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Data rate and handoff rate analysis for user mobility in cellular networks
Conference Paper · April 2018
DOI: 10.1109/WCNC.2018.8377167
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Tokyo Institute of Technology
Tokyo Institute of Technology
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Data Rate and Handoff Rate Analysis
for User Mobility in Cellular Networks
Kiichi Tokuyama
Naoto Miyoshi
Tokyo Institute of Technology
Tokyo, Japan
tokuyama.k.aa@m.titech.ac.jp
Tokyo Institute of Technology
Tokyo, Japan
miyoshi@is.titech.ac.jp
Abstract—The expected data rate and the handoff rate are
important performance metrics in mobile wireless communications. In this paper, we consider a single-tier homogeneous
cellular network and provide a stochastic geometric framework
for analysis of the expected downlink data rate and the handoff
rate for a moving user equipment (UE). To investigate a tradeoff between frequent and infrequent handoffs, we consider two
scenarios, in one of which a UE experiences a handoff whenever
it crosses a boundary between two coverage areas of base
stations (BSs), and in the other a UE does not experience any
handoffs during a fixed period of time. In each scenario, we
derive analytical expressions for the two performance metrics
for a moving UE. From the analysis, we find that, when a UE
experiences a handoff whenever it crosses a boundary between BS
coverage areas, the expected downlink data rate per unit of time
is invariant from that for a static UE. On the other hand, when
a UE does not do during a fixed period of time, both the handoff
rate and the expected data rate depend on the distribution of
the moving speed even when its average is preserved. We expect
that our study can make a step forward in understanding data
transmission in the situation where UEs are moving with variable
speed.
Index Terms—Wireless networks, cellular networks, mobility,
data rate, handoff rate, stochastic geometry.
I. I NTRODUCTION
Theory of spatial point processes and stochastic geometry
has become a major tool for performance analysis of wireless
communication networks and numerous theoretical/practical
results have been developed so far. Among them, many studies
have analyzed the data rate for a user equipment (UE) in
various settings (see, e.g., [1]–[3]) as one of the primary
performance metrics. However, most of them assume that a
UE is fixed at a certain position. On the other hand, there
are studies concerning mobility of UEs in the framework of
stochastic geometry, which are rather involved in the handoff
rate (see, e.g., [4]–[6]). In terms of data transmission, it would
be better for a UE to be associated with a base station (BS)
offering higher data rate, which may encourage a moving
UE to have frequent handoffs. However, frequent handoffs
increase the risk of disconnection and signaling overhead. In
other words, there is a trade-off between the data rate and the
handoff rate when a UE is moving. Our goal in this paper is
to provide a framework for analysis of both the data rate and
the handoff rate for a moving UE in a cellular network.
As related work on stochastic geometric analysis of mobility
in wireless communications, we first take up Baccelli and
Zuyev [4], which is the first one to propose a use of spatial
point processes and stochastic geometry in the study of mobile
communications. They considered a single-tier homogeneous
cellular network, where BSs are arranged according to a homogeneous Poisson point process (PPP), and derived analytical
expressions for distributions of the number of active UEs in
the typical BS coverage area (cell) and of the number of
handoffs during a fixed period of time when a UE moves along
a straight line. Lin et al. [5] proposed a modified random
waypoint (RWP) model to describe mobility of a UE, and
applying this model to homogeneous networks, where BSs are
arranged according to a hexagonal grid or a homogeneous PPP,
they derived analytical results on the handoff rate for a UE and
the expected sojourn time in the typical BS cell. However, the
above results do not consider the data rate. Bao and Liang [6]
considered a multi-tier heterogeneous network configured by
overlaid independent homogeneous PPPs and derived exact
expressions for the intra-tier and inter-tier handoff rates for
a UE moving on an arbitrary trajectory. In addition, they
suggested an optimal tier selection by considering a balance
between the handoff rate and the expected downlink data
rate. In their setting, it is not necessary to take the speed
of a UE into consideration since a UE always follows a
stationary BS association (see Proposition 2 below and the
remark thereafter). After the current paper was accepted for
presentation, the authors encountered Chattopadhyay et al. [7],
which considers a two-tier heterogeneous cellular network,
where static UEs are associated with both macro and micro
BSs while mobile UEs are associated only with the macro
BSs, and gives analytical expressions for the data rate and the
throughput for static and mobile UEs when the mobile UE is
moving along a straight line.
In this paper, we consider a single-tier homogeneous cellular
network, where BSs are arranged according to a homogeneous
PPP, and following [6], we analyze the handoff rate and the
expected downlink data rate for a moving UE as performance
metrics. To investigate the trade-off between the two metrics,
we compare two scenarios, in one of which a UE experiences
a handoff whenever it crosses a boundary between two BS
cells, and in the other it does not do during a fixed period
of time. In each scenario, we derive analytical expressions for
the two performance metrics for a moving UE. Especially, we
find from our analysis that, when a UE experiences a handoff
whenever it crosses a boundary between BS cells, the expected
downlink data rate per unit of time is invariant from that for
a static UE in a stationary setting. On the other hand, when a
UE does not experience any handoffs during a fixed period of
time, both the handoff rate and the expected data rate depend
on distribution of the moving speed. The results of comparison
are demonstrated through numerical experiments.
II. S YSTEM M ODEL
A. Network Model
We consider a homogeneous cellular network, where all BSs
transmit signals with the same power level (normalized equal
to one) utilizing a common spectrum bandwidth. We adopt a
conventional assumption that the BSs are arranged according
to a homogeneous PPP Φ on R2 with intensity λ (∈ (0, ∞)),
where the points X1, X2, . . . of Φ are numbered in an arbitrary
order. We also assume Rayleigh fading and power-law pathloss on the downlinks, but ignore shadowing effects; that is,
when a UE at a position u ∈ R2 receives a signal from the
BS located at Xi ∈ Φ at time t, the received signal power is
represented by Hi,t |Xi − u| −β , where Hi,t , i ∈ N = {1, 2, . . .},
t ∈ N0 = N ∪ {0}, are mutually independent and exponentially
distributed random variables with unit mean (Hi,t ∼ Exp(1))
representing the fading effects, and β (> 2) denotes the pathloss exponent.
We suppose that, in the beginning, each UE is associated
with the nearest BS; that is, the BS cells form a PoissonVoronoi tessellation, a sample of which is illustrated in Fig. 1.
Due to the stationarity of the network model, it is no loss of
generality to focus on a UE which is assumed to be at the
origin at time zero and we refer to this UE as the typical UE.
Let bo denote the index of the nearest point of Φ from the
origin; that is, {bo = i} = {|Xi | ≤ |X j |, j ∈ N}. Then, the
probability density function of Rbo = |Xbo | is well known as
(see, e.g., Sec. 2.3 of [8])
fbo (r) = 2πλ r e−λπr ,
2
r ≥ 0.
(1)
We further suppose that UEs are moving on the twodimensional plane and a BS transmits a signal to each of its
serving UEs at every certain unit of time. When the typical
UE is at a position u ∈ R2 at time t ∈ N0 and is associated
with the BS at Xi ∈ Φ, the downlink signal-to-interferenceplus-noise ratio (SINR) of this UE is represented by
SINRu,i =
Hi,t |Xi − u| −β
,
σ 2 + Iu,i
(2)
where σ 2 denotes a positive constant representing the noise
power and Iu,i denotes the interference power to the typical
UE given by
∑
H j,t
Iu,i =
.
(3)
|X j − u| β
j ∈N\{i }
Then, the expected downlink data rate per unit of time is
defined as
τu,i (λ, β) = E[log(1 + SINRu,i )].
(4)
Fig. 1. A sample of Poisson-Voronoi tessellation.
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Fig. 2. An image of a UE’s trajectory in our mobility model.
B. Mobility Model for a Moving UE
We propose a simple and tractable random walk model to
describe the mobility of a UE. We assume that positions of
UEs are monitored at every fixed s units of time and refer
to each period of s units of time as a movement period.
Recall that the typical UE is at the origin at time zero. Let
{Y1, Y2, . . .} denote a sequence of independent and identically
distributed (i.i.d.) random variables on R2 . Then, the position
of the typical UE after n movement periods is given by the
two-dimensional random walk;
n
∑
Pn =
Yk , n = 1, 2, . . . ,
k=1
with P0 = o = (0, 0). During each movement period, we regard
it as moving on the line segment at a constant velocity; that
is, the velocity during the nth movement period is equal to the
vector Yn /s for n = 1, 2, . . .. A trajectory image of the typical
UE is illustrated in Fig. 2.
This random walk model is a little more restrictive than the
RWP model proposed in [5] but can capture different mobility
patterns by choosing the distribution of Yn . Let Yn = (Ln, ψn ) in
polar coordinates. If Ln is stochastically larger (resp. smaller),
then the speed of the UE is stochastically higher (resp. lower).
Also, if Ln is more (resp. less) variable, then the speed is also
more (resp. less) variable. Furthermore, if P(Ln = 0) > 0, it
can represent a pause of the UE in s units of time. On the other
hand, distribution of ψn represents the spread of a direction
change of the UE. For instance, if the distribution of ψn is
given by the Dirac measure δa with mass at a constant a ∈
[0, 2π), the UE always goes straight.
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III. H ANDOFF R ATE AND DATA R ATE A NALYSIS
In this section, we analyze the performance of transmission
provided to a moving UE. We investigate the handoff rate
and the expected downlink data rate for the typical UE in
the following two scenarios: Scenario 1 is that the typical UE
is always associated with its nearest BS. This implies that
the UE experiences a handoff whenever it crosses a boundary
between two BS cells. On the other hand, Scenario 2 is that
the typical UE does not experience any handoffs during a
movement period. After a movement period, if the UE has
crossed one or more boundaries of BS cells, then it experiences
a handoff and is associated with the nearest BS from the new
position. Throughout this section, we focus only on the first
movement period and fix the movement of the typical UE as
Y1 = (l, 0) for l ≥ 0; that is, the typical UE starts from the
origin and moves to (l, 0) in s units of time.
A. Handoff Rate Analysis
We define the handoff rate as the expected number of
handoffs experienced by the typical UE per movement period. Let N1 (l, λ) and N2 (l, λ) denote the handoff rates in
Scenarios 1 and 2, respectively. Clearly, N1 (l, λ) is evaluated
as the expected number of intersections of a line segment
with length l and boundaries of Poisson-Voronoi cells. On
the other hand, N2 (l, λ) is evaluated as the probability that the
line segment with length l has one or more intersections with
boundaries of Poisson-Voronoi cells.
Proposition 1: Consider Scenario 1 for the homogeneous
cellular network model described in the preceding section.
Then, the handoff rate of a UE moving through a distance l
is given by
√
4 λl
N1 (l, λ) =
.
(5)
π
Proof: Let Ξ denote a collection of midpoints of sides
constituting boundaries of Poisson-Voronoi cells generated by
Φ with intensity λ. Then, it is known that the intensity of Ξ is
3λ and the length √
of each side constituting a cell boundary
has its mean 2/(3 λ) (see, e.g., [9] and Chap. 9 in [8]).
Let ϕ (∈ [0, π)) denote the angle between the trajectory line
segment and a boundary side of a Poisson-Voronoi cell, and
let X denote the length of this boundary side. Then, the
trajectory crosses this boundary side if the midpoint of the
boundary side is in the parallelogram domain B with base l and
height X sin ϕ, as illustrated in Fig. 3. Now, let Ξx,ω denote
the point process consisting of midpoints of boundary sides
whose lengths and angles are in dx × dω. Regarding
Ξx,ω as )a
(
thinning of Ξ, its intensity is given by 3λ P (X, ϕ) ∈ dx × dω .
Then, the expected number of points of Ξx,ω in the domain B
with (x, ω) amounts to
(
)
E[Ξx,ω (Bx,ω )] = 3λ l x sin ω P (X, ϕ) ∈ dx × dω .
ŽŵĂŝŶ‫ܤ‬
Fig. 3. An image of parallelogram domain B.
Hence, integrating it over (x, ω) ∈ (0, ∞)×[0, π), we obtain the
right-hand side of√(5) since X and ϕ are mutually independent
with E[X] = 2/(3 λ) and ϕ ∼ U(0, π).
Note that our result (5) is consistent with the corresponding
ones in [5] and [6].
Theorem 1: Consider Scenario 2 for the homogeneous
cellular network model described in the preceding section.
Then, the handoff rate of a UE moving through a distance l
is approximated by
√
N2 (l, λ) ≈ 1 − e−N1 (l,λ) = 1 − e−4
λ l/π
.
(6)
Proof: Let Ξ and Ξx,ω as in the proof of Proposition 1.
Approximating Ξ and Ξx,ω as a PPP and its independent
thinning, we have the probability that there are no points of
Ξx,ω in the domain B with (x, ω) as
(
)
P(Ξx,ω (Bx,ω ) = 0) ≈ e−3λ lx sin ω P (X,ϕ)∈dx×dω .
Take distinct x1, x2, . . . , xn ∈ (0, ∞) and ω1, ω2, . . . , ωm ∈
[0, π). Then, Ξxi ,ω j (Bxi ,ω j ), (i, j) ∈ {1, 2, . . . , n}×{1, 2, . . . , m},
are mutually independent under our approximation and
(∩
)
n ∩
m
P
{Ξxi ,ω j (Bxi ,ω j ) = 0}
i=1 j=1
{
}
n ∑
m
∑
(
)
≈ exp −3λ l
xi sin ω j P (X, ϕ) ∈ dxi × dω j .
i=1 j=1
Hence, letting (n, m) → (∞, ∞) to cover the space (0, ∞) ×
[0, π), we have the probability that a line segment with length l
has no intersections with boundaries of Poisson-Voronoi cells
as
{
}
∫ ∞∫ π
(
)
exp −3λ l
x sin ω P (X, ϕ) ∈ dx × dω = e−N1 (l,λ),
0
0
which completes the proof.
B. Data Rate Analysis
Next, we consider the expected downlink data rate, which
we define as the expected amount of data received by the
typical UE per movement period; that is, per movement
through a distance l in s units of time. Let D1 (s, λ, β) and
D2 (l, s, λ, β) denote the expected data rate in Scenarios 1
and 2, respectively. Namely, the former represents that in the
case where the typical UE experiences a handoff whenever
it crosses a boundary between two BS cells, and the latter
represents that when the typical UE does not experience any
handoffs during the movement period. First, we provide a
formula for D1 (s, λ, β), which is derived by a direct application
of Theorem 3 in [1].
Proposition 2: Consider Scenario 1 for the homogeneous
downlink cellular network model described in Section II. Then,
the expected data rate of a UE moving through a distance l in
s units of time is given by
D1 (s, λ, β) = s τ1 (λ, β),
where
τ1 (λ, β) =
∫ ∞∫
0
with
0
∞
ρ1 (z, u, λ, β)
dz du,
1+z
(7)
(8)
{
( ) β/2
u
ρ1 (z, u, λ, β) = exp −σ 2 z
πλ
(
)}
∫
2z2/β ∞ v 2/β−1
−u 1+
dv .
β
1/z 1 + v
In Proposition 2, we can confirm that τ1 (λ, β) in (8) is equal
to the expected data rate for a static UE per unit of time
in a homogeneous downlink cellular network, considered in
Theorem 3 of [1].
Proof: Suppose that the typical UE is at a position u =
(u, 0), 0 ≤ u ≤ l, on the trajectory at time t. Note that u = lt/s
due to constant speed in a movement period. Let bu denote
the index of the nearest BS from the position u and let Ru =
|Xbu − u|. Then, from (2) and (4), the amount of received data
per unit of time at the position u is given by
(
)
Hb ,t Ru −β
ξ1 (u, β) = log 1 + 2u
,
(9)
σ + Iu,bu
it keeps to be associated with the BS that is the nearest from
the starting point.
Theorem 2: Consider Scenario 2 for the homogeneous
downlink cellular network model described in Section II. Then,
the expected data rate of a UE moving through a distance l in
s units of time is approximated by
∫
s l
D2 (l, s, λ, β) ≈
τ2 (u, λ, β) du,
(11)
l 0
where
τ2 (u, λ, β)
∫ 2π∫
=λ
0
s
[ ( lt )]
∑
D1 (s, λ, β) =
E ξ1 , β .
s
t=1
(10)
Since the point process Φ is stationary (the distribution is
invariant under translation), the distribution of Xbu − u is
identical to that of Xbo . Furthermore, since Hi,t , i ∈ N,
t ∈ {1, 2, . . . , s}, are i.i.d., Iu,bu and therefore ξ1 (u, β) in (9)
are identically distributed for any u. Thus, (10) reduces to
D1 (s, λ, β) = s E[ξ1 (0, β)].
The expectation on the right-hand side above is just the
expected data rate per unit of time considered in Theorem 3
of [1]. Hence, in the same way as the proof in [1] or using
Lemma 1 of [10]1 , we obtain (7) with (8).
Proposition 2 implies that, when a moving UE is always
associated with its nearest BS, the expected data rate per unit
of time is equal to that for a static UE in a homogeneous network. This comes from the stationarity assumption and similar
results would hold for more general stationary frameworks. A
consistent description is found in Remark 2 of [7].
On the other hand, we see a different result in Scenario 2,
where a UE is not always associated with its nearest BS, but
can obtain the same expression in either way.
0
∞
−λπr 2
∫
∞
re
0
ρ2 (z, r, θ|u, λ, β)
dz dr dθ,
1+z
(12)
ρ2 (z, r, θ|u, λ, β)
{
}
2π 2 λ
2π
= exp −σ 2 ru,boβ z −
ru,bo2 z2/β csc
,
β
β
and
and we have
1 We
Fig. 4. An example of relative positions of BSs and the typical UE.
√
ru,bo = r 2 + u2 − 2 ru cos θ.
(13)
Note that τ2 (u, λ, β) in (12) approximates the expected data
rate per unit of time for a UE at the position u = (u, 0), when
it is associated with the BS that is the nearest from the origin.
Proof: As in the proof of Proposition 2, we suppose that
the typical UE is at a position u = (u, 0), 0 ≤ u ≤ l, on the
trajectory at time t. Recall that Xbo denotes the nearest point
of Φ from the origin. Let Xbo = (Rbo , Θ) in polar coordinates.
Then, the distance from the typical UE to Xbo is given by
√
Ru,bo = |Xbo − u| = Rbo2 + u2 − 2Rbo u cos Θ,
where we should note that R0,bo = Rbo . An example of the
relative positions is illustrated in Fig. 4. The data rate per unit
of time received at the position u is given by
(
)
Hbo,t Ru,bo−β
ξ2 (u, β) = log 1 +
,
(14)
σ 2 + Iu,bo
and we have
D2 (l, s, λ, β) =
s
[ ( lt )]
∑
E ξ2 , β .
s
t=1
(15)
Note that, unlike the case of Scenario 1, the summand on the
right-hand side above depends on t, which makes its analysis
where ru,bo is given in (13). Applying Lemma 1 of [10] to the
conditional expectation on the right-hand side above yields
[ (
)
]
Hbo,t
E log 1 + 2
X
=
(r,
θ)
bo
σ ru,boβ + ru,boβ Iu,bo
∫ ∞
exp(−σ 2 ru,boβ z)
=
1+z
0
[
]
(
)
× E exp −ru,boβ z Iu,bo Xbo = (r, θ) dz,
(18)
where the Laplace transform E[e−z Hi, t ] = (1 + z)−1 is applied
due to Hi,t ∼ Exp(1). Furthermore, the expression of interference in (3) leads to
[
]
(
)
E exp −ru,boβ z Iu,bo Xbo = (r, θ)
]
[ ∏
) }
{
(r
u,b o β
Xbo = (r, θ)
=E
exp −z Hi,t
Ru,i
i ∈N\{b }
[ ∏o {
]
) β } −1
(r
u,b o
Xbo = (r, θ)
=E
1+z
Ru,i
i ∈N\{b o }
(
)
∫ ∞{
1 ( v ) β } −1
≈ exp −2πλ
1+
v dv ,
(19)
z ru,bo
0
where, we use the Laplace transform of Hi,t ∼ Exp(1),
i ∈ N \ {bo }, in the second equality, and in the last approximation, we apply the Laplace functional of a homogeneous
PPP by ignoring the information that there are no points of
Φ in the ball b(o, r) centered at o with radius r. Substituting
t = z−1 (v/ru,bo )β to the integral above, we have
∫
∫ ∞{
ru,bo2 z2/β ∞ t 2/β−1
1 ( v ) β } −1
1+
v dv =
dt
z ru,bo
β
1+t
0
0
π ru,bo2 z2/β
2π
=
csc
. (20)
β
β
Finally, plugging (17)–(20) into (16) leads to the result.
Note that, contrary to the expected data rate in Scenario 1,
D2 (l, s, λ, β) in (11) of Theorem 2 is a function of both l and s.
This implies that the expected data rate in Scenario 2 depends
on the speed of a UE during a movement period.
Remark 1: The Riemann approximation in (16), of course,
tends to be exact as s becomes large. In the other approximation in (19), we approximate the integral over R2 \ b(o, r) by
that over R2 . We note that a similar approximate approach is
often found in the literature (e.g., [11]). Figure 5 shows some
comparison results between numerically computed τ2 (u, λ, β)
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Since Rbo ∼ fbo in (1) and Θ ∼ U(0, 2 π), we have
∫ 2π∫ ∞
2
E[ξ2 (u, β)] =
λr e−λπr
]
)
[ (0 0
Hbo,t ru,bo−β
Xbo = (r, θ) dr dθ, (17)
× E log 1 +
σ 2 + Iu,bo
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ĐĂůĐƵůƵƐ;ɲсϰ͕ʄсϱͿ
Fig. 5. Comparison results between the approximate analysis of τ2 (u, λ, β)
and the mean of 10,000 independent samples of ξ2 (u, β) via simulation.
in (12) and the mean of 10,000 independent samples of ξ2 (u, β)
in (14) computed by Monte Carlo simulation. We can find
some gaps between the approximate analysis and simulation,
especially when the moving distance of the UE is small. On the
other hand, the gaps tend to be small as the moving distance
becomes large. We conjecture that this is because the impact
of the hole b(0, r) tends to be small as moving distance u
becomes large. Furthermore, we can see that the expected data
rate is smaller when the density λ of BSs is larger or the pathloss exponent β is smaller even when the moving distance u
remains the same. This would come from the fact that the
interference power increases as λ increases or β decreases.
IV. E VALUATION OF T RANSMISSION P ERFORMANCE
In this section, we evaluate the performance of transmission
for a moving UE on the basis of our analysis in the preceding
section. We here relax the condition of fixed moving distance
in the preceding section and consider random moving distance
in a movement period as in Section II-B. To evaluate the tradeoff between the handoff rate and the expected data rate, we
define a performance measure for Scenario 1 as
Q1 (s, λ, β) = UD1 (s, λ, β) − C E[N1 (L1, λ)],
where U represents the utility for one bit of data transmission and C denotes
√ the cost of a handoff. Note here that
E[N1 (L1, λ)] = 4 λ E[L1 ]/π from (5). Similarly, we define
a measure for Scenario 2 as
Q2 (s, λ, β) = UE[D2 (L1, s, λ, β)] − C E[N2 (L1, λ)].
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ǀĞƌĂŐĞǀĞůŽĐŝƚLJ;ŬŵͬŚͿ
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YŽ^ϭͺŝŶƚĞŐƌĂů
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YŽ^ϭͺĐŽŶƐƚĂŶƚ
YŽ^ϮͺĐŽŶƐƚĂŶƚ
ܳͳሺ‫ݏ‬ǡɉǡȾሻ
Fig. 6. A comparison result of Q1 and Q2 , where two cases of deterministic
L1 = l and exponentially distributed L1 with mean l are examined.
√
Note that E[N2 (L1, λ)] ≈ 1 − L L (4 λ/π) from (6), where
L L denotes the Laplace transform of L1 . We see that Q1
depends on L1 only through its mean while Q2 depends on the
distribution of L1 . We should also note that, since Li is i.i.d.
and the system model is stationary and isotropic, Qi (s, λ, β),
i = 1, 2, can evaluate the performance per movement period
over the whole trajectory.
Figure 6 shows a comparison result of Q1 (s, λ, β) and
Q2 (s, λ, β) for the two cases where L1 is deterministic and
where L1 follows an exponential distribution. There is only
one curve exhibited for Q1 because it depends on L1 only
through its mean. The abscissa of the figure denotes l = E[L1 ]
and the other parameters are set as (s, λ, β, σ 2, U, C) =
(100, 2, 4, 0, 1, 15). From the result, we find that, at least in this
parameter setting, it is always better for a UE to be associated
with the nearest BS. Furthermore, from the two curves of Q2 ,
we find that the performance of transmission is influenced by
the distribution of moving speed of a UE in Scenario 2 even
if the average speed remains the same.
V. C ONCLUSION
In this paper, we have investigated the performance of
transmission provided to a moving UE in a homogeneous
downlink cellular network. Modeling the movement of a UE
by a simple two-dimensional random walk, we have analyzed
the handoff rate and the expected downlink data rate in two
scenarios; that is, Scenario 1 is the case where a moving UE
is always associated with the nearest BS and Scenario 2 is the
case where a UE does not experience handoffs in a certain
movement period. We have found from the analysis that the
expected data rate per unit of time in Scenario 1 is invariant
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from that for a static UE, while both the handoff rate and the
expected data rate depend on the speed of a UE in Scenario 2.
Moreover, we have observed that the distribution of speed of
a UE has an impact on the performance of transmission in
Scenario 2 even if its average remains the same.
For further study, it would be expected to extend our
analysis to more realistic heterogeneous networks. On the
other hand, we have introduced some approximations in our
analysis, which cause some errors especially when a UE is
close to the starting point in Scenario 2. A kind of remedy
against these errors would also be expected.
Finally, we expect that our study can make a step forward
in understanding the data transmission in the situation where
UEs are moving with variable speed.
ACKNOWLEDGMENTS
The authors would like to thank Bartek Błaszczyszyn
kind discussion of the contents and for letting them know
reference [7]. The second author’s work was supported by
Japan Society for the Promotion of Science Grant-in-Aid
Scientific Research (C) 16K00030.
for
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for
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