Massive Random Access: Fundamental Limits, Optimal Design, and Applications to M2M Communications

Transcription

1 Massive Random Access: Fundamental Limits, Optimal Design, and Applications to M2M Communications Lin Dai Department of Electronic Engineering City University of Hong Kong March, 2018 Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to1 M2M / 64 C

2 Multiple Access Multiple nodes transmit to a common receiver: How to share the channel? Centralized Access: A central controller performs resource allocation/optimization. Random Access: Each node determines when/how to access in a distributed manner. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to2 M2M / 64 C

3 Applications of Random Access WiFi networks Cellular networks Sensor networks Machine-to-machine (M2M) communications, Vehicle-to-vehicle (V2V) communications, Internet-of-things (IoT),... Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to3 M2M / 64 C

4 Design of Random-Access Networks: Three Key Questions For each node: When to start a transmission? When to end a transmission? What if the transmission fails? Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to4 M2M / 64 C

5 Question 1: When to Start a Transmission? Transmit if packets are awaiting in the queue. Aloha [Abramson 1970] A more polite solution: Transmit if packets are awaiting in the queue and the channel is sensed idle. Carrier Sense Multiple Access (CSMA) [Kleinrock&Tobagi 1975] Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to5 M2M / 64 C

6 Question 2: When to End a Transmission? Stop when a packet transmission is completed. Any smarter solution? Stop when other on-going transmissions are sensed. What if nodes cannot sense the channel while transmitting? Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to6 M2M / 64 C

7 Question 3: What if the Transmission Fails? The definition of transmission failure depends on what type of receivers is adopted. Various assumptions on the receiver have been made, which can be broadly divided into three categories. Collision: When more than one node transmit their packets simultaneously, a collision occurs and none of them can be successfully decoded. A packet transmission is successful only if there are no concurrent transmissions. Capture: Each node s packet is decoded independently by treating others as background noise. A packet can be successfully decoded as long as its received signal-to-interference-plus-noise ratio (SINR) is above a certain threshold. Joint-decoding: Multiple nodes packets are jointly decoded. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to7 M2M / 64 C

8 Question 3: What if the Transmission Fails? Backoff if the transmission fails. Probability-based: Retransmit with a certain probability at each time slot. Window-based: Choose a random value from a window and count down. Retransmit when the counter is zero. In general, backoff can be characterized as a sequence of transmission probabilities {q t }, where q t denotes the transmission probability of the head-of-line (HOL) packet in each node s buffer at time slot t. It is usually assumed that the transmission probability q t is adjusted according to the number of collisions that the HOL packet has experienced by time slot t, i.e., q t = Q(i), where Q(i) is an arbitrary monotonic non-increasing function of the number of collisions i. With Exponential Backoff [Metcalfe&Boggs 1976], for instance, Q(i) = 2 i. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to8 M2M / 64 C

9 Massive Random Access Due to uncoordination among nodes, the access performance would quickly degrade as the network size increases if backoff parameters are not properly chosen. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, and March, Applications 2018 to9 M2M / 64 C

10 Massive Access of M2M Communications M2M communications is expected to become the dominant communications paradigm for a wide range of services in smart grid, transportation, health care, manufacturing and monitoring. Features of M2M communications Massive number of MTDs Infrequent transmissions Short packet payload How to efficiently facilitate the massive access from MTDs? Random access with optimized parameter setting Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

11 Performance Analysis of Random-Access Networks: Three Key Questions How to model a random-access network? How to evaluate the performance of a random-access network? How to optimize the performance of a random-access network? Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

12 Question 1: How to Model a Random-Access Network? A random-access network can be regarded as a multi-queue-single-server system. Numerous models have been proposed, which can be broadly divided into two categories: channel-centric and node-centric. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

13 Question 1: How to Model a Random-Access Network? Channel-centric modeling: to characterize the aggregate traffic of all the nodes. [Abramson 1970], [Kleinrock&Tobagi 1975],...: The aggregate traffic is modeled as a Poisson random variable. The aggregate traffic is determined by the input traffic and backoff mechanism of each node, which may not always be approximated as a Poisson random variable. Difficult to analyze the queueing performance of each node. Node-centric modeling: to characterize the queueing behavior of each node. [Tsybakov 1979]: A two-node buffered Aloha network is modeled as a 2-dimensional random walk. [Rao&Ephremides 1988], [Anantharam 1991],...: Generalization to an n-node buffered Aloha network. Modeling complexity quickly increases with the number of nodes. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

14 Question 1: How to Model a Random-Access Network? To establish a scalable node-centric model [Dai 12], [Dai 13]: Treat each node s queue as an independent queueing system with identically distributed service time. Characterization of the service time distribution includes two parts: State characterization of each individual head-of-line (HOL) packet; Fixed-point equations of steady-state probability of successful transmission of HOL packets. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

15 Question 2: How to Evaluate the Performance of a Random-access Network? Network Throughput: the average number of successfully transmitted packets of the network per time slot. Delay 1) Queueing delay (waiting time): the time interval from the packet s arrival to the instant that it becomes the HOL packet; 2) Access delay (service time): the time interval from the instant that it becomes the HOL packet to its successful transmission. Stability 1) The network is stable if the network throughput is equal to the aggregate input rate. 2) The network is stable if the mean access/queueing delay is finite.... Network Sum Rate: the average number of successfully transmitted information bits of the network per time slot. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

16 Question 2: How to Evaluate the Performance of a Random-access Network? To establish a unified theoretical framework within which effects of key system parameters on various performance metrics can be evaluated in a systematic manner: Aloha CSMA DCF M2M in LTE Network Throughput [Dai 12] [Dai 13], [Sun- Dai 16] [Dai-Sun 13], [Gao-Sun-Dai 13], [Gao-Dai 13], [Gao-Sun-Dai 14], [Sun-Dai 15], [Sun-Dai 16], [Gao- Dai-Hei 17] [Dai-Sun 13], [Sun-Dai 15], [Sun- Dai 16] Delay [Dai 12] [Dai 13], [Sun- Dai 16] Stability [Dai 12] [Dai 13] [Dai-Sun 13] [Zhan-Dai 18] Network Sum Rate [Li-Dai 16] [Sun-Dai 17] Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

17 Question 3: How to Optimize the Performance of a Random-access Network? Performance of random-access networks crucially depends on backoff parameters. With fixed backoff parameters, a random-access network suffers from significant performance degradation as the network size or the traffic input rates increase. For given network size and traffic input rate of each node, how to properly set the backoff parameters to optimize the network performance? Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

18 Question 3: How to Optimize the Performance of a Random-access Network? Network Throughput Optimization: Aloha: [Dai 12] CSMA: [Dai 13] DCF: [Dai-Sun 13] Finite Retry Limit [Sun-Dai 16] Heterogeneous [Gao-Sun-Dai 13], [Gao-Dai 13], [Gao-Sun-Dai 14] General Backoff [Sun-Dai 15] Finite Retry Limit [Sun-Dai 16] Multiple Access Points [Gao-Dai-Hei 17] M2M in LTE: [Zhan-Dai 18] Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

19 Question 3: How to Optimize the Performance of a Random-access Network? Delay Optimization: Aloha: [Dai 12] CSMA: [Dai 13] DCF: [Dai-Sun 13] Finite Retry Limit [Sun-Dai 16] General Backoff [Sun-Dai 15] Finite Retry Limit [Sun-Dai 16] Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

20 Question 3: How to Optimize the Performance of a Random-access Network? Network Sum Rate Optimization: Aloha: [Li-Dai 16] CSMA: [Sun-Dai 17] DCF: [Sun-Dai 17] Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

21 References L. Dai, Stability and delay analysis of buffered Aloha networks, IEEE Trans. Wireless Commun., vol. 11, no. 8, pp , Aug L. Dai, Toward a coherent theory of CSMA and Aloha, IEEE Trans. Wireless Commun., vol. 12, no. 7, pp , Jul L. Dai and X. Sun, A unified analysis of IEEE DCF networks: stability, throughput and delay, IEEE Trans. Mobile Computing, vol. 12, no. 8, pp , Aug Y. Gao, X. Sun, and L. Dai, Throughput Optimization of Heterogeneous IEEE DCF Networks, IEEE Trans. Wireless Commun., vol. 12, no. 1, pp , Jan Y. Gao and L. Dai, Optimal Downlink/Uplink Throughput Allocation for IEEE DCF Networks, IEEE Wireless Commun. Letters, vol. 2, no. 6, pp , Dec Y. Gao, X. Sun, and L. Dai, IEEE e EDCA Networks: Modeling, Differentiation and Optimization, IEEE Trans. Wireless Commun., vol. 13, no. 7, pp , July Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

22 References X. Sun and L. Dai, Backoff Design for IEEE DCF Networks: Fundamental Tradeoff and Design Criterion, IEEE/ACM Trans. Networking, vol. 23, no. 1, pp , Feb Y. Li and L. Dai, Maximum Sum Rate of Slotted Aloha with Capture, IEEE Trans. Commun., vol. 64, no. 2, pp , Feb X. Sun and L. Dai, Performance Optimization of CSMA Networks with A Finite Retry Limit, IEEE Trans. Wireless Commun., vol. 15, no. 9, pp , Sept X. Sun and L. Dai, Fairness-constrained Maximum Sum Rate of Multi-rate CSMA Networks, IEEE Trans. Wireless Commun., vol. 16, no. 3, pp , Mar Y. Gao, L. Dai and X. Hei, Throughput Optimization of Multi-BSS IEEE Networks With Universal Frequency Reuse, IEEE Trans. Commun., vol. 65, no. 8, pp , Aug W. Zhan and L. Dai, Massive Random Access of Machine-to-Machine Communications in LTE Networks: Modeling and Throughput Optimization, to appear in IEEE Trans. Wireless Commun. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

23 A Unified Theory of Random Access Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

24 Node-Centric Modeling An n-node buffered random-access network can be modeled as an n-queue-single-server system. Key assumption: Each node s queue can be regarded as an independent queueing system when the number of nodes n is large. Key steps: Characterization of each head-of-line (HOL) packet s state transition and steady-state probability of successful transmission of HOL packets. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

25 State Characterization of HOL Packet The state transition of each HOL packet can be modeled as a discrete-time Markov renewal process (X h,v h ) = {(Xj h,vh j ),j = 0,1,...}. The embedded Markov chain X h = {X h j } is: Without Sensing q 0 p t p t T 1-q0 p t p t p t R 1-p t 1-p 0 R t p t 1-p R t K-1 R K q 0 (1-p t ) 1-p t K: cutoff phase. The HOL packet stays at State R K if the number of transmission failures exceeds K. p t : probability of successful transmission of HOL packets at time slot t. lim t p t = p. q 0 : initial transmission probability of a fresh HOL packet. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

26 State Characterization of HOL Packet The state transition of each HOL packet can be modeled as a discrete-time Markov renewal process (X h,v h ) = {(Xj h,vh j ),j = 0,1,...}. The embedded Markov chain X h = {X h j } is: With Sensing T p t p t p t p t R 0 R 1... R K-1 R K pt 1-p 1 1 t 1-p t 1-p t 1 F 0 F 1... F K-1 F K The states of {Xj h } are divided into three categories: 1) waiting to request (State R i, i = 0,...,K), 2) failure (State F i, i = 0,...,K) and 3) successful transmission (State T). p t : probability of successful transmission of HOL packets at mini-slot t given that the channel is idle at t 1. lim t p t = p. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

27 State Characterization of HOL Packet The state transition of each HOL packet can be modeled as a discrete-time Markov renewal process (X h,v h ) = {(Xj h,vh j ),j = 0,1,...}. The mean holding time in each state: τ Ri : determined by the backoff scheme, i.e., transmission probability sequence {q i }. Without sensing: τ T = 1 time slot. With sensing: τ T and τ F vary under different system settings. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

28 Service Rate and Service Time Distribution For each node s queue, it has a successful transmission if and only if the HOL packet is in State T. Let { π i } denote the limiting state probabilities of the Markov renewal process (X h,v h ). Service rate: π i = π i τ i j S π j τ j, i S, S is the state space of X h. The node throughput is determined by the service rate when each node s queue is saturated. Let D i denote the time spent from the beginning of State i until the service completion. Service time distribution: The probability generating function of D i, G Di (z), can be calculated based on the Markov renewal process of HOL packet. The service time of each node s queue is also the access delay of each packet. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

29 Network Steady-state Points The network steady-state points are characterized based on the fixed-point equations of the limiting probability of successful transmission of HOL packets, p = lim t p t. Given that the network is in unsaturated or saturated conditions, different fixed-point equations of p can be established. The fixed-point equation of p in unsaturated conditions may have multiple roots, but not all of them are steady-state points. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

30 Network Throughput The network throughput is defined as the average number of successfully transmitted packets of the network per time slot. Network Throughput ˆλ out = { aggregate input rate nλ aggregate service rate n π T unsaturated saturated. The maximum network throughput: max {qi } ˆλ out. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

31 Access Delay The access delay of each packet is the service time of each node s queue. Moments of access delay can be obtained from the probability generating function of service time. The minimum mean access delay: min {qi }E[D]. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

32 Sum Rate The sum rate is defined as the average number of successfully transmitted information bits of the network per time slot. Let R denote the information encoding rate of each packet. The network sum rate R s = R ˆλ out. The maximum sum rate: max R,{qi }R s. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

33 Summary The key to node-centric modeling lies in proper characterization of 1) the state transition process of each HOL packet, and 2) the steady-state probability of successful transmission of HOL packets. Based on the proposed unified analytical framework, effects of key parameters on a wide range of performance metrics such as network throughput, access delay and sum rate, of various random-access networks can be evaluated in a systematic manner. The proposed analytical framework can further facilitate performance optimization to reveal the fundamental limits of random-access networks, and to show how to properly set the key system parameters to achieve the limiting performance. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

34 Application to WiFi (IEEE ) Networks Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

35 Distributed Coordination Function (DCF) of IEEE Networks Carrier Sense Multiple Access (CSMA) with Binary Exponential Backoff (BEB). Two access mechanisms: basic access and request-to-send/clear-to-send (RTS/CTS) access. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

36 Basic Access and RTS/CTS Access Basic Access: node A DIFS packet transmission SIFS ACK DIFS packet transmission DIFS node B DIFS busy channel DIFS packet transmission DIFS RTS/CTS Access: node A DIFS RTS SIFS CTS SIFS packet transmission SIFS ACK DIFS RTS DIFS node B DIFS busy channel DIFS RTS DIFS Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

37 Backoff Choose a random value from {0,...,W i 1}, where W i is the backoff window size after the i-th collision, i = 0,1,... Count down when the channel is idle. Binary Exponential Backoff (BEB): W i = W 2 min(i,k), where K is the cutoff phase. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

38 Modeling of IEEE DCF Networks Node-Centric Modeling State characterization of Head-of-Line (HOL) packet T p t p t p t p t R 0 R 1... R K-1 R K pt 1-p 1 1 t 1-p t 1-p t 1 F 0 F 1... F K-1 F K Characterization of network steady-state points is based on the fixed-point equations of limiting probability of successful transmission of HOL packets p = lim t p t. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

39 State Characterization of HOL Packets: State T State T: The HOL packet makes a successful transmission. Mean holding time τ T (in unit of time slots) at State T depends on the access mechanism. Basic Access: PHY MAC Packet Payload SIFS ACK DIFS τ Basic T RTS/CTS Access: = PHY+MAC+Payload+SIFS+ACK+DIFS slot time RTS SIFS CTS SIFS PHY MAC Packet Payload SIFS ACK DIFS τ RTS T = RTS+SIFS+CTS+SIFS+PHY+MAC+Payload+SIFS+ACK+DIFS slot time Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

40 State Characterization of HOL Packets: State F i State F i : The HOL packet experiences a failure. Mean holding time τ F (in unit of time slots) at State F i depends on the access mechanism. Basic Access: PHY MAC Packet Payload DIFS τ Basic F = PHY+MAC+Payload+DIFS slot time RTS/CTS Access: RTS DIFS τ RTS F = RTS+DIFS slot time Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

41 State Characterization of HOL Packets: State R i State R i : The HOL packet waits to request a transmission. Mean holding time τ Ri (in unit of time slots) at State R i depends on the backoff window size W i. t 1 W i t 1 W t i t W W i i B t t 0 B 1 B t 2... t B W 1 1 t 1 1 t 1 t 1 t 1 i τ Ri = 1 2α (1+W i), where α = lim t α t is the limiting probability of 1 sensing the channel idle, which is given by α = 1+τ F τ F p (τ T τ F )plnp. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

42 Network Steady-State Points Desired steady-state point p L ( {W 0 p L =exp ˆλ(1+τ F )/τ T 1 (1 τ F /τ T )ˆλ exp { }) } ˆλτ F /τ T ˆλτ F /τ T +. 1 (1 τ F /τ T )ˆλ 1 (1 τ F /τ T )ˆλ p L is determined by the aggregate input rate ˆλ, and the holding time in successful transmission and collision states, τ T and τ F. Undesired steady-state point p A When the network becomes saturated, it shifts to the undesired stable point p A, which is the root of the following fixed-point equation: p = exp W 2n ( ( p 2p p 2p 1 )(2(1 p)) K). p A is determined by the network size n and the backoff parameters, i.e., initial backoff window size W and the cutoff phase K. W 0 (.) is the principal branch of the Lambert W function. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

43 Maximum Network Throughput The maximum network throughput ˆλ max of IEEE DCF networks is ) 1 W 0 ( e(1+1/τ F ) ˆλ max = ). 1 τ F /τ T (1 τ F /τ T )W 0 ( e(1+1/τ F ) The optimal initial backoff widow size W m for achieving ˆλ max is ( ) 4(1+τ F) 1 τ F W 0 e(1+1/τ F ) 2 W m = n ( ) ( ( )). 1+τ F 1 τ F W 0 e(1+1/τ F ) ln 1+τ F 1 τ F W 0 e(1+1/τ F ) To achieve the maximum network throughput, the initial backoff window size should be linearly increased with the network size n. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

44 Maximum Network Throughput: Basic Access versus RTS/CTS Access Table : Parameter Setting (802.11n) Packet payload 4096B MAC header 36B PHY header 20µs ACK 14B+PHY header RTS 20B+PHY header CTS 14B+PHY header Slot Time 9µs SIFS 16µs DIFS 34µs Basic Rate 6 Mbps Data Rate 57.8 Mbps Basic Access τt Basic τf Basic ˆλ Basic = 75.7 time slots and = 69.5 time slots. max = = 10.4n. W Basic m RTS/CTS Access τt RTS τf RTS ˆλ RTS = 88.7 time slots and = 9 time slots. max = = 2.7n. W RTS m Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

45 Access Delay D 0 : Service time of HOL packets (which is also the access delay of packets). Based on the state transition of HOL packets, we can obtain the probability generating function G D0 (z), from which the n-th moment of D 0 can be derived, n = 1,2,... Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

46 Access Delay Mean Access Delay: j=i+1 E[D 0 ]=τ T + 1 p p τ F+ 1+τ F τ F p (τ T τ F )plnp 2 ( K 1 ) (1 p) i W i + (1 p)k W K + 1. p p i=0 Second Moment of Access Delay: E[D0]= 2 3+p 3αp ( ) ( 2 6α 2 p 2 + α +(2 p)τ (1 p)τf F p 2 + τ T + 2(1 p) τ F + 1 ) τ T p αp ( 1 α + 2α ) 2α 2 p +pτ T+(1 p)τ F (1 p) i W i + 1 ( τ F + 1 ) αp α 2α i=0 i=0 (1 p) j W j + 1 3α 2 (1 p) i Wi α 2 W i (1 p) j W j. i=0 i=0 j=i+1 Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

47 Mean Access Delay with BEB At the desired steady-state point p L 1 E[D 0,p=pL ] = τ T + 1+W 2. At the undesired steady-state point p A ( 1 p A E[D 0,p=pA ]= τ T +τ F +(1+τ F (1 p A ) (1 τ F )p A lnp A ) p A ( 1 + W ( ( 1 1 2p A 2 2p A ))) )(2(1 p A )) K. p A 2p A 1 E[D 0,p=pA ] is inversely proportional to the network throughput. min W E[D 0,p=pA ]= n ˆλ max, which is achieved when W = W m. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

48 Second Moment of Access Delay with BEB At the undesired stable point p A E[D 2,K= 0,p=p A ] = when W 4n 3ln n # of packets in the buffer capture time(s) Capture phenomenon: Some node captures the channel and produces a continuous stream of packets, while others have to wait for a long time. Poor queueing delay performance Short-term unfairness Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

49 Effect of Backoff In general, a backoff scheme can be characterized by a sequence of backoff window sizes {W i }. With a monotonic increasing sequence of backoff window sizes {W i }, the limiting growth rate of backoff window size is W i+1 lim 1. i W i Accordingly, we can divide the backoff schemes into two categories: Aggressive Backoff: lim i W i+1 W i > 1. Mild Backoff: lim i W i+1 W i = 1. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

50 Tradeoff between Throughput and Delay Theorem The maximum network throughput ˆλ max is given by ) 1 W 0 ( e(1+1/τ F ) ˆλ max = ). 1 τ F /τ T (1 τ F /τ T )W 0 ( e(1+1/τ F ) Corollary ˆλ max is achievable as n if and only if K = and lim i W i+1 W i > 1. Theorem If lim i W i+1 W i W lim i+1 i W i n > n. = 1, E[D 2,K= 0,p=p A ] < for any finite n < ; otherwise, if > 1, there exists n < such that E[D 2,K= 0,p=p A ] = when Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

51 Tradeoff between Throughput and Delay Both aggressive backoff and mild backoff have the same maximum network throughput ˆλ max, which is solely determined by the access mechanism, i.e., the basic access or the RTS/CTS access. With aggressive backoff schemes, the maximum network throughput can be achieved even as the network size n goes to infinity. But an infinite second moment of access delay may be incurred if the network size exceeds a certain threshold. Mild backoff schemes can reach a better balance: The maximum network throughput and a bounded second moment of access delay can both be achieved as long as the network size is finite. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

52 2 Comparison of BEB and Quadratic Backoff (QB): Fairness and Second Moment of Access Delay QB QB BEB EIED W=32 W=128 Analysis Simulation Analysis Simulation Simulation F t BEB EIED EILD(d=64) EILD(d=32) E [ D ] p p A 0, t (second) K Jain s Fairness Index F t versus time t in saturated IEEE DCF networks with BEB, QB, EIED and EILD. W = 32, K = 6 and n = 50. Second moment of access delay E[D 2 0,p=p A ] versus cutoff phase K in saturated IEEE DCF networks with BEB, QB and EIED. n = 50. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

53 Further Extensions From homogeneous to heterogeneous: Distinct traffic input rates: [Gao-Sun-Dai 13] Distinct priority levels: [Gao-Sun-Dai 14] Distinct data transmission rates: [Sun-Dai 17] From infinite retry limit to finite retry limit: [Sun-Dai 16] From single access point to multiple access points: [Gao-Dai-Hei 17] Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

54 Application to M2M in LTE Networks Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

55 Random Access Process of LTE Networks Connection-based Random Access In LTE networks, a connection would first be established between a device and the base station (BS) before the device starts to transmit its data packets. The connection-based random access adopted in the LTE networks differs from the conventional packet-based random access in that the data packets do not contend for the channel individually. Instead, each device with data packets to transmit first sends a connection request to the BS, and if a device s request is successfully received, then the BS will allocate resource blocks for the device to clear its data queue. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

56 Random Access Process of LTE Networks Periodical PRACH Subframes Orthogonal Preambles Each device randomly chooses one out of M orthogonal preambles. If more than one devices transmit the same preamble over the same PRACH subframe, then a collision occurs and all of them fail. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

57 Random Access Process of LTE Networks ACB Check and Uniform Backoff ACB check: Each access request is transmitted with probability q. That is, a random number between 0 and 1 is generated, and compared with the ACB factor q (0,1]. If the number is less than q, then the access request is transmitted. Otherwise, it is barred temporarily. Uniform Backoff: If an access request is transmitted but involved in a collision, then it randomly selects a value from [0,W], and counts down until it reaches zero. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

58 Network Throughput Focus on the average number of devices that can successfully access the BS per PRACH subframe. Network throughput is defined as the average number of successful access requests per time slot (a time slot is defined as the interval between two consecutive PRACH subframes). How to properly tune the ACB factor q and the uniform backoff window size W to maximize the network throughput? Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

59 Node-centric Modeling Double-queue Model of Each Device n Each device has one data queue and one request queue. Each newly arrival data packet generates an access request, but only one request can be kept since each device can have at most one ongoing access request regardless of how many data packets in its buffer. Upon successful transmission of the access request, the BS will assign sufficient resources for the device to clear its data buffer. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

60 Node-centric Modeling State Characterization of Access Request q 1 p / W t qp t 1 pt qp t 1 q q T 0 W 1 2 W p 1 t 1 q q W q 1 p / W t Characterization of network steady-state points is based on the fixed-point equations of limiting probability of successful transmission of access requests p = lim t p t. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

61 Maximum Network Throughput and Optimal Setting The maximum network throughput ˆλ M max = Me 1, where M is the number of orthogonal preambles. The optimal ACB factor q,m and uniform backoff window size W,M should satisfy ( ) e 1 q,m 2 W,M 1 = n M e 1 λ. (1) where n is the total number of devices, and λ is the traffic input rate of each device. W = 1: q,m W=1 = λ nλ M e 1. ( ) n q = 1: W,M 2 q=1 = M e 1 λ e 1 Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

62 Maximum Network Throughput and Optimal Setting 10 1 ˆM 10 1 max 10e ˆM 6 1 max 6e 10 0 *, M q qw 1 Analysis Simulation 10-1 M= *, M W Wq 1 Analysis Simulation ˆM out M=6 q 1, W 8 1 Analysis Simulation 10-5 q 0.5, W 21 Analysis Simulation n With the standard setting (fixed q and W): The network throughput quickly deteriorates as the number of devices n increases. With the optimal setting: The maximum network throughput ˆλ M max can always be achieved, which does not vary with the number of devices n. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

63 Summary The proposed unified analytical framework for random access has been successfully applied to WiFi and LTE networks. The modeling complexity is independent of the number of nodes even with the queueing behavior of each node taken into consideration, which is highly attractive in the massive access scenario. The analysis reveals how to optimally tune the backoff parameters based on the statistical information such as the traffic input rate of each node and the total number of nodes, which is crucial for random-access networks especially when the number of nodes is large. Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C

64 The End Thank You! Lin Dai (City University of Hong Kong) Massive Random Access: Fundamental Limits, Optimal Design, March, and Applications to M2M / 64 C