Performability Modeling in Wireless Mobile Communication Systems

1
Performability Modeling in Wireless Mobile
Communication Systems
Yonghuan Cao

• Committee
• Dr. Kishor S. Trivedi (Chair)
• Dr. David J. Brady
• Dr. Krishnendu Chakrabarty
• Dr. Andrew J. Rindos
• Dr. Amin Vahdat

2
Agenda

• Introduction
• Motivation and objective
• Overview of all topics
• Selected topics (a post-prelim report)
• Performance of downlink scheduling
• Delay impact to capacity-on-demand
• Conclusion

3
A Little Modeling Philosophy

• 3 ways of system evaluation
• Measurement-based evaluation
• Most accurate
• Time-consuming expensive (System must exist!)
• Discrete-event simulation (Monte-Carlo)
• Long construction time long run-time
• Analytical modeling
• Less cost and shorter time
• May at the expense of accuracy believability

Every model is wrong! Some models are useful.
K. S. Trivedi
4
Wireless Mobile Challenges

• Restricted Spectrum
• Scarce bandwidth ( 10Kbps 100Kbps 4Mbps )
• Error-prone and Time-varying Link
• Channel fading, multiple path, building blocking,
  
• High mobility
• Needs mobility management
• Complex distributed location DBs
• Complicated by data services mobile IP
• Service diversity
• Traditional voice/paging
• Increasing demand for data services
  (email,stock,www, )

5
What Degrades Service?
Resource limit Channels, Buffer, Bandwidth,
Long waiting-time, Time-out, Service blocking,
Resource FULL
Outage-recovery Failures, Upgrades, Maintenance, H
uman-errors,
Incomplete service, Loss of information,
Resource LOSS
6
Performability Modeling

• New technologies, services standards needs new
  models
• Traditional performance model may not be
  applicable without proper treatment
• Pure performance modeling too optimistic!
• Outage-and-recovery behavior not considered

Performability modeling Performance
Availability Performability A more complete and
balanced picture Both steady-state and transient
solutions are informative
7
Modeling Background

• Stochastic Processes Used
• Discrete-time Markov Chains (DTMC)
• Continuous-time Markov Chains (CTMC)
• Semi-Markov Processes (SMP)
• Markov Regenerative Process (MRGP)
• Stochastic Formalism and Tools
• Stochastic Reward Nets (SRN)
• A Variant of Stochastic Petri Net (SPN)
• Automated Tool
• Stochastic Petri Net Package (SPNP)

8
Agenda

• Introduction
• Motivation and objective
• Overview of all topics
• Selected topics (a post-prelim report)
• Performance of downlink scheduling
• Delay impact to capacity-on-demand
• Conclusion

9
Overview of All Topics

• Availability bounds for systems w/
  non-exponential outages
• Performability of upgrade schemes in load-sharing
  clusters
• Performability of cellular control channel
  protection

• Uplink performance of wireless packet-switched
  data (GPRS)
• Performance of a wireless downlink scheduling
  policy
• The performance impact of access delay to
  capacity-on-demand multiple access

10
Availability Bounds of Systems with
Non-exponentially Distributed Outages
Y. Cao, H.-R. Sun and K. S. Trivedi, System
Availability with Non-exponentially Distributed
Outages, Submitted to IEEE Transactions on
Reliability (in review), 1999
11
The Problem

• Availability models preferred in practice assume
  that times to outage and recovery are
  exponentially distributed.
• How accurate will the all-exponential models be
  for systems w/ limited information of
  outage/recovery?
• Can we give availability bounds for such systems?

12
A General Availability Model

• For a system with multiple types of
  outage-recovery, the underlying stochastic
  process is a semi-Markov process (SMP).
• We give a close-form formula of system
  availability.
• Findings
• Only the mean value of time-to-recovery (ETTR)
  affects Asys. The distribution does not matter.
• However, the distribution of Time-to-outage (TTO)
  does affect availability.

13
Availability Bounds

• Availability bounds are given for systems with
  outages of which limited statistical information
  is known the bounds of Time-to-outage (TTO).
• AD(T1) lt AB(T1,T2) lt AD(T2).
• For systems with planned (bounded TTO) and
  unplanned outage (exponential), we give criteria
  to determine when the all-exponential model will
  underestimate or overestimate system availability.

14
Performability Analysis of Different Upgrade
Schemes in a Load-sharing Clustering System
Y. Cao, H.-R. Sun, K. S. Trivedi and J. J. Han,
Availability Evaluation for Redundant
Load-sharing Communication Systems with Planned
Outage under Different Upgrade Schemes,
Software, Telecommunications and Computer
Networks, (SoftCOM 2000), Croatia, Oct., 2000.
15
The Problem

• Load-sharing clustering is common in wireless
  networks and server systems.
• How to take advantage of the cluster structure
  and redundancy to upgrade hardware and software
  components?
• How to quantify system performance for different
  upgrade schemes?

Active node
Standby node
16
Upgrade Schemes

• Direct transfer
• Simple, but long downtime, for non-realtime-critic
  al system.
• Phased upgrade
• Almost zero downtime, upgrade paradox, version
  incompatibility, etc.

Baseline model
17
Performability Modeling and Optimization of
Cellular Systems with Control Channel Failure and
Automatic Protection Switch (APS)

• Y. Cao, H.-R. Sun and K. S. Trivedi,
  Performability Analysis of TDMA Cellular Systems,
  PQNet2000, Japan, Nov., 2000.
• H.-R. Sun, Y. Cao, K. S. Trivedi and J. J. Han,
  Availability and performance evaluation for
  automatic protection switching in TDMA wireless
  system, PRDC99, 15-22, Dec., 1999
• H.-R. Sun, Y. Cao, K. S. Trivedi and J. J. Han,
  Method and Apparatus for control channel
  restoration in cellular systems, patent filed by
  Motorola Patent Office in 2000 (Grant in process)

18
A TDMA Cellular System

• Each cell has Nb base repeaters (BR)
• Each BR provides M TDM channels
• One control channel resides in one of the BRs

19
Automatic Protection Switch

• Upon control_down, the failed control channel is
  automatically switched to a channel on a working
  base repeater.

20
Numerical Results
Handoff Call Blocking Probability Improvement
by APS
Unavailability in handoff call dropping
probability
21
Packet-level Performance Analysis of ALOHA
Reservation-based MAC in GPRS under Bursty Data
Traffic
Y. Cao, H.-R. Sun and K. S. Trivedi, Performance
Analysis of Reservation-based Media Access
Protocol with Access Queue and Serving Queue
under Bursty Traffic in GPRS/EGPRS, Wireless
Network (in review), January, 2001.
22
Background

• GPRS, a 2.5G system, to evolve todays TDMA-based
  GSM and tdmaOne towards 3G.
• Circuit-switched voice and packet-switched data
  services coexist. Voice has higher priority.
• Capacity-on-demand concept and multi-slot
  capability. Theoretical data rate up to 172 kbps.

23
Uplink Data Transfer

• Slotted-ALOHA Reservation Protocol
• Capture capability to reduce collision
• Access queue (AQ) to alleviate contention
• Serving queue (SQ)
• Cross the TDMA frame boundaries, dynamic channel
  allocation
• Bursty data traffic

24
The SRN Model
LLC arrival on-off
Finite buffer Connection
pmf of LLC frame size
The tagged mobile
The rest (N-1) mobiles
25
Model Accuracy
Simulation 95 CI Written in C
SRN Model Using SPNP
26
Components of Frame Delay

• Waiting time in access queue dominates delay (due
  to limited channel).
• Contention delay negligible due to AQ and
  capture.

27
Agenda

• Introduction
• Motivation and objective
• Overview of all topics
• Selected topics (a post-prelim report)
• Performance of downlink scheduling
• Delay impact to capacity-on-demand
• Conclusion

28
Performance of Queue Length Channel Quality
Based Wireless Scheduling Policies
Y. Cao, H.-R. Sun and K. S. Trivedi, Performance
of queue length and channel quality based
wireless scheduling policies, CACC Technical
Report, March, 2001.
29
The Problem
A
A Scheduling Scenario
B
Wired Network
C
c
a
b
In one time slot, only one of the three downlink
streams (A-a, B-b, C-c) is allowed to transmit!
Which to choose?
30
Another Look
Scheduler
a
b
c
Base Station
Incoming Traffic
Wireless Link
Terminals
31
Harder Than Wire-line
Wire-line scheduling always assumes error-free
links w/ high bandwidth.
c
a
b

• Wireless Link
• High error rates / bursty errors
• Location-dependent capacity
• Time-varying link quality
• Very low bandwidth

Wireless scheduling needs to consider
time-varying channel quality.
32
A Quality-aware Scheduler
a

• Two Schedulers
• Naïve Round Robin
• (NRR)
• Best-Quality-First
• (BQF)

Link Capacity _at_ t
b
c
time
NRR
Throughput under backlogged traffic
BQF
BQF Throughput Optimal!!
33
Problem with BQF
Starvation may occur to queues with low average
quality.
Good channel
Bad channels
Queues with bad channels blow up.
A scheduler needs to take into account not only
link quality but also queue length.
34
GWQL Scheduling
q1(t)
m1(t)
q2(t)
m2(t)
qn(t)
mn(t)
Generalized Weighted Queue Length (GWQL)
Scheduling Define score wi zi qi(t) mi(t), zi
gt 0 In each time slot, data is transmitted to the
mobile with the highest score. In case of tie,
one of them is randomly chosen.
35
What GWQL Can Be?
GWQL (Generalized Weight Queue Length)
wi zi qi(t) mi(t)
zi 1
WQL (Weighted Queue Length)
mi(t) m
qi(t) q
BQF (Best-quality-first)
LQF (Longest-queue-first)
36
What Makes a Good Scheduler?
Ideal Scheduler
GWQL
Simplicity Flow Isolation Optimal Throughput Uti
lization Heterogeneous QoS Guarantee
Yes. Only q-length and link-status! Depend on
traffic pattern? and channel variation? Yes.
Throughput Optimal! Tassiulas92, McKeown96,
Wasserman97 Need to set zi properly?
37
Need A Performance Model

• To study the performance impact of traffic
  burstiness and channel variation.
• To evaluate the capability of satisfying
  heterogeneous QoS requirements.

38
Traffic Model

• Traffic Model
• Markov Modulated Poisson Process (MMPP) FMH92
• Able to capture inter-arrival correlations
• Able to characterize traffic burstiness
• Yet still analytically tractable!

OFF
ON
ON
A 2-state MMPP traffic model
39
Channel Model

• Bursty-error Channel Model
• The well-known Gilbert-Elliot Model Gil60
• A two-state Markov chain (Good Bad)
• Extension to the GE model
• Finite-state Markov channel Wang95
• Model parameters can be derived from channel
• fading distribution and mobile speed.

a0
Bad
m2
Good
m1
a1
40
A Stochastic Petri Net Model
Building the Markov chain by hand is tedious and
not necessary. We use stochastic Petri net (SPN).
L
a0
s0
a1
a1
m (g)
l
Link model
Two-state MMPP Traffic
Finite Buffer
GWQL scheduling policy is embodied in the guard
function (g).
41
Measures of Interest

• Blocking Probability
• The probability that an arriving packet sees a
  full queue.
• Packet Delay
• The response time experienced by a packet
  accepted to the queue.
• Individual and System Throughput
• The amount of packets transmitted in a time unit.

42
Burstiness Effect
Blocking Probability
q1(t)
Poisson
m1(t)
q2(t)
MMPP
m2(t)
Same channels
Burstiness Measure of MMPP Index of Dispersion
for Counts (IDC) IDC 1 for Poisson IDC gt 1 for
MMPP
Burstiness (IDC)
43
Burstiness Impact
Packet Delay
Throughput
Burstiness (IDC)
Burstiness (IDC)
44
Channel Variation
Blocking Probability
q1(t)
Poisson
m1(t)
Poisson
q2(t)
m2(t)
Measure of Channel Variation Squared coefficient
of variation C2m Varm/Em2 C2m 1/a1 Bad
Duration, if Em fixed
Bad Duration
45
Effect of Channel Variation
Throughput
Packet Delay
Bad Duration
Bad Duration
46
Tuning GWQL
Performance of an individual mobile is
bounded Upper bound when zi ? very large,
the queue always has the highest priority,
served whenever queue is not empty. Lower
bound when zi ? very small, the queue always
has the lowest priority, served only when all
other queue are empty. Each bound is also
determined by the channel.
47
QoS Tuning Capability
Blocking Probability
z1
q1(t)
Poisson
m1(t)
Poisson
q2(t)
m2(t)
Identical Channels
z2
z2 /z1
48
GWQL Tuning Capability
Packet Delay
Throughput
z2 /z1
z2 /z1
49
GWQL Conclusion

• Traffic burstiness not only deteriorates one
  mobile, but also the rest mobiles sharing the
  same link.
• Traffic regulation is needed for flow
  isolation.
• Large channel variation has significant negative
  impact to all mobiles.
• Second-moment channel information may improve.
• Tuning capability is bounded. Performance
  appears sensitive to the values of zis.
• The model developed is useful in search for
  proper zi.

50
Agenda

• Introduction
• Motivation and objective
• Overview of all topics
• Selected topics (a post-prelim report)
• Performance of downlink scheduling
• Delay impact to capacity-on-demand
• Conclusion

51
The Effect of Access Delay in Capacity-on-demand
over a Wireless Link Under Bursty
Packet-switched Data
Y. Cao, H.-R. Sun and K. S. Trivedi,The Effect of
Access Delay in Capacity-on-demand over a
Wireless Link Under Bursty Packet-switched Data,
Performance Evaluation (submitted), March, 2001.
52
Problem Definition
Access Scenario
c
a
b
Radio resource (the number of channels) is
limited. A number of mobile with data to send
compete radio links. A mobile may experience
access delay. How does access delay affect
individual performance?
53
Capacity-on-demand
Todays common wireless data applications (www,
email, stock, )
Traffic A
Traffic B
Call (session) duration
For Traffic A, worth to dedicate a channel for
the entire call duration. For Traffic B, not a
good idea wasting resource in silent periods.
Capacity-on-demand to optimize the utilization
of radio links. Only establish connection when
having data to send, Release connection once data
is emptied.
54
Impact of Access Delay
Traffic
Packet may drop if access too long.
A Access Delay S Service
A
A
S
S
Connection
Access delay may cause buffer overflow, long
waiting-time, etc.
55
Cause of Access Delay

• Access delay is determined by a strongly coupled
  system
• The number of mobiles,
• Traffic pattern on each mobiles (user
  behaviors),
• Available radio resource (number of channels)
• The particular multiple access (MA) mechanism

The distribution of access delay is virtually
unknown and can be arbitrarily general.
56
Objective
Random variable A Access Delay Want to
understand 1. How the distribution (shape)
of access delay may affect performance. 2.
Is the mean value EA enough? 3. Can a
simple distribution (such as exponential) be
used for good approximation?
57
A Queueing Model
L
G/Activation
MMPP
MMPP/G/1/L with server activation
Note 1. MMPP arrivals Bursty traffic 2.
Service time (G) Arriving packets of diff.
sizes 3. Server activation (A) Link access delay
58
Exhaustive Principle
Once connection is established, all buffered data
and arrivals during the connection will be
transmitted. Connection is released immediately
after buffer is emptied.
59
Model Analysis
A state (l,s,m) l No. of packets in buffer
(0, 1, , L) s Server off/on (0, 1) m MMPP
state (1, 2, , M)
State-space based approach
60
2 Types of Transitions
MMPP Counting Process
Exponential Transition ?
Server off
Server on
General Transition --?
61
An MRGP
In a semi-Markov process (SMP), state does not
change between two consecutive regenerative
points. When a general transition is enabled,
the exponential transitions (of the MMPP counting
process) keep going on and state may change. The
process is more complicated than an SMP. It is a
Markov regenerative process (MRGP).
62
CTMC ? SMP ? MRGP
CTMC
SMP
state
state
t
t
T Exp
T Gen
T Exp
state
MRGP
t
T1 Gen
T1 Gen
63
MRGP Analysis
Two kernels Global Kernel K(t)
Kij(t) Kij(t) (t) PrY1 j, T1 lt t Y0
i Local Kernel E(t) Eij(t) Eij(t)
PrZ(t) j, T1 gt t Z(0) i Define V(t)
Vij (t), Vij (t) PrZ(t) j Y0
i V(t) E(t) K V(t)
64
Steady-state Solution
1. Steady-state solution of the embedded DTMC
with P K( )
2. The integral
Uniformization method used
3. The steady-state probability vector
4. Measures of interest can be derived from p
65
Measures of Interest

• Blocking Probability (Pb)
• The probability that an arriving packet sees a
  full queue.
• Packet Delay (t)
• The response time experienced by a packet
  accepted to the queue.
• Activation Rate (rA)
• Number of times that the server needs to set up
  per unit time. Overhead of capacity-on-demand.

66
Effect of Access Delay
1. Traffic model two-state MMPP
2. Service time pmf of packet size

• Distributions of Access delay
• Exponential
• 2-stage Erlang
• 3-stage Erlang
• Deterministic

67
Blocking Probability
Blocking probability
EA
68
Packet Delay
Mean Packet Delay
EA
69
Server Busy/Idle Time
Mean busy time
Mean Idle time
EA
EA
70
Effect of Traffic Pattern
Comparison of Poisson Arrival and MMPP (Same Ave.
Rates)
Mean Packet Delay
Blocking probability
EA
EA
71
Activation Rate
Poisson
MMPP
72
Access Delay Conclusion

• A general queueing model with server activation
  is used to study the impact of access delay to
  bursty wireless data applications.
• Have developed efficient numerical method to
  solve the model.
• From numerical results steady-state performance
  measures appear not very sensitive to the
  distribution of access delay.
• Good news for further system-level evaluation.

73
Agenda

• Introduction
• Motivation and objective
• Overview of all topics
• Selected topics (a post-prelim report)
• Performance of downlink scheduling
• Delay impact to capacity-on-demand
• Conclusion

74
Conclusion

• High-performance wireless systems
• Resource sharing
• GPRS uplink
• Downlink GWQL scheduling
• Capacity-on-demand
• Resource maintenance
• Availability bounds
• Redundancy and upgrade
• Control channel protection

75
The End Thank you!