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Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless Networks

Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless Networks. R. Srikant Coordinated Science Laboratory and Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Joint work with Jian Ni and Bo Tan. Wireless Networks.

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Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless Networks

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  1. Hybrid Q-CSMA: A Distributed Scheduling Algorithm for Wireless Networks R. Srikant Coordinated Science Laboratory and Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Joint work with Jian Ni and Bo Tan

  2. Wireless Networks • Links may not be able to transmit simultaneously due to interference. • Scheduling algorithm determines which links transmit at each time instant. • Performance metrics: throughput and delay. 5 2 9 7 1 4 6 8 3

  3. Throughput-Optimal Scheduling • A schedule is a collection of links that can be activated simultaneously. • MaxWeight Scheduling (centralized, high complexity) [Tassiulas-Ephremides ‘92] • Associate a weight with each link, equal to its queue length • Find schedule x which maximizes w(x); w(x): weight of a schedule x is the sum of the weights of the links in the schedule • Observation [Eryilmaz-Srikant-Perkins’05]: Throughput-optimal even under the following modification: pick the max-weight schedule with high probability, going to one as the weight of the MWS goes to infinity

  4. Distributed Algorithms • Jiang-Walrand (‘08): Distributed algorithms which pick schedule x with probability • Distribution realized using a continuous-time model. • Also see Boorstyn et al (‘87), Rajagopalan-Shah-Shin (’08). • Related work: Marbach, Eryilmaz, Ozdaglar (‘07) • Goal: Discrete-time model which explicitly models contentions and allows the algorithm to be combined with heuristics leading to dramatic delay reduction

  5. Modeling Assumption • Divide each time slot into a control slot and a data transmission slot: • Links contend in control mini-slots to determine a collision-free schedule in the data slot. • Collisions are allowed in the control mini-slots • A Key Result: Two control mini-slots are sufficient to achieve the product-form distribution. (Even one mini-slot is sufficient, thanks to Libin Jiang.) time slot t time slot t+1 control mini-slots data slot control mini-slots data slot

  6. Interference Graph • Each vertex in the interference graph represents a link in the network. • If two links interfere with each other, they are neighbors in the interference graph. • A feasible schedule: a set of nodes such that no two nodes have an edge between them • We consider one-hop traffic only. schedule x = {a, d, g} e b g g a a d d f c

  7. Basic Scheduling Algorithm • Step 1. In control slot t, select a “decision schedule” m(t): a set of links that may decide to change their state from the previous slot; other links cannot change their state • Step 2. For any link i in m(t) do • If no links in its conflict set N(i) were active in the previous data slot, link i will decide to become • active with probability pi: xi(t)=1 • inactive with probability 1-pi: xi(t)=0 • Else, link i will be inactive:xi(t)=0 • Step 3. In the data slot, use x(t) as the transmission schedule.

  8. Illustration of Scheduling Algorithm • Current schedule: {a, e} • Decision schedule, m(t): {c, f} • Allowed decisions for links in m(t): • Link c, xc(t)=0 (no choice) • Link f, xf(t)=1 (w.p. pi) • Other links’ states are unchanged. • New schedule x(t)={a, e, f} e e b g a a d f f f c c c

  9. Product-Form Distribution • Schedule Evolution is a Markov chain • Proposition 1. If the set of possible decision schedules includes all the links, then the DTMC is reversible and the steady-state probability of using schedule x is • Proof:  (x) p(x,y) = (y) p(y,x)

  10. Throughput Optimality • Choose pifor link i (whose weight is wi) as pi/(1-pi)=exp(wi), then the probability of choosing a schedule x with weight w(x)is given by Thus, a schedule with a large weight is picked with high probability. • Question: How to pick the decision schedule?

  11. Queue-Length Based CSMA (Q-CSMA) • Each time slot is divided into a data slot and control mini-slots • The control mini-slots are used to determine the decision schedule in a distributed manner; each link iselects a random control mini-slot Ti in [1,W]. • Roughly, the idea is that a link will send a message announcing its intent to make a decision during its chosen control mini-slot if it does not hear such a message from its neighbors. INTENT Message link i : Ti = 3 (W = 4) data slot control mini-slots

  12. Case 1 • If link i hears an INTENT message from a link in its neighborhood N(i) before its chosen mini-slot, it will keep its state unchanged from the previous time-slot. • If it was active in the previous time slot, it will continue to be active; will be inactive otherwise. INTENT Message link j : Tj = 2 control mini-slots data slot link i : Ti = 3 control mini-slots data slot

  13. Case 2 • Otherwise, link iwill broadcast an INTENT message to links in N(i) in the Ti-th control mini-slot. • Case 2: If there is a collision, link i will not change its state. INTENT Message link j : Tj = 3 control mini-slots data slot INTENT Message link i : Ti = 3 control mini-slots data slot

  14. Case 3 • If there is no collision, link i will make its decision: • If no links in N(i) were active in the previous data slot, then link i’s state is chosen as follows:active with probability piinactive with probability1-pi • Otherwise: inactive link j : Tj = 4 control mini-slots data slot INTENT Message link i : Ti = 3 control mini-slots data slot

  15. Key Property of Q-CSMA Proposition 2. The Q-CSMA algorithm achieves the product-form distribution if the window size W¸ 2. • Any maximal schedule will be selected as the decision schedule with positive probability. • The set of maximal schedules includes all the links. • Modification: Works even if W=1. A link chooses to participate in the decision schedule with probability ½. Again, one can show that the above result is still valid.

  16. Performance • Q-CSMA is a randomized algorithm, the delay performance can be bad • What are the alternatives? • MaxWeight algorithm: • Performance is very good; but high complexity, centralized implementation • Maximal matching: • Add links to the schedule till no more links can be added • Very low complexity; decentralized implementation?; throughput can be small in certain networks • Longest Queue First (LQF) or Greedy Maximal Matching (GMS)

  17. LQF/GMS • Algorithm: • add link with the longest queue to the schedule • Remove the added link and its “neighbors” from the graph and repeat • very low complexity; distributed implementation? • Networks that are unstable under maximal scheduling can be stable under LQF • Dimakis-Walrand, 2006; Brzezinski-Zussman-Modiano, 2006; Joo-Lin-Shroff, 2008; Leconte-Ni-Srikant, 2009 • Performance is very good in simulations; but not always provably throughput-optimal

  18. Hybrid Q-CSMA • Choose a weight threshold w0; choose a schedule with probability p(x) (defined previously) among those links whose weights exceed the threshold • Add additional links with weight smaller than the threshold, if possible, using a distributed approximation of the longest-queue-first policy • Key Result: the hybrid algorithm is still throughput optimal; Question: does it improve performance over Q-CSMA?

  19. Simulation Evaluation (1) 24-Link Grid Network (one-hop interference model)

  20. Simulation Evaluation (2) 9-Link Ring Network (two-hop interference model)

  21. Ongoing work • Performance of Hybrid Q-CSMA • Relationship between mixing time of the Markov chain and expected delays • Mixing time estimates are reasonable at light loads but not at heavy loads • w/ Jiang and Walrand • Paradigm shift: Finite-sized flows • Instability with fading (vande Ven-Borst-Schneer ‘09) • Very different algorithms are needed, somewhat surprisingly being greedy is good (Liu-Ying-Srikant ‘09) • Ad hoc networks are very different, w/ Shroff and Tan

  22. Ongoing Work • Paradigm shift: packets with deadlines • MaxWeight works here too!: Hou-Borkar-Kumar (‘09), Hou-Kumar (‘09), Hou-Kumar (‘09) • Derivation using purely optimization considerations: Jaramillo-Srikant ; allows extensions to ad hoc networks, fits into the dual decomposition view of network architecture (parallels the interpretation of the Tassiulas/Ephremides result in Lin/Shroff, Neely/Modiano/Li, Eryilmaz/Srikant and Stolyar) • GMS/LQF type ideas seem to work here too • TCP timeout and heavy-tailed file-sizes • Impact of wireless link losses on files with heavy-tailed distributed file sizes (w/ Towsley)

  23. Summary • Q-CSMA can achieve max throughput in wireless networks with a fully distributed implementation. • Performance can be improved dramatically by using a hybrid algorithm, combining Q-CSMA with approximations of longest queue first algorithm. • Ongoing work addresses extensions, and several other network control problems in complex wireless networks

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