Analytic Modeling of Handoffs in Wireless Cellular Networks

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Analytic Modeling of Handoffs in Wireless
Cellular Networks
K. S. Trivedi, S. Dharmaraja, Xiaomin Ma

• Center for Advanced
• Computing and Communication
• Dept. of Electrical Computer Eng
• Duke University
• Durham, NC 27708-0294

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Outline

• Motivations
• Introduction Handoffs in wireless cellular
  networks and research issues
• Loss formulas and optimization for cellular
  networks without failures
• Loss formulas for cellular networks with failures
• Conclusions

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Motivation Objective

• Handoff is an important function of mobility
  management in wireless cellular networks
• Intense research efforts to achieve efficient use
  of scarce spectrum for cellular communications
  develop handoff schemes
• Characterize handoff problems Analytic models
  and simulation methods
• Closed form solutions to performance indices in
  wireless cellular networks with and without
  failures

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Wireless Cellular System Traffic in a Cell
Common Channel Pool
A Cell
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Handoffs in Wireless Cellular Networks

• Handoff When an mobile station (MS) moves across
  a cell boundary, the channel in the old base
  station (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

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Performance Measures Loss Formulas or
Probabilities

• When a new call (NC) is attempted in an cell
  covered by a 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

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Guard Channel Scheme

• Handoff dropping less desirable than new call
  blocking!

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Stochastic Petri Net Modeling
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.
Idle-channels
N
Assumptions
g1

• Poisson arrival stream of new calls
• Poisson stream of handoff arrivals
• Limited number of channels N
• Exponentially distributed complete time of on
  going calls
• Exponentially distributed cell departure time of
  ongoing calls

g

Call-completion
new

In-use
Handoff-out
Handoff-in
Stochastic Petri net Model of wireless handoff
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Markov Chain Model

• Set C(t) the number of busy channels at time t,
  we get Markov chain model
• Solve the Markov chain to get closed form
  solution for steady-state probabilities

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Blocking Dropping Formulae

• Notation if we set g0, the above expressions
  reduces to the classical Erlang-B loss formula

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Computational Aspects and Optimization Problems

• Overflow and underflow might occur if N is large
• Numerically stable methods of computation are
  required
• Recursive computation of dropping probability
• Recursive computation of blocking probability
• Optimization Problems for the Loss Formulas
• Monotonic properties of the loss formulas
• Optimal number of guard channels
• Optimal number of channels

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Loss Formulas Fixed Point Iteration

• A fixed point iteration scheme is applied to
  determine the Handoff Call arrival rate
• We have theoretically proved the given fixed
  point iteration exists and is unique

The arrival rate of HCsthe actual throughput of
handoff departures leaving the cell
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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

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Need 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
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Loss Formulas for Cellular Systems with Failures
Y. Cao, H. Sun, and K. S. Trivedi,
Performability analysis of TDMA cellular systems
based on composite and hierarchical Markov chain,
Proc. of PQNet2000 ,Japan, 2000.

• Each cell has Nb base repeaters (BR)
• Each BR provides M TDM channels
• One control channel resides in one of the BRs
• Control channel down leads to System down(!)
• Failures in System and recovery Automatic
  protection switching (APS)
• Platform_down
• Control_down
• Base_repeater_down

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Failures in Cellular Systems

• 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_down
• The base repeater where the control channel
  resides going down causing the system as a whole
  to go down.
• Base_repeater_down
• Any 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).

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Automatic Protection Switch

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

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Hierarchical Decomposition

• Parameters on different time scales ?
  stiffness
• Mean-time-to-failure months
• Recovery minutes or hours
• Call completion time minutes
• Call inter-arrival time seconds
• Hierarchical decomposition
• Numerically well-behaved, less time-consuming
• Good approximation

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2-level Decomposition

• High level availability
• Failure/recovery of base repeaters, and platform
  of system
• Low level performance
• New call blocking probability and handoff call
  dropping probability for a given number of
  working base repeaters
• Combine together
• Lower level performance measures as reward rates
  assigned to states on high level.

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Hierarchical Decomposition
High level - availability Failure/recovery of
base repeaters, and platform of system
0,Nb
0,0
0,b
1,Nb
1,0
1,b
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Decomposition High Level
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Decomposition Low Level

• Low level performance
• New call blocking probability and handoff call
  dropping probability for a given number of
  working base repeaters

A birth-death process (BDP) Conditioned on the
number of available BRs b n Mb - 1 channels
available
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Combination of two Losses Reward Rate Assignment

• Calls can be blocked (or dropped) due to system
  either being down or being full
• Possible Losses
• Channel failure Unavailabilitychannel shortage
• Limited channel resources Cell overload
• Combine two types of losses by reward rate
  assignment
• Closed form overall dropping and blocking
  probability

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Reward Rate Assignment (without APS)
State of High Level Availability Model
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Reward Rate Assignment (with APS)
State of High Level Availability Model
Assigning reward rates for system w/ APS
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Performability Indices
Overall New Call Blocking Prob.
Overall Handoff Call Dropping Prob.
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Numerical Results (1)
New Call Blocking Probability Improvement by APS
Unavailability in new call blocking probability
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Numerical Results (2)
Handoff Call Blocking Probability Improvement
by APS
Unavailability in handoff call dropping
probability
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Conclusions

• Loss formulas for wireless cellular networks with
  and without failures.
• Monotonic properties of the loss formulas are
  theoretically proven. Fixed point strategies are
  developed.
• Computational aspects and optimization problems
  are considered.
• Loss formula calculator
• http//www.ee.duke.edu/kst/wireless.htm
  l
• Further reading
• http//www.ee.duke.edu/kst/wireless.htm
  l

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The End Thank you!