Communications and Network, 2013, 5, 426-429
http://dx.doi.org/10.4236/cn.2013.53B2078 Published Online September 2013 (http://www.scirp.org/journal/cn)
Copyright © 2013 SciRes. CN
Dropping Rate Simulation for a Handover Scheme Using
Importance Sampling*
Dong Liang, Gan Ding, Wuling Qin, Mugen Peng
Wireless Signal Processing and Network Lab, Key Laboratory of Universal Wireless Communications
(Ministry of Education), Beijing University of Posts and Telecommunications, Beijing, China
Email: liangdong@bupt.edu.cn, dinggan@bupt.edu.cn, qinwulin@bupt.edu.cn, pmg@bupt.edu.cn
Received June 2013
ABSTRACT
The process of changing the channel associated with the current connection while a call is in progress is under consid-
eration. The estimation of dropping rate in handover process of a one dimensional traffic system is discussed. To reduce
the sample size of simulation, dropping calls at base station is considered as rare event and simulated with importance
sampling - one of rare event simulation approaches. The simulation results suggest the sample size can be tremendously
reduced by using importance sam pling.
Keywords: Handover; Importance Sampling; Monte Carlo; Dropping Rate
1. Introduction
Handover is the process of changing the channel (fre-
quency, time slot, spreading code, or combination of them)
associated with the current connection while a call is in
progress [1]. Usually, continuous service is achieved by
supporting handover from one cell to another [2,3]. As
shown in Figure 1, it is often initiated eith er by crossing
a cell boundary or by deterioration in quality of the sig-
nal in the current channel [4].
The handover process starts when the power received
by the mobile station from a neighboring cell’s base sta-
tion (BS) exceeds the power received from the BS of the
current cell by a certain amount, called handover thre-
shold. This is the threshold in the received power, below
which acceptable communication with the BS of the cur-
rent cell is no longer possible [5]. If the power level from
the current BS falls below the receiver threshold prior to
the mobile being assigned to a channel by the target BS,
the call is terminated and the handover attempt fails.
Queuing priority schemes give possibility to reduce the
blocking probability of new calls, where the calls queuing
in handove r queues. Que uing pri ori ty channel assignment
strategy is described in [6]. Analysis of a mobile cellular
system with handover priority and hysteresis control is
given in [7].
Queuing of handover requests is possible, because the
mobile station spends some time in handover area, where
communications with the current BS decrease in depen-
dence of the speed of moving of the mobile station. Each
next request into the handover queue can be served ac-
cording to certain service discipline.
In nowadays broadband wireless networks probabilis-
tic parameters of Quality of Service (QoS) like probabil-
ity of dropped calls because all channels at the BS are
busy is very small, less than109. In such cases the Monte
Carlo simulation, which is implemented for probabilities
not less than 105 [8] is useless and for estimation of
handover QoS parameters as blocking probabilities is
suggested implementation of rare event simulation.
Rare event simulation helps to speed up the simulation
process, as studied probabilistic parameters of quality of
service have very small probability between 108 and 1012,
and they can’t be reached with standard Monte Carlo.
2. Modeling of Handover Scheme
A simplified handover mechanism is shown in Figure 2,
Figure 1. Handover in cell edge.
*This work was supported in part by the Fundamental
Research Funds
for the Central Universities (Research on efficient algorithm and con-
fidence probability in system level simulatio ns in wireless communica-
tions) (2012RC0113), the Stat e Major Science and Technology Special
Projects (Grant No. 2011ZX03003-002-
01, 2012ZX03001028), the
Beijing Natural Science Foundation (Grant No. 4131003).
D. LIANG ET AL.
Copyright © 2013 SciRes. CN
427
1
1
2
3
………
Handover Queue
2
3
………
N
A
B
v
Figure 2. Handover Scheme.
where A is the channel array for BS and B is the han-
dover queue. Here, the number of the BS channels is N,
and the hand over traffic coming rate for B is v.
For arbitrary time instant k, denote
()
i
ak
as
1, the -th channel is available
() 0, the -th channel is ocuppied
i
i
ak i
=
(1)
and denote
()
i
bk
to be the occupied time for the i-th
channel till time instant k,
()1, 2,
i
bk=
. The numerical
relations between
( 1)
i
ak+
and
can be written
as
[ ]
(1)( )
ii
akhb k+=
(2)
Usually, when
increase,
[ ]
Pr(1) 1
i
ak+=
also
increase, but unfortunately the closed form solution of h
is always hard to achieve.
Let
()xk
to be the total number of available channels
in time instant k, obviously
1
() ()
N
i
i
xka k
=
=
(3)
Let
()sk
to be the number of the incoming handover
traffic at time instant k, the average coming rate for han-
dover traffic is defined as
()vsfsds= ⋅
(4)
Here
()fs
is the probability density function (PDF)
of s.
If
() ()sk xk<
, all the incoming handover traffic can
be allocated with no latency, otherwise, some need to be
stored in Queue B temporarily and the number is
()() ()rksk xk= −
(5)
For Queue B, denote
()
j
dk
to be the waiting time for
the j-th element till time instant k. If
()
j
dk
α
(6)
thej-th handover traffic in Queue B is dropped at time
instant k, where
α
is the dropping threshold. The final
question here is to find the average dropping rate under
given conditions (included but not limited to N, v, α,
()h
, and
()f
), but unfortunately the closed form solu-
tion is hard to achieve, we always use Monte Carlo si-
mulation to find the numeric results.
3. Monte Carlo Simulation
By Monte Carlo method, the average dropping rate can
be estimated as
K
pL
=
(7)
Here L is the total number of handover traffic (also
called as sample size) and K is t he dropped n umber.
For the l-th sample, defi ne 2 -value variable
l
Z
as
1, the -th sample droped
0, else
l
l
Z
=
(8)
The average dropping rate p also can be expressed as
1
ˆ
L
l
l
Z
pL
=
=
(9)
The variance of p can be calculated as
2
ˆ2
11
11
LL
pl l
ll
D ZDZ
LL
σ
= =
 
= =
 
 
∑∑
(10)
If all the samples are independent,
2
ˆ
p
σ
can be simpli-
fied as
( )
2
ˆ2
11
(1 )
pl
p
LDZp p
LL
L
σ
=⋅⋅= ⋅⋅−≈
(11)
The accuracy of
ˆ
p
is always defined as
ˆ
ˆp
p
p
σ
ε
=
(12)
then
ˆ
11
p
K
pL
ε
= =
(13)
In order to assure the accuracy, for very small p, we
need to run large number of L to find enough K, which
means large amount of simulation time.
4. Improved Simulation Using Importance
Sampling
The most famous approach for rare event simulation is
Importance Sampling. Importance Sampling is connected
with change the probability density distribution for in-
creasing the frequency of appearance of more “signifi-
cant” for simulation events.
The basic purpose of this simulation technique is to
reduce dispersion or other estimation function, received
as a result of computer simulation. During the simulation,
process is expected to receive samples proportional of
their importance to expected results.
D. LIANG ET AL.
Copyright © 2013 SciRes. CN
428
The Importance Sampling estimators can receive in
advance given accuracy and in this way the simulation
time can be shorten. For generation of significant sample
is used limited number of independent variables with
normal distribution [9]. Then the conditional probability
of appearance of rare event is changed with conditional
probability of appearance less rare event with similar
distribution [10].
In this research, the average dropping rate p also can
be ex pressed as
() ()pq sfsds=
(14)
Where
()qs
is the probability for certain s.
By using importance sampling, the above equation can
be re-expressed as
()
() ()()
fs
pqsfsds
fs
=
(15)
Here
()fs
is the importance sampling PDF for s,
while
()
() ()
fs
ws fs
=
(16)
is the weighting f unction. Here, s follows negative expo-
nential distribution, and
()fs
is chosen to increase the
probability of dropping through change the exponent.
5. Simulation Results
The simulation parameter is shown in Table 1. The si-
mulation results between dropping rate p and average
handover traffic coming rate v is shown in Figure 3. It
can be seen p decreases with increasing of v.
The numerical relations between Monte Carlo simulation
sample size LMC and average handover traffic coming
rate v is shown in Figure 4. Here LMC is the least sample
size to assure the simulation accurac y of p is smaller than
10%.
Define sample size reduction efficiency as
MC
IS
L
L
β
=
(17)
the numerical relations between
β
and average han-
dover traffic coming rate v is shown in Figure 5. It can
be seen
β
decreases with increasing of v. Typically,
when
0.1v=
,
β
approaches to 104, which is a tre-
mendous reduction.
6. Conclusions
The processes of changing the radio channel associated
with the current connection, while a call in progress is
under consideration. A queue handover scheme for broad-
band mobile communication is suggested.
Table 1. Simulation parameter.
N 64
()f
negative exponential distribution
α 3
()h
negative exponential distribution
Figure 3. p ~ v.
Figure 4. LMC ~ v.
Figure 5. β ~ v.
A simulation approach using importance sampling for
estimation of probabilistic parameters of handover drop-
ping rate at broadband wireless networks with rare event
estimation is suggested.
D. LIANG ET AL.
Copyright © 2013 SciRes. CN
429
The simulation results show that the dropping rate de-
decreases with increasing of average handover traffic
coming rate v. By using importance sampling, the sample
size reduction efficiency
β
decreases with increasing
of v. typically, when
v
is very small and
β
appro-
aches a tremendous reduction.
REFERENCES
[1] C. H. M. De L ima, M. Bennis and M. Latva-aho, “Statis-
tical Analysis of Self-Organizing Networks with Biased
Cell Association and Interference Avoidance,IEEE
Transac- tions on Vehicular Technology, Vol. 62, No. 5,
2013, pp. 1950-1961.
[2] Y. Zhang, Handoff Performance in Wireless Mobile
Networks with Unreliable Fading Channel,IEEE Trans-
actions on Mobile Computing, Vol. 9, No. 2, 2010, pp.
188-200. http://dx.doi.org/10.1109/TMC.2009.115
[3] Q.-A. Zeng and D. P. Agrawal, Handoff in Wireless
Mobile Networks, Handbook of Wireless Networks and
Mobile Computing,” John Wiley & Sons, New York,
2002.
[4] H. Kwon, M.-J. Yang, A.-S. Park and S. Venkatesan,
“Handover Prediction Strategy for 3G-WLAN Overlay
Networks,” IEEE Network Operations and Management
Symposium, NOMS 2008, 2008.
[5] 3GPP TS 23.009: Handover Procedures.
[6] F. Tsvetanov, D. Radev, E. Otsetova-Dudin and S. Rade-
va, Rare Event Simulation for a Handover Priority
Scheme,” 20th Telecommunications Forum (TELFOR)
Belgrade, 20-22 November 2012.
[7] S. Radev and D. Radev, Modeling of Handover Priority
Schemes for Broadband Wireless Networks,” Interna-
tional Journal of Applied Research on Information Tech-
nology and Computing (IJARITAC), Vol. 1, No 3, 2010,
pp. 322-335.
http://dx.doi.org/10.5958/j.0975-8070.1.3.025
[8] J. Bucklew, “An Introduction to Rare Event Simulation.
Springer Series in Statistics,” Springer-Verlag, Berlin,
2004. http://dx.doi.org/10.1007/978-1-4757-4078-3
[9] E. Ivanova, S. Radeva and D. Radev, “Rare Events and
Quality of Services for IPv6 Networks,” Journal of Elec-
tro Techniques and Electronics, Vol. 46 No. 7-8, 2011,
pp. 12-17.
[10] A. Masmoudi, F. Bellili, S. Affes and A. Stephenne, “A
New Importance-Sampling-Based Non-Data-Aided Maxi-
mum Likelihood Time Delay Estimator,” IEEE Wireless
Communications and Networking Conference (WCNC),
2011, pp. 1682-1687.