Network Control Modelling and Analysis circuit-switched networks - PowerPoint PPT Presentation

1/37 Game Theory Bruno Tuffin Introduction: goals and methods Control in Network Control Modelling and Analysis circuit-switched networks Control in datagram networks Bruno Tuffin Control in virtual circuit switched networks INRIA Rennes - Bretagne Atlantique Conclusions PEV: Performance EValuation M2RI - Networks and Systems Track Rennes

2/37 Outline Game Theory Bruno Tuffin Introduction: goals and methods Introduction: goals and methods Control in 1 circuit-switched networks Control in Control in circuit-switched networks datagram networks 2 Control in virtual circuit switched networks Control in datagram networks 3 Conclusions Control in virtual circuit switched networks 4 Conclusions 5

3/37 Few references Game Theory Bruno Tuffin Introduction: goals and methods J. Walrand and P. Varaiya. High-Performance Communication 1 Control in Networks . Morgan Kaufmann Publishers, 2nd Edition, 2000. circuit-switched networks S. Keshav. An Engineering Approach to Computer Networking , 2 Addison-Wesley, 1997. Control in datagram networks Ferguson P., Huston G. Quality of Service: Delivering QoS on the 3 Control in virtual Internet and in Corporate Networks . John Wiley & Sons, Inc., circuit switched networks 1998. Conclusions F. Kelly. Models for a self-managed Internet. Philosophical 4 Transactions of the Royal Society A358, 2335-2348, 2000. L. Mamatas, T. Harks and V. Tsaoussidis. Approaches to 5 Congestion Control in Packet Networks. Journal of Internet Engineering , Vol.1, No.1, 2007. Network Traffic Modelling and Control 6 http://www.opalsoft.net/qos/ (very practical view).

4/37 Introduction Game Theory Bruno Tuffin Goal: describe concepts and techniques (from the Introduction: goals and methods modelling point of view) to control Control in Circuit-switched networks circuit-switched networks datagram (or packet-switched) networks (Internet) Control in virtual circuit-switched networks (ATM). datagram networks A proper control mechanism allows to carry more traffic Control in virtual circuit switched with the same quality of service (QoS). networks Conclusions Also related to capacity planning. Different ways to operate: admission control routing flow and congestion control resource allocation pricing (cf course on game theory and pricing). Non-exhaustive view! Just few illustrations.

5/37 Control methods Game Theory Different control methods at different time scales Bruno Tuffin Admission control (for circuit or virtual circuit switched Introduction: goals and methods networks) determine which connection request can be Control in accepted, depending on the network status. Can be circuit-switched networks delayed, or totally rejected. Control in Routing decides the path from source to destination. datagram networks Multicast or unicast can be envisaged. It can be Control in virtual circuit switched dynamic or static. networks Conclusions Congestion control (for datagram or virtual circuit switched networks), accelerates or slows down transmission according to congestion signals (ex: TCP). Can be seen as traffic shaping. Resource allocation (for virtual circuit switched networks) consists in controlling bandwidth and buffer allocated to a virtual circuit. This can also ba applied statically or dynamically. Pricing...

6/37 QoS Game Theory Bruno Tuffin There is a wide range of QoS levels, from very small Introduction: goals and methods loss probability and delay, to Best Effort, with, in Control in between, guaranteed bounded loss or delay. circuit-switched networks Example: in optical fibers: transmission error probability Control in 10 − 10 , and delay of 1 ms acceptable. datagram networks Control in virtual Best effort: we do our best, without any guarantee, it circuit switched networks depends on available resources. Conclusions In between, you may ask for some loss probability and/or average or max delay requirements. Defining the level of desired QoS depends on the application (Video, Audio, email, file transfer have very different requirements), and how stringent the user is (wireless users less stringent than fixed telephony...) Service differentiation can be applied.

7/37 Blocking in circuit-switched networks Game Theory Bruno Tuffin Introduction: goals Ex: telephone networks. QoS is the blocking probability and methods (all lines busy). Control in circuit-switched Designer problem: select the number of lines and networks switches, topology... Control in datagram networks If the network has K switches, L links, link i having C i Control in virtual circuit switched circuits. networks R routes, given by matrix A with A r , i = 1 if route r Conclusions goes through link i , 0 otherwise (fixed routing). Calls along route r : Poisson process with rate λ r , and exponentially distributed with rate µ r . State: n = ( n 1 , . . . , n R ) with n i number of active calls on route r . State space X = { n | � r r =1 n r A r , i ≤ C i ∀ i } .

8/37 Blocking and Loss models (2) Game Theory Bruno Tuffin Product-form solution (to be verified from the balance equations) ∀ n ∈ X : Introduction: goals and methods � n r � λ r R Control in π ( n ) = 1 µ r circuit-switched � networks G n r ! r =1 Control in datagram networks nr � λ r � R Control in virtual µ r with G normalizing constant, G = � . ✁ circuit switched n ∈ X r =1 n r ! networks From PASTA property, B r = � n : n r = C r π ( n ) . Conclusions Closed-form solution, but simulation needed for very large systems (complexity issue)! For generalities on loss networks: K.W. Ross, Multiservice Loss Networks for Broadband Telecommunications Networks , Springer-Verlag, 1995. Online at http://cis.poly.edu/~ross/LossNetworks/LossNetworks.htm . For an example of protocol design and performance analysis: P. Dietrich and R.R. Rao. Request Resubmission in a Blocking, Circuit-Switched, Interconnection Network. IEEE Transactions on Computers , Vol. 45, No. 11, 1996.

9/37 Blocking and handoff in wireless (2G) networks Game Theory Bruno Tuffin See G. Haring, R. Marie, R. Puigjaner, K.S. Trivedi. Introduction: goals Loss Formulas and their Application to Optimization for and methods Cellular Networks. IEEE Transactions on Vehicular Control in circuit-switched Technology , 50(3):664-673, 2001. networks Control in Exercice: datagram networks Consider a cell in a wireless (2G) cellular network. Control in virtual New calls arrive according to a Poisson process with rate λ 1 and circuit switched “handoff” calls, i.e., those coming from a change of cell but were networks already initiated, according to a Poisson process with rate λ 2 . Conclusions Each call (new or handoff) ends with rate µ 1 , but each call can also leave the cell (due to mobility) , with rate µ 2 . The number of channels is limited to n . When a handoff call arrives and a channel is free, the call is accepted, otherwise, it is lost. When a new call arrives, it is accepted only if at least g + 1 cahcannels are available, otherwise it is blocked. This allows a better QoS, with priority to handoff calls. The transition diagram is given as follows, where state k means k occupied channels. k n−g n 0 1

10/37 Handoff exercice: questions Game Theory What kind of process do we have? 1 Bruno Tuffin 2 Write the transition rates on the transition diagram. Let λ = λ 1 + λ 2 , µ = µ 1 + µ 2 , A = ρ = λ/µ and A 1 = λ 2 /µ . show that Introduction: goals 3 and methods steady-state probabilities are Control in A k circuit-switched π k = π 0 k ! if k ≤ n − g , networks A n − g Control in A k − ( n − g ) π k = π 0 if n − g + 1 ≤ k ≤ n , datagram networks 1 k ! Control in virtual with circuit switched 1 networks π 0 = . ✂ n − g − 1 ✂ n A k − ( n − g ) A k A n − g k ! + Conclusions k =0 k = n − g 1 k ! Using PASTA property, prove that the loss probability of a handoff call is 4 A n − g A g n ! 1 P d ( n , g ) = . ✂ n − g − 1 ✂ n A k − ( n − g ) A k A n − g k ! + k =0 k = n − g 1 k ! 5 From the same property, determine the blocking probability of a new call, i.e., that it is not accepted by the system. It is ✂ n A n − g A k − ( n − g ) k = n − g k ! 1 P b ( n , g ) = . ✂ n − g − 1 ✂ n A k A n − g A k − ( n − g ) k ! + k = n − g k =0 k ! 1 From this, we can find the value of g that maximizes a global cost 6 function.

11/37 Routing in circuit-switched networks Game Theory Bruno Tuffin Introduction: goals In our previous model with K switches, L links and R and methods routes, routes were fixed. Control in circuit-switched Now routing can be selected to minimize costs or networks maximize revenue. Control in datagram networks Static routing: Control in virtual circuit switched There may be several route r from point A to B . networks Revenue W = � r w r λ r (1 − B r ), with w r revenue for Conclusions route r . Goal: to partition call rates λ AB among routes r from A to B to maximize revenue. Optimization under contraints. Adaptive routing: Looks for an available route. Makes use of all available resource, but increases overhead.