Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multi-Channel Wireless Networks Nitin Vaidya Illinois Center for Wireless Systems University of Illinois at Urbana-Champaign September 5, 2007 Capacity of Multi-channel Wireless Networks with Random (c, f) Assignment Vartika Bhandari & Nitin H. Vaidya Motivation: Switching Constraints 915 MHz 2.4 GHz 5 GHz Increased push towards opening up spectrum for unlicensed use: Total available spectrum may be large, and divided into multiple (possibly non-contiguous) channels 60 GHz Devices may have only one or few interfaces; may not be able to switch over entire frequency range •Hardware limitations •Policy Issues Some Previously Proposed Models Adjacent (c, f) assignment Random (c, f) assignment Adjacent (c, f) Assignment Each node assigned a block location i from 1, 2, …, c-f+1 with prob. 1/c-f+1 each; can then switch on channels: i, i+1, .., i+f-1 For all channels i, Pr[ a node can switch on channel i] = min{i, c-i+1, f, c-f+1}/c Example: f=2, c=8 Random (c, f) Assignment Each node is assigned a random f-subset of channels Pr[ a node can switch on channel i] = f/c, for all i Example: f=2, c=8 Network Model 1 s(1) 3 s(2) … … 4 s(f) 6 5 … Each node has one interface … … n nodes randomly deployed over a unit area torus No. of channels c=O(log(n)) c orthogonal channels 2 c Each channel has bandwidth W/c Interface can switch between f channels 2≤f≤c Network Model Protocol Model [Gupta&Kumar] for interference X→Y transmission is successful if • XY ≤ r • ZY≥(1+Δ)r, for other concurrently transmitting Z Each node is source of exactly one flow Chooses its destination as node nearest to a randomly chosen point (same as in [Gupta&Kumar]) Avg. src-dst distance is Θ(1) Network Capacity lim Pr[ can guarantee each flow a throughput λ(n)=c1(f(n)) ] =1 but lim Pr[ can guarantee to each flow a throughput λ(n)=c2(f(n)) ]<1 Per flow capacity is Θ(f(n)) Factors Affecting Capacity Connectivity [Gupta&Kumar] D S D S Sufficient TX range: all SD pairs connected Small TX range: some node S isolated Interference [Gupta&Kumar] Each receiver “occupies” circle of radius Δr/2 ≤r ≥(1+Δ)r Δr/2 Δr/2 ≥(1+Δ)r ≤r Factors Affecting Capacity Interface Constraint [Kyasanur&Vaidya] In multi-channel case, if not enough interfaces, some channels unutilized Example: c=10; m=1; only 8 nodes in region; can use only 4 channels at a time Destination Bottleneck [Kyasanur&Vaidya] A node can be destination of multiple flows; restricts per-flow capacity New Factors Affecting Capacity (5, 7) (1, 4) (3, 4) (4, 5) (5,6) (4, 6) (5, 6) (3, 4) (1, 2) (4, 5) (6, 7) (3, 6) (6, 7) (7, 8) (1, 3) (6, 7) (2, 5) (4, 5) Connectivity A device can communicate directly with only a subset of the nodes within TX range Node isolated despite having other nodes in range Bottleneck Formation (1, 3) (1, 2) A B (1, 2) C (1, 2) D (1, 5) (1, 4) Both flows forced to use channel 1; cannot transmit concurrently Some channels may be scarce in certain network regions, leading to possible overload on some channels/nodes Prior Results at a Glance Unconstrained assignment Adjacent (c,f) Random (c,f) Use c channels Use f common channels Gap: Bounds did not match Recap of Prior Result: Sufficient Condition for Connectivity Want to show that any pair of nodes x, y are connected through some path Divide network into square cells of area y Choose r(n)=√(8a(n)) x For each node can construct a connected backbone spanning all cells Backbone(x): tree rooted at x Show that w.h.p. backbones for all nodes have a point of connection Connectivity Results No switching constraint f=Ω(√c) Adjacent (c,f) Random (c,f) f=c [Gupta-Kumar] : Convergence of Comm. Probability Random (c, f) Adjacent (c, f) Random (c, f) probability converges to 1 much faster than adjacent (c, f) probability Random (c, f) Assignment: Capacity Lower Bound A lower bound construction that achieves capacity Optimal Construction (1) Divide torus into square cells of area a(n) Every cell has Θ(na(n)) nodes w.h.p. r/√8 Cell Division based on [El Gamal] Optimal Construction (2) In each cell select nodes as “backbone candidates” The rest are deemed “transition facilitators” Optimal Construction (3) Notion of proper channels: A channel i is said to be proper in cell D if the number of backbone candidate nodes in cell D that can switch on channel i is at least By choice of cell-area a(n), the number of proper channels in any cell is at least: Optimal Construction (4) Utilizes a notion of “partial backbones” y x backbone(x) grows into cells traversed by flows for which x is either src or dst Flow’s packets proceed most of the way on src-backbone; when c2/f2 hops left to destination, try to jump onto dst-backbone If straight-line route too short, perform detour routing Ensuring Load-Balance Straight-line source-backbones grown in lock-step One hop at a time At each step, incremental load-balance ensured Inductive procedure Channel/Node assignment algorithm at each cell in each step involves computing matchings on a bipartite graph Growing Backbones Consider a backbone that must enter cell D in step i ? D Then its previous hop node must lie in an adjacent cell Need to select: 1. Channel on which to schedule incoming backbone link 2. Node in D that will act as next relay Channel Allocation D Link entering cell D Previous hop node u Link will be allocated a channel from amongst the channels proper in cell D that u can switch on; no. of such choices available to u is at least: Bipartite Graph for Allocating Channels to Links Entering D Channel allocation cast as problem of computing a matching that saturates all proved vertices in set L Existence of such a matching using Hall’s Marriage Theorem Set L: A vertex for each backbone-link entering the cell at this step If such a matching exists then each incoming link gets a channel and no channel gets more than k incoming links Set P : k vertices for each proper channel in the cell k= Relay-Node Allocation Suppose a link was allocated channel i for entering cell D in step i These nodes switch on channel i D Can again show via a matching argument that we can entering cell D allocate relayLink nodes ensuring that no node is assigned channel i links in step i more than 14onincoming Link will be allocated a relay node from amongst the nodes in cell D that can switch on channel i Since i is proper in D, the no. of possible choices is at least Mu Transmission Schedule Summing over all steps, can show that no channel or node gets overloaded in any cell of the network Destination/detour backbones can be grown without load-balance concerns Thereafter obtain a 2-level transmission schedule Coloring of cell-interference graph yields inter-cell schedule Within each cell-slot, obtain an intra-cell schedule via coloring a conflict graph of links to be scheduled The New Picture Prior Results No switching constraint Use c channels [Kyasanur-Vaidya] Adjacent (c,f) f=c Random (c,f) Recent Result Use f common channels Factor of improvement capacity is: √c-switchability yields order-optimal capacity √c-threshold Random (c, f) assignment At least in asymptotic sense: √c-switchability as good as full-switchability Interesting point of trade-off √c-switchability may cost less than full-switchability Might want to design systems around this operating point! Are there other assignment models that yield order-optimality with additional desirable properties? √c: reminiscent of distributed quorums [Maekawa] If willing to allow Θ(√c)-switchability, can leverage quorum ideas to get deterministic connectivity Some further work on this theme Insights Insight #1: There is a strong coupling between interface-selection at hop i and channel-selection at hop i+1, leading to a coupling across hops Insight #2: Two spatially proximate interfaces that both switch on channel i are not necessarily interchangeable; in smaller-scale networks, care is needed in both channel and interface selection Joint channel and interface selection problem at each link Practical Relevance 802.11a 802.11a Interface heterogeneity an increasingly likely scenario 802.11a/b/g 802.11a/b/g 802.11b/g 802.11b Similar issues will arise; insights from asymptotic constructions useful Ongoing/Future Work Heterogeneous multichannel wireless networks Non-asymptotic regime Forms of Heterogeneity Different operational channel sets: “Switching Constraints” Different number of interfaces at each node Channels with different data-rate/ propagation characteristics Time-variations in channel quality What kind of routing and link-layer protocols are needed to handle such scenarios? Alternative Interpretations Results can be viewed in context of random key predistribution Each node pre-assigned a random-set of keys Neighboring nodes can communicate only if they have a common preloaded key Network Utility Optimization in Multi-Channel Multi-Interface Networks Simone Merlin Nitin Vaidya Problem statement Resource allocation (Possibly joint/cross layer solutions) : Channel loading Interface to channel binding Transmission scheuling Congestion control Different approaches: Theoretical bounds (no algorithms) Practical heuristic protocols (no analytical properties) Practical algorithms with provable performance System model Utility maximization (network flow problem): Utiliy Flow conservation Rate region Algorithm overview The optimization problem is decomposed in subproblems: • Rate control • Channel allocation NEW CONTRIBUTION • Routing & Scheduling (interfaces to channel binding / trnsmission scheduling) A dynamic algorithm is used to solve each sub-problem Algorithm overview [Motivated by work of Srikant, Shroff] Rate control:. Queues length represent a ‘price’ for the rate allocation. Channel allocation: (vitual links allocation) local at each node Routing/Scheduling: Based on Backpressure algo [Tassiulas] Proposal: Algorithm Load the channel with the shortest queue, provided the difference beween input queue and channel queue is positive Back pressure algorithm Algorithm evaluation Scenario: grid/random topologies exclusive interference model • Scheduling becomes an NP-Hard problem. A greedy heuristic is used as scheduler in order to show the algorithm behavior » A lower bound on the value of the solution can be proved, » which depends on the interference degree. Logarithmic utility function: proportional fairness Performance are shown as a function of: Number of channels Number of interfaces Number of multihop traffic flows • • • Algorithm evaluation: Utility Grid totpology The algorithm shows the theoretically predicted behavior 2 interfaces are enough 4 interfaces are enough Algorithm evaluation: Rate Similar to the utility behavior Algorithm evaluation: Delay All this cases reach the maximum throughput More channels allow for a reduced delay Algorithm evaluation: Capacity Simulations results Asymptotic result Algorithm evaluation: Comparison Bounds Comparison with an upper bound in M. Kodialam and T. Nandagopal. Characterizing the capacity region in multi-raadio multi-channel wireless Networks, MobiCom, 2005. Our Algorithm Conclusions Algorithms/protocols with analytical basis need to be developed. The proposed algorithm a step toward this direction. Many other issues remain open: Reliable broadcast Efficient routing mechanism Practical protocol desing / overhead estimation Fully distributed scheduled More realistic interference models Rate and Carrier Sense Adaptation in Wireless Networks Zhongning Chen Nitin Vaidya Adaptive Rate and Carrier Sense Adaptation Dynamic adaptation can help improve spatial reuse Our prior work developed such an adaptive algorithm Continuing on this work: we have improved the adaptation algorithm to achieve better performance in fading environments Details in Zhongning Chen’s thesis Thanks! [email protected]