Power Controlled FCFS Splitting Algorithm for Wireless Networks

Transcription

1 Power Controlled FCFS Splitting Algorithm for Wireless Networks Ashutosh Deepak Gore Abhay Karandikar Department of Electrical Engineering Indian Institute of Technology - Bombay COMNET Workshop, July 2007

2 1 Introduction 2 System Model 3 PCFCFS Algorithm 4 Throughput Analysis 5 Performance Evaluation 6 Conclusion

3 Random Access in Wireless Networks Joint PHY-MAC design of wireless networks Choice of MAC depends on source traffic characteristics, wireless channel model and QoS requirements of users Random access protocols suitable for bursty traffic and higher # users Classification of random access protocols: Stabilized Aloha Carrier Sense Multiple Access Splitting/tree/stack algorithms FCFS splitting algorithm achieves a maximum stable throughput of We propose a power controlled splitting algorithm for wireless networks under the requirements of: realistic physical interference model transmission of ful packets in an FCFS manner

4 Assumptions Slotted system Poisson packet arrival process with rate λ Path loss wireless channel model Power-based capture: Packet transmission from transmitter t i to receiver r is ful if P i D β (t i,r) N 0 + M j=1 j i {0, 1, c, e} immediate feedback Gated channel access algorithm P j D β (t j,r) γ c All users are at the same distance D from the receiver

5 Motivation Generalization of high-throughput FCFS splitting algorithm to wireless networks Suppose all contending nodes transmit with equal power P: When only one node transmits, its packet reception is ful if P γ c N 0 D β When M 2 transmit, the SINR corresponding to i th transmission is SINR i = P D β N 0 + (M 1) P D β < 1 Since γ c > 1 in practice,all M transmissions are unful. In a wireless network, transmission power of a node provides an extra degree of freedom.

6 Motivation (cont d) With relatively small attempt rates, a collision is most likely between only two packets [Gallager] Collision between two nodes N 1 and N 2 can be avoided by using variable transmission powers: N 1 transmits with least possible power P 1 for a packet to be ful P 1 = γ c N 0 D β N 2 transmits with minimum power P 2 for its packet to be ful, in the presence of exactly one other node transmitting at nominal power P 1 P 2 = γ c (1 + γ c )N 0 D β Design a high-throughput random access algorithm incorporating this power control technique

7 Preliminaries Slot k := time interval [k, k + 1) For every slot k, packets that arrived in allocation interval [T (k), T (k) + φ(k)) are transmitted according to an algorithm φ 0 = maximum size of allocation interval a i = arrival time of i th packet P i (k) = transmission power of i th packet in slot k Every allocation interval is termed as a left (L) or right (R) interval PCFCFS algorithm is the set of rules by which the users compute allocation interval parameters and transmission power for slot k + 1 in terms of the feedback and allocation interval parameters for slot k

8 FCFS Interval Splitting Algorithm First Come First Serve splitting algorithm generate Poisson(λ) arrivals in [0, τ) T (1) 0; φ(1) min{φ 0, 1}; σ(1) R for k 1 to τ do transmit packets whose arrival times [T (k), T (k) + φ(k)) if feedback = e then T (k + 1) T (k); φ(k + 1) φ(k) 2 ; σ(k + 1) L elseif feedback = 1 and σ(k) = L T (k + 1) T (k) + φ(k); φ(k + 1) φ(k); σ(k + 1) R elseif feedback = 0 and σ(k) = L T (k + 1) T (k) + φ(k); φ(k + 1) φ(k) 2 ; σ(k + 1) L else T (k + 1) T (k) + φ(k); φ(k + 1) min{φ 0, k T (k)} σ(k + 1) R end if end for

9 PCFCFS Interval Splitting Algorithm Power Controlled FCFS splitting algorithm generate Poisson(λ) arrivals in [0, τ) T (1) 0; φ(1) min{φ 0, 1}; σ(1) R; feedback = 0 for k 1 to τ do if feedback c then packets whose a i [T (k), T (k) + φ(k) 2 ) assigned power P 2 packets whose a i [T (k) + φ(k) 2, T (k) + φ(k)) assigned power P 1 end if transmit packets whose a i [T (k), T (k) + φ(k)) if feedback = c then T (k + 1) T (k) + φ(k) 2 else same as FCFS end if end for φ(k) ; φ(k + 1) 2 ; σ(k + 1) R

10 Example allocation interval waiting interval k time T(k) P 1 P 1 T(k) + φ(k) current time allocation interval L R waiting interval k + 1 time T(k + 1) k + 2 T(k + 1) + φ(k + 1) current time allocation interval waiting interval RL RR time T(k + 2) P 2 P 1 T(k + 2) + φ(k + 2) current time allocation interval RLR waiting interval k + 3 time T(k + 3) P 1 T(k + 3) + φ(k + 3) current time

11 Methodology 1 Evolution of a Collision Resolution Period (CRP) can be represented by a Discrete Time Markov Chain (DTMC) 2 Every state in the DTMC is a pair (σ, i), where σ {L, L, R, R, C} and i is the number of times the original allocation interval has been split 3 Expected number of packets in an interval split i times = G i = 2 i λφ 0 4 Determine: 1 transition probabilities as functions of G 0 2 probability of entering any state (X, i) given that you start from (R, 0) 3 expected number of slots in a CRP 4 expected fraction of original interval returned to waiting interval

12 DTMC representation of a CRP idle idle L, 2 L, 3 L, 4... collision collision collision L, 1 L, 2 L, 3 L, 4... PL1,L2 PL2,L3 PL3,L4 idle/ collision PR0,R0 PR0,L1 capture R, 0 C, 1 PR0,C1 PC1,R0 PL1,R1 capture idle PL1,C2 PR1,L2 capture capture capture R, 1 C,2 R, 2 C, 3 R, 3 C, 4 R, 4... PR1,C2 PR2,C3 PR3,C4 PC2,R0 P R 2,R0 P L1,L 2 collision P L 2,R 2 PC3,R0 PR 3,R0 PL2,R2 PC4,R0 P R 4,R0 collision capture capture PR2,L3 P R 2,L3 PL2,C3 collision PL 2,L3 capture collision idle PL3,C4 collision collision PL 2,L 3 PL 3,L 4 PL 2,C3 PL PL2,L 3,L4 3 PL3,R3 capture capture capture collision PL 3,C4 PL 3,R 3 PL 4,R 4 PR 2,C3 P R 3,C4 R, 2 R, 3 R, 4... idle PR3,L4 PL3,L 4 PR 3,L4 PL4,R

13 Main Result Proposition The maximum stable throughput of the PCFCFS splitting algorithm is Also, the maximum stable throughput of the PCFCFS algorithm occurs when initial allocation interval = φ 0 = 2.54.

14 Framework We compare the performance of the following algorithms: FCFS with uniform power P 1 and φ 0 = 2.6 PCFCFS with variable power and φ 0 = 2.54 Let n suc denote the number of ful packets in [0, τ) and d i denote the departure time of the i th packet The performance metrics are: throughput = n suc τ average delay = average power = nsuc i=1 (d i a i ) nsuc i=1 n suc di k= a i P i(k) n suc

15 Throughput vs. Arrival Rate γ c = 7.0 db, N 0 = 90 dbm, β = 4.0, D = 100 m, P 1 = 0.5 mw, P 2 = 3.0 mw α 0 = 2.6 s, φ 0 = 2.54 s, τ = s 0.5 throughput (packets/sec) FCFS PCFCFS packet arrival rate λ (packets/sec) We use prototypical values of system parameters in wireless networks.

16 Delay vs. Arrival Rate average delay per ful packet (s) γ c = 7.0 db, N 0 = 90 dbm, β = 4.0, D = 100 m, P 1 = 0.5 mw, P 2 = 3.0 mw α x = 2.6 s, φ 0 = 2.54 s, τ = s FCFS PCFCFS packet arrival rate λ (packets/sec)

17 Power vs. Arrival Rate γ c = 7.0 db, N 0 = 90 dbm, β = 4.0, D = 100 m, P 1 = 0.5 mw, P 2 = 3.0 mw α 0 = 2.6 s, φ 0 = 2.54 s, τ = s 6 average power per ful packet (mw) FCFS PCFCFS packet arrival rate λ (packets/sec)

18 Observations Simulation results demonstrate that the maximum stable throughput of PCFCFS is between 0.55 and 0.56, i.e., they corroborate our main result. The PCFCFS algorithm achieves higher throughput and lower average delay than the FCFS algorithm, albeit at the cost of expending higher average power. At λ = 0.55, PCFCFS achieves 13.3% higher throughput and 96.7% lower average delay than FCFS.

19 Contributions Contributions of our work: We developed a new random access algorithm for wireless networks under the physical interference model. The proposed splitting algorithm, which varies the transmission powers of users based on quaternary channel feedback, achieves higher throughput and lower delay than the well known FCFS algorithm with constant transmission power. We show that the maximum stable throughput of PCFCFS is The proposed algorithm can be implemented in wireless networks whose users do not have stringent energy requirements, for example, fixed subscriber stations in a WiMAX network.

20 Future Work Future work: Variable user distances from the receiver Collision multiplicity in feedback Questions? Thank you.

21 Future Work Future work: Variable user distances from the receiver Collision multiplicity in feedback Questions? Thank you.