connection-oriented networks? Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

44. Questions from Form G111 -Analysis of previous and related work • Research papers on book-ahead bandwidth sharing • Most of these papers use simulations • None of them considers book-ahead calls with multiple acceptable options • Our results show that a book-ahead mechanism that specifies only one call-initiation time may perform worse than an immediate-request mechanism • File transfers • List scheduling: all proposed algorithms use fixed allocations • Bin packing: cannot break a block into pieces to fit into bins • TCP improvements: determine fair share for a flow faster and more accurately, while we determine share for a flow during setup • Optical connection-oriented testbeds • e.g.: ESnet4, NSF DRAGON, CA*net4, UKLight, JGN2, etc. • Focus: implementation & inter-domain usage • Our work: mixed study of IR and BA; theoretical modeling + implementation Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

45. Questions from Form G111 -Success criteria • Has the student adequately defined the measure(s) of success to be used to evaluate the work? Is there a well defined metric with a goal? Does the metric adequately represent the desired success criteria? • Success criteria • Session-type BA requests • BA-n: better performance than IR • BA-First: a model that scales to m>100 • Data-type BA requests • At least the same performance as packet switching • IR mode • Stable network deployment and software implementation • Metrics • Session type: express call blocking probability as a function of utilization • Data type: express mean transfer delay as a function of utilization Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

46. Questions from Form G111 - Solution • Is the approach taken well executed? Does it appear to be correct? Is the work technically challenging? Does the student utilize appropriate professional standards? • A combination of analytical, simulation, and experimental methods. • Two book-ahead mechanisms for session-type requests • Analytical and simulation models for these mechanisms • One book-ahead mechanism for data-type requests • A simulation model for this mechanism • A wide-area testbed for experimental study of the immediate-request mechanism • Testbed deployment • Software implementation • Experimentation and measurements Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

47. Questions from Form G111 - Innovation and risk • Two new Markov chain models for book-ahead bandwidth-sharing schemes (first Markov chain models for book-ahead schemes) • An approximate solution for the M/D/m/p queueing system • One of the first deployments of a wide-area high-speed dynamic circuit network Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

48. Questions from Form G111 -Broader implications(Social, economic, political, technical, ethical, business, etc.) • Demonstrated the readiness of off-the-shelf circuit switches for actual service offering (business and technical) • Designed efficient bandwidth-sharing algorithms for high-speed connection-oriented networks • Circuit switches are less complex than packet switches, which means • Less expensive (economic) • Consume less power (environmental) Ph.D. Dissertation Defense Department of Computer Science, University of Virginia

49. Backup slides

50. Assumptions Link capacity m = 1 Advance-reservation horizon K = 3 Number of classes L = 2 Holding time for class-1 calls h1 = 1 Holding time for class-2 calls h2 = 2 Number of options n = 1 System transition happens at the end of each timeslot Example: state (0, 0, 1) A call arrives and reserves the third timeslot -> state (0, 1, 1) Pr=(1/3)pr1 A call arrives and reserves the first timeslot -> state (1, 1, 0) Pr=(1/3)pr1 No call arrives or the arrived call is blocked -> state(0, 1, 0) Pr=1-(2/3)pr1 # of reserved channels 1 Time Current time t t+k (Backup slides) BA-n - Example of the analytical model for the BA-n scheme Ph.D. Dissertation Defense Department of Computer Science, University of Virginia