Stochastic Modeling and Analysis of Home Page Multichannel SW-ARQ - PowerPoint PPT Presentation

Stochastic Modeling and Analysis of Home Page Multichannel SW-ARQ Title Page ◭◭ ◮◮ ◭ ◮ Candidate: Jun Li, M.Sc. Supervisor: Dr. Yiqiang Q. Zhao Page 1 of 36 Go Back School of Mathematics and Statistics Carleton University Full Screen Close Quit

Outline Home Page ————————————————————————————————– Title Page 1. Motivations and List of Contributions ◭◭ ◮◮ 2. Models of Multichannel SW-ARQ ◭ ◮ 3. Resequencing Analysis of MSW-ARQ-inS Page 2 of 36 4. Packet Delay Analysis Go Back Full Screen 5. Conclusion and Future Work Close Quit

Wireless Ad-Hoc Data Networks ————————————————————————————————– Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 3 of 36 Go Back • Each node generates independent data Full Screen • Each node can communicate with its neighboring nodes Close • Data transmitted in packets are error-intolerable Quit • Unreliable wireless links (typically bi-directional) can cause packets to be lost or erroneously received

Automatic Repeat Request (ARQ) ————————————————————————————————– Home Page • A technique of recovering the lost and the erroneously received Title Page packets through retransmission of packets • Assumptions: ◭◭ ◮◮ 1. Bidirectional channels: forward and backward (feedback) ◭ ◮ 2. Reliable error detection scheme (e.g., cyclic redundancy check (CRC) code) Page 4 of 36 • Classical ARQ protocols: Go Back 1. Stop-and-wait ARQ (SW-ARQ) Full Screen 2. Go-back-N ARQ (GBN-ARQ) 3. Selective-repeat ARQ (SR-ARQ) Close Quit

Studies on ARQ over a Single Channel Home Page ————————————————————————————————– Title Page • A single channel connects two nodes (transmitter and receiver) ◭◭ ◮◮ • One ARQ protocol, SW-ARQ or GBN-ARQ or SR-ARQ, is used for packet error correction ◭ ◮ • Packet errors in the channel may either occur independently or be correlated over time Page 5 of 36 • ARQ protocols over a single channel with both time-invariant Go Back (e.g., [Anagnostou, Fantacci, Rosberg]) and time-correlated (e.g., [Badia, Kim, Vuyst]) error models have been extensively Full Screen studied Close Quit

Studies on ARQ over Multiple Channels ————————————————————————————————– Home Page • An arbitrary number of parallel channels connect the transmitter- receiver pair (e.g., a multiple-input multiple-output (MIMO) Title Page system) to increase data transmission rate ◭◭ ◮◮ • Multichannel ARQ protocols have been proposed to use in real- world communication systems ◭ ◮ • Assumption: error models of parallel channels are independent Page 6 of 36 of each other • ARQ protocols for the time-invariant error model of channels Go Back have been studied in [Chang, Ding, Fujii, Shacham, Wu], but far less completely Full Screen • No studies on ARQ over time-varying multiple channels have Close been reported Quit

List of Contributions Home Page ————————————————————————————————– Title Page • Stochastic modeling of multichannel SW-ARQ • Derivation of the probability generating function for the rese- ◭◭ ◮◮ quencing buffer occupancy ◭ ◮ • Derivation of the probability mass function of the resequencing delay Page 7 of 36 • Development of a systematic method for analysis of the packet Go Back delay • Identification of the impact on the model performance numeri- Full Screen cally and through simulation Close Quit

Outline Home Page ————————————————————————————————– Title Page 1. Motivations and List of Contributions ◭◭ ◮◮ 2. Models of Multichannel SW-ARQ ◭ ◮ 3. Resequencing Analysis of MSW-ARQ-inS Page 8 of 36 4. Packet Delay Analysis Go Back Full Screen 5. Conclusion and Future Work Close Quit

MSW-ARQ Model ————————————————————————————————– channel 1 Home Page channel 2 TX RX Title Page channel M ◭◭ ◮◮ feedback channel ◭ ◮ (M = 3, m = 5) Page 9 of 36 channel 1 6 4 4* 5 1 Go Back channel 2 TX RX 7 5* 5 2 6* Full Screen channel 3 Close 8 7 6 6 3 *, TX, RX denote transmission error,transmitter, receiver, respectively. Quit Integer numbers in boxes are sequence numbers of packets.

Model Description of MSW-ARQ ————————————————————————————————– 1. The transmitter is saturated with packets ordered by their se- quence numbers Home Page 2. Transmission rate for each channel is 1 packet per slot Title Page 3. Transmitter sends out M packets every m slots, one packet per (forward) channel ◭◭ ◮◮ 4. Packet transmitted over a channel could be erroneously received ◭ ◮ according to some channel error model (discussed next) 5. Acknowledgement packets (ACKs/NACKs) are sent via the Page 10 of 36 error-free feedback channel from receiver to transmitter Go Back 6. Transmitter retransmits the packet with the smallest sequence number among all erroneously received packets as well as pack- Full Screen ets with sequence numbers larger than that Close 7. Receiver only delivers a correctly received packet for which all packets ahead of it were received without an error to the upper Quit layer

MSW-ARQ-inS Model ————————————————————————————————– time tm (t+4)m (t+3)m (t+2)m (t+1)m Error detected and negligible time for sending NACKs Home Page channel 1 8 4* 4* 4 1 Title Page channel 2 ◭◭ ◮◮ TX 9 RX 5 5* 2 7 channel 3 ◭ ◮ 10 8* 7* 6 3 Page 11 of 36 6 5 6 contents of Go Back the resequencing buffer *, TX, RX denote transmission error,transmitter, receiver, respectively. Integer numbers in boxes are sequence numbers of packets. Full Screen Close 1. – 5. Same as MSW-ARQ 6. Only erroneously received packets are retransmitted Quit 7. The resequencing buffer is provided at the receiver for buffering undeliver- able packets

Channel Models & Packet Scheduling ————————————————————————————————– • Channel Model: defines the statistical property of transmission errors for a channel when transmitting packets 1. iid model: A time-invariant packet error rate is assumed for a Home Page channel Title Page 2. Markov model: Error rate is time-varying but determined by a two-state Markov chain ◭◭ ◮◮ • Packet Scheduling Policy: is a packet-to-channel assignment rule when transmitter simultaneously transmits M packets over ◭ ◮ M channels Page 12 of 36 1. Static scheduling policy: An old packet is retransmitted over the same channel as originally assigned one Go Back 2. Dynamic scheduling policy: The packet with the k th smallest Full Screen sequence number is assigned to the channel having the k th smallest error rate Close Note: Our analytical results are based the dynamic scheduling pol- Quit icy. Simulation results for the static scheduling policy are given for performance comparisons.

Outline Home Page ————————————————————————————————– Title Page 1. Motivations and List of Contributions ◭◭ ◮◮ 2. Models of Multichannel SW-ARQ ◭ ◮ 3. Resequencing Analysis of MSW-ARQ-inS Page 13 of 36 4. Packet Delay Analysis Go Back Full Screen 5. Conclusion and Future Work Close Quit

Resequencing for iid Channel Model ————————————————————————————————– • We assume the error rate of channel i is p i ∈ (0 , 1) ; p i might be different from p j for i � = j ; the M channels are numbered from 1 to M such that p 1 ≤ p 2 ≤ · · · ≤ p M Home Page • We define, Title Page 1 0 0 · · · 0   ◭◭ ◮◮ 0 · · · 0 P 10 P 11   · · · 0 P 20 P 21 P 22 P =  , (1) ◭ ◮   . . . ... . . . . . . . . .  P M, 0 P M, 1 P M, 2 · · · P M,M Page 14 of 36 Go Back and 1 0 0 · · · 0   Full Screen � 1 0 0 · · · 0 q 1 p 1 �  · · · 0  q 2 Q 21 Q 22 Close Q = =  . (2)   q T . . . ... . . . . . . . . .  Quit q M Q M 1 Q M 2 · · · Q MM

Resequencing for iid Channel Model (Cont.) ————————————————————————————————– • Let q k = 1 − p k , Ω i = { 1 , · · · , i } , B i,j is a subset of Ω i of size j , Home Page B c i,j = Ω i \ B i,j , � k ∈ Φ q k = � k ∈ Φ p k = 1 . Title Page • In (1), ◭◭ ◮◮   �  � �  . P ij = p k q k (3) ◭ ◮ k ∈ B c B i,j ⊆ Ω i k ∈ B i,j i,j Page 15 of 36 • In (2), Go Back   Full Screen � � �  . Q ij = p i p k q k (4)  Close k ∈ B c B i − 1 ,j − 1 ⊆ Ω i − 1 k ∈ B i − 1 ,j − 1 i − 1 ,j − 1 Quit