Cellular Networks and Mobile Computing COMS 6998 -11, Fall 2012
Performability Analysis of Wireless Cellular Networks Center for Advanced Computing and...
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Transcript of Performability Analysis of Wireless Cellular Networks Center for Advanced Computing and...
Performability Analysis of Wireless Cellular Networks
Center for Advanced Computing and Communication
Department of Electrical and Computer Engineering
Duke University
Durham, NC 27705
Email: [email protected]: www.ee.duke.edu/~kst
Dr. Kishor S. TrivediSPECTS2002 and
SCSC2002, July, 2002
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Challenges in Wireless Networks
Limited radio spectrum Huge demand but limited bandwidth
Error-prone radio link Fading signal, less reliable link
High mobility Mobility management complicated
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Wireless “ilities” besides performance
Performability measures of the network’s ability
to perform designated functions
Reliabilityfor a specified operational time
Availabilityat any given instant
SurvivabilityPerformance under
failures
R.A.S.-ability concerns grow. High-R.A.S. not only a selling point for equipment vendors and service providers. But, regulatory outage
report required by FCC for public switched telephone networks (PSTN) may soon apply to wireless.
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Causes of Service Degradation
Resource full
Resource loss
Long waiting-timeTime-out
Service blocking
Service InterruptionLoss of information
LimitedResources
Equipment failures
Software failures
Planned outages(e.g. upgrade)
Human-errors in operation
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
The Need of Performability Modeling
New technologies, services & standards need new modeling methodologies
Pure performance modeling: too optimistic!Outage-and-recovery behavior not considered Pure availability modeling: too
conservative!Different levels of performance not considered
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang Loss Pure Performance Model
Let be the steady state probability for the Continuous Time Markov Chain
telephone switching system : n channels call arrival process is assumed to be Poissonian with rate
call holding times exponentially distributed with rate
j
Blocking Probability: nbP
Expected number of calls in system:
n
jjjNE
0
][
Desired measures of the form:
n
jjjrME
0
][
_
_
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang Loss Pure Availability Model A telephone switching system : n channels The times to channel failure and repair are exponentially distributed
with mean and , respectively./1
/1
Let be the steady state probability for the CTMCj
Steady state unavailability:
Expected number of non-failed channels:
Desired measures of the form:
0A
n
jjjNE
0
][
n
jjjrME
0
][
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Continuous Time Markov Chains are
useful models for performance as well as
availability prediction
Extension of CTMC to Markov reward
models make them even more useful
Attach a reward rate ri to state i of CTMC
X(t) is instantaneous reward rate of CTMC
Markov Reward Models (MRMs)
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Define Y(t) the accumulated reward in the interval [0,t)
Computing the expected values of these measures is easy
Markov Reward Models (MRMs) (Continued)
t
dXtY0
)()(
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Expected instantaneous reward rate at time t:
this generalizes instantaneous availability Expected steady-state reward rate:
this generalizes steady-state availability
Markov Reward Models (MRMs) (Continued)
i
ii trtXE )()]([
i
iirXE ][
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
MRM Measures Expected accumulated reward in
interval [0,t)
i
t
ii dxxrtYE0
)()]([
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
MRM: Measures Expected steady-state reward rate Expected reward rate at given time Expected accumulated reward in a given
interval Distribution of accumulated reward in a
given interval Expected task completion time Distribution of task completion time See for more detailsK. S. Trivedi, Probability and Statistics with Reliability, Queuing, and
Computer Science Applications, 2nd Edition, John Wiley, 2001.
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang loss composite model
A telephone switching system : n channels The call arrival process is assumed to be
Poissonian with rate , the call holding times are exponentially distributed with rate
The times to channel failure and repair are exponentially distributed with mean and , respectively
The composite model is then a homogeneous CTMC
/1 /1
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang loss composite model
The state (i, j ) denotes i non-failed channels and j ongoing calls in the system
CTMC with (n+1)(n+2)/2 states
Total call blocking probability:
Example of expected reward rate in steady state
State diagram for the Erlang loss composite model
1
1,,
n
iiinnb AT
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Total call blocking probability
1
1,,
n
iiinnb AT
Blocked due to buffer full
Blocked due to buffer full in degraded
levels
Blocked due to unavailability
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Problems in composite performability model
Largeness: Number of states in the Markov model is rather large
Automatically generate Markov reward model starting with an SRN (stochastic reward net)
Use a two-level hierarchical model Stiffness: Transition rates in the Markov
model range over many orders of magnitude Potential solution to both problems is a
hierarchical performability model
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang loss hierarchical model
Upper availability model
Lower performance model
The hierarchical performability model
provides an approximation of the exact composite model
Each state of pure availability
model keeps track of the number of non-failed
channels. Each state of the performance model
represents the number of talking channels in the
system Call blocking probability is computed from pure
performance model and supplied as reward rates to the
availability model states
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang loss model (cont’d) The steady-state system
unavailability
The blocking probability with i non-failed channels
Total blocking probability
Blocked due to buffer full
Blocked due to unavailability
(u)
)( li
(u)
A
1
1
)()( )()(n
i
uib
unb iPnPA
Blocked due to buffer full in degraded
levels
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Erlang loss model (cont’d)
Total blocking probability in the Erlang loss modelTotal blocking probability in the Erlang loss model
Compare the exact total blocking probability
with approximate result
Advantages of the hierarchical
Avoid largeness Avoid stiffness More intuitive No significant loss
in accuracy
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Total blocking probability Has three summands
Loss due to unavailability (pure availability model will capture this)
Loss when all channels are busy (pure performance model will capture this)
Loss with some channels busy and others down (degraded performance levels)
Performability models captures all three types of losses
Higher level, lower level model or both can be based on analytic/simulation/measurements
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Performability Evaluation (1) Two steps
The construction of a suitable model The solution of the model
Two approaches are used Combine performance and availability
into a single monolithic model Hierarchical model where lower level
performance model supplies reward rates to the upper level availability model
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Performability Evaluation (2) Measures of performability [Triv
01,Haver01]
Expected steady-state reward rate Expected reward rate at given time Expected accumulated reward in a given
interval Distribution of accumulate reward Expected task completion time Distribution of task completion time
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Handoffs in wireless cellular networks Handoff: When an MS moves
across a cell boundary, the channel in the old BS is released and an idle channel is required in the new BS
Hard handoff: the old radio link is broken before the new radio link is established (AMPS, GSM, DECT, D-AMPS, and PHS)
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Wireless Cellular System Traffic in a cell
A Cell
New Calls
Handoff Calls From
neighboring cells
CommonChannel
Pool Call completion
Handoff outTo neighboring
cells
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Performance Measures: Loss formulas or
probabilities When a new call (NC) is attempted in an cell
covered by a base station (BS), the NC is connected if an idle channel is available in the cell. Otherwise, the call is blocked
If an idle channel exists in the target cell, the handoff call (HC) continues nearly transparently to the user. Otherwise, the HC is dropped
Loss Formulas New call blocking probability, Pb : Percentage of new
calls rejected Handoff call dropping probability, Pd : Percentage of
calls forcefully terminated while crossing cells
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Guard Channel Scheme
Handoff dropping less desirable than new call blocking!
Handoff call has Higher Priority: Guard Channel Scheme
GCS: g channels are reserved for handoff calls.
g trade-off between Pb & Pd
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
#
Modeling for cellular network with hard handoff
#
g
g+1n
Stochastic Petri net Model of wireless hard handoff
Idle-channels
new
Handoff-in Handoff-out
Call-completion
Assumptions
Poisson arrival stream of new calls
Poisson stream of handoff arrivals
Limited number of channels: n Exponentially distributed
completion time of ongoing calls Exponentially distributed cell
departure time of ongoing calls
G. Haring, R. Marie, R. Puigjaner and K. S. Trivedi, Loss formulae and their optimization for cellular networks, IEEE Trans. on Vehicular Technology, 50(3), 664-673, May 2001.
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Markov chain model of wireless hard handoff
Steady-state probability
C(t): the number of busy channels at time t
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Loss formulas for wireless network with hard handoff
Dropping probability for handoff:
Blocking probability of new calls:
Notation: if we set g=0, the above expressions reduces to the classical Erlang-B loss formula
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Computational aspects Overflow and underflow might occur if n is large Numerically stable methods of computation are
required Recursive computation of dropping probability for
wireless networks Recursive computation of the blocking probability For loss formula calculator, see webpage: http://www.ee.duke.edu/~kst/wireless.html
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Optimization problems Optimal Number of Guard
Channels
Optimal Number of Channels
O1: Given n, A, and A1, determine the optimal integer value of g so as to
0)( that such )( minimize ddb PgPgP
O2: Given A and A1, determine the optimal integer values of n and g so as to
.0
0
),(
),( that such minimize
dd
bb
PgnP
PgnPn
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
#
#
g
g+1n
Stochastic Petri net Model of wireless hard handoff
Idle-channels
new
Handoff-in Handoff-out
Call-completion
Fixed-Point Iteration
Handoff arrival rate will be a function of new call arrival rate and call completion rates
Handoff arrival rate will have to be computed from the throughput of handoff-out transition
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Loss Formulas—Fixed Point Iteration A fixed point iteration scheme is applied
to determine the Handoff Call arrival rates:
We have theoretically proven: the given fixed point iteration is existent and unique
The arrival rate of HCs=the actual throughput of departure call leaving the cell
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Modeling cellular systems with failure and repair (1) The object under study is a typical cellular
wireless system The service area is divided into multiple cells There are n channels in the channel pool of a BS Hard handoff. g channels are reserved exclusively for
handoff calls Let be the rate of Poisson arrival stream of new calls and
be the rate of Poisson stream of handoff arrivals Let be the rate that an ongoing call completes service and
be the rate that the mobile engaged in the call departs the cell
The times to channel failure and repair are exponentially distributed with mean and , respectively.
/1 /1
1 2
1 2
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Modeling cellular systems with failure and repair (2) Upper availability model (same as
that in Erlang loss model)
The steady state unavailability
(u)A
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Modeling cellular systems with failure and repair (3) Lower performance model
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Modeling cellular systems with failure and repair (4) Solve the Markov Chain, we get
pure performance indices The dropping probability
The blocking probability
)()( iP ld
)()( iP lb
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Modeling cellular systems with failure and repair (5)
Total dropping probability
Total blocking probability
Loss probability (now call blocking or handoff call dropping) is computed from pure performance model and supplied as reward rates to the
availability model states
1
1
)()()()( ))(()(n
i
ld
ui
ld
und iPnPAT
1
1
)()()()(
1
)( ))(()(n
gi
lb
ui
lb
un
g
i
uib iPnPAT
Unavailability
Buffer full
Degraded buffer full
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov Reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Hierarchical model for APS in TDMA system (1)
Each cell has Nb base repeaters (BR)Each BR provides M TDM channelsOne control channel resides in one of the BRs
Control channel down
System down(!)
A TDMA Cellular System
Y. Cao, H.-R. Sun and K. S. Trivedi, Performability Analysis of TDMA Cellular Systems, P&QNet2000, Japan, Nov., 2000.
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Hierarchical model for APS in TDMA system (2)
Platform_down The controller or the local area network connecting the
base repeaters and controller going down causing the system as a whole to go down.
Control_downThe base repeater where the control channel resides going
down causing the system as a whole to go down.
Base_repeater_downAny other base repeater where the control channel does not
reside going down does not cause the system as a whole to go down, but system is degraded (partially down).
Failure in System
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Hierarchical model for APS in TDMA system (3)
Upon control_down, the failed control channel is automatically switched to a channel on a working base repeater.
control_down causes only system to go partially down
no longer a full outage!
Asys Pb Pd
Automatic Protection Switching
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Hierarchical model for APS in TDMA system (4)
High level: availability modelFailure/recovery of base repeaters, and platform of system
Lower level: performance modelNew call blocking probability and handoff call dropping
probability for a given number of working base repeaters
Combine togetherLower level performance measures as reward rates
assigned to states on higher level and finally the overall steady-state expected reward rate provides the total blocking (dropping) probability
2-level Decomposition
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Hierarchical model for APS in TDMA system (5)
0,Nb
0,00,b
1,Nb
1,01,b
High level - availability
Failure/recovery of base repeaters, and platform of
system
0 1 2 n-g-1 n-g n-g+1 n-1 n
Low level - Performance
New call blocking/handoff dropping
A birth-death process (BDP) n = Mb - 1 channels available
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Performability Indices
SystemUnavailabili
ty
Overall New Call
Blocking Prob.
Overall Handoff
Call Dropping
Prob.
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Numerical Results (1)
New Call Blocking
Probability
Improvement by APS
Unavailability in new call blocking
probability
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Numerical Results (2)
Handoff Call Dropping
Probability
Improvement by APS
Unavailability in handoff call
dropping probability
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Outline Overview of wireless mobile systems Why performability modeling? Markov Reward models Erlang loss performability model Modeling cellular systems with failure Hierarchical model for APS in TDMA Conclusion
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Conclusions Performability: an integrated way
to evaluate a real-world system Two approaches
Composite models Hierarchical models
CTMC and MRM models for performability study of a variety of wireless systems
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Future work Performability study in more general
systems Call holding times generally distributed
[Logothetis and Trivedi, submitted] Handoff interarrival times generally
distributed [Dharmaraja et al. spects 2002] multiple control channels and corresponding
fault-tolerant protection schemes other fault detection, isolation and
restoration strategies in cellular system
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
Future work Performability study in advanced
systems voice+data, multi-media wireless
system Differentiated QoS services over
multiple interconnected networks Packet-switched traffic: IP wireless
mobile system Survivability of cellular systems
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
References1. Y. Ma, J. Han and K. S. Trivedi,
Composite Performance & Availability Analysis of Wireless Communication Networks, IEEE Trans. on Vehicular Technology, 50(5): 1216-1223, Sept. 2001.
2. G. Haring, R. Marie, R. Puigjaner and K. S. Trivedi, Loss formulae and their optimization for cellular networks, IEEE Trans. on Vehicular Technology, 50(3), 664-673, May 2001.
3. K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition, John Wiley, 2001 (especially Section 8.4.3).
4. Y. Cao, H.-R. Sun and K. S. Trivedi, Performability Analysis of TDMA Cellular Systems, P&QNet2000, Japan, Nov., 2000.
5. H.-R. Sun, Y. Cao, K. S. Trivedi and J. J. Han, Availability and performance evaluation for automatic protection switching in TDMA wireless system, PRDC’99, pp15--22, Dec., 1999
6. http://www.ee.duke.edu/~kst/wireless.html
7. B. Haverkort et al, Performability Modeling, John Wiley, 2001
8. D. Selvamuthu, D. Logothetis, and K. S. Trivedi, Performance analysis of cellular networks with generally distributed handoff interarrival times, Proc. of SPECTS2002, July 2002.
Center for Advanced Computer and CommunicationDepartment of Electrical and Computer Engineering, Duke
University
The EndThank you!