Optimal Threshold Policy for Opportunistic Network Coding Under Phase Type Arrivals

100 Pages·2016·1.48 MB·English

Optimal Threshold Policy for Opportunistic Network
Coding Under Phase Type Arrivals
by
Charith Gunasekara
A dissertation submitted to The Faculty of Graduate Studies
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Electrical and Computer Engineering
The University of Manitoba
Winnipeg, Canada
April 2016
Copyright (cid:13)c 2016 by Charith Gunasekara
Dedicated to my parents.
Abstract
Network coding allows each node in a network to perform some coding operations on the
data packets and improve the overall throughput of communication. However, network
coding cannot be done unless there are enough packets to be coded so at times it may be
advantageous to wait for packets to arrive.
We consider a scenario in which two wireless nodes each with its own buffer communicate
via a single access point using network coding. The access point first pairs each data packet
being sent from each node and then performs the network coding operation. Packets arriving
at the access point that are unable to be paired are instead loaded into one of the two buffers
at the access point. In the case where one of the buffers is empty and the other is not
network coding is not possible. When this happens the access point must either wait for
a network coding opportunity, or transmit the unpaired packet without coding. Delaying
packettransmissionisassociatedwithanincreasedwaitingcostbutalsoallowsforanincrease
in the overall efficiency of wireless spectrum usage, thus a decrease in packet transmission
cost. Conversely, sending packets un-coded is associated with a decrease in waiting cost but
also a decrease in the overall efficiency of the wireless spectrum usage. Hence, there is a
trade-off between decreasing packet delay time, and increasing the efficiency of the wireless
spectrum usage.
We show that the optimal waiting policy for this system with respect to total cost, under
phase-typepacketarrivals, istohaveaseparatethresholdforthebuffersizethatisdependent
on the current phase of each arrival. We then show that the solution to this optimization
problem can be obtained by treating it as a double ended push-out queueing theory problem.
We develop a new technique to keep track of the packet waiting time and the number of
packets waiting in the two ended push-out queue. We use the resulting queueing model to
resolve the optimal threshold policy and then analyze the performance of the system using
numerical approach.
ii
Acknowledgments
I would like to express heartiest gratitude to my advisors Professor Attahiru S. Alfa and Pro-
fessor Pradeepa Yahampath for their continuous support, guidance and financial assistance
throughout my research tenure for the last 5 years at the University of Manitoba.
I would also like to thank my family and all my friends for their love and support which
helped me to achieve this stage.
iii
Table of Contents
List of Figures vi
List of Acronyms vii
1 Introduction 1
1.1 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Contribution and Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . 5
2 Background and Literature Survey 8
2.1 Network Coding Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Opportunistic Network Coding in Wireless Two Way Relay . . . . . . . . . . 16
2.3 Related Queueing Theoretic Analysis of Opportunistic Network Coding . . . 21
2.4 General Arrivals and Use of Phase Type Distribution . . . . . . . . . . . . . 23
3 Determining the Optimal Waiting Policy 26
3.1 System Model and Problem Statement . . . . . . . . . . . . . . . . . . . . . 27
3.2 Markov Decision Process for the System . . . . . . . . . . . . . . . . . . . . 28
3.3 Proof of the Optimal Threshold Policy . . . . . . . . . . . . . . . . . . . . . 31
3.4 Convexity of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5 Optimal Threshold Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Special Case of Systems with Unobservable Arrival Phase . . . . . . . . . . . 42
4 Discrete Time Markov Chain to Solve for the Optimal Thresholds 45
4.1 Arrival Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Service Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Discrete Time Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Solving the Discrete Time Markov Chain . . . . . . . . . . . . . . . . . . . . 54
4.5 Finding the Optimal Solution Using a Gradient Descent Algorithm . . . . . 57
5 Numerical Results 60
6 Conclusion and Future Work 72
6.1 Possible Future Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A Derivation of the rest of the DTMC in (4.3) 78
iv
Bibliography 81
v
List of Figures
1.1 Network Coding in a Butterfly Network . . . . . . . . . . . . . . . . . . . . . 2
1.2 Network Coding at an Access Point. . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Network Coding for Unicast Data . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Network Coding for Multicast Data . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Two Way Relay Access Point with Phase Type Packet Arrivals . . . . . . . . 27
3.2 Markov Decision Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1 Proposed Two Ended PH/PH/1 Queue: Push-out Senario . . . . . . . . . . 46
4.2 Proposed Two Ended PH/PH/1 Queue: Coded Packet Transmission . . . . 47
4.3 Level Dependant QBD Structure . . . . . . . . . . . . . . . . . . . . . . . . 55
5.1 Average Number of Waiting Packets in Each Queue: Queue 1: Arrival 2,
Queue 2: Arrival 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Average Waiting Time per Packet vs Buffer Size: Queue 1: Arrival 2, Queue
2: Arrival 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3 Average Number of Transmissions vs Buffer Size: Queue 1:Arrival 2, Queue
2: Arrival 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Comparison of Average Cost: Queue 1:Arrival 1, Queue 2: Arrival 3 . . . . 69
5.5 Comparision of Average Cost: (a) Arrival 1 and Arrival 2, (b) Arrival 1 and
Arrival 2, (c) Arrival 1 and Arrival 4 . . . . . . . . . . . . . . . . . . . . . . 70
5.6 Comparision of Coding Ratio (a) Arrival 1 and Arrival 2 (b) Arrival 1 and
Arrival 3 (c) Arrival 1 and Arrival 4 . . . . . . . . . . . . . . . . . . . . . . . 71
6.1 TDMA Wireless Start Network . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.2 Time Slot Arrangement of One TDMA Cycle . . . . . . . . . . . . . . . . . 74
6.3 Reduced transmittion time slots with network coding . . . . . . . . . . . . . 75
6.4 Proposed New Data Queues Pairs in the AP . . . . . . . . . . . . . . . . . . 75
6.5 Network Throughput vs M (N=30). . . . . . . . . . . . . . . . . . . . . . . . 76
vi
List of Acronyms
ANC Analog Network Coding
AP Access Point
COPE Opportunistic Coding Architecture
CPPA Coded Packets Priority Access
DMAP Discrete time Markov Arrival Process
DT Direct Transmission
DTMC Discrete Time Markov Chain
EM Expected Maximization
FIFO First In First Out
FSMH Four-Slot Multi Hopping
GDA Gradient Descent Algorithm
HBC Hybrid Broadcast
HoL Head of Line
MABC Multiple Access Broadcast
MAC Medium Access Protocol
MDP Markov Decision Process
vii
P2P Peer-to-Peer
PH Phase Type Distribution
PH/PH/1 Phase/ Phase/1 Server
QBD Quasi Birth Death
TCP Transport Control Protocol
TDBC Time Division Broadcast
TDMA Time Division Multiple Access
UDP User Datagram Protocol
viii