Minimizing the cost of two-tier cellular network with queuing handoff calls in microcell using genetic algorithm

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Minimizing the cost of two-tier cellular network with

queuing handoff calls in microcell using genetic

algorithm

Pankaj Goel

1

* and D.K. Lobiyal

2

Abstract

Call dropping probability is less desirable rather than call blocking probability for modeling of two tier cellular network design. To reduce call dropping probability queuing for handoff calls in microcell may be the one solution. Determining number of cells in each tier without compromising the quality can realize the network design as an optimization problem. In this paper, we have considered cost optimization problem of a two tier cellular network design. In this problemM/M/c/kqueuing model is used in microcell for hadling the handoff calls. A two dimensional Markov chain model has been developed to determine the steady state probabilities of number of calls served by macrocells and microcells. This optimization problem has been solved by using genetic algorithm. The results of the proposed solution are compared with the results of Simulated Annealing based algorithm using guard channel CAC without queuing.

Keywords

Cellular Network; Tier; Genetic Algorithm; Simulated Annealing; Markov Chain; GACN; Queuing model.

1,2_{School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi, Delhi 110067, India.}

*Corresponding author:[email protected];[email protected]

Article History: Received24December2017; Accepted21January2018 c2018 MJM.

1. Introduction

In last decade exponential growth has been seen in the inverse of mobile users. People show more interest in digital payment, mobile banking, digital news, and digital locker due to digital India program. New network operator like Jio comes in market. Due to policies of new operator there is

tremendous increase in mobile users which put pressure on bandwidth. There are many factors like Quality of service, lower power usages and ever- present mobile coverage play important role to select the mobile operator by the users.

Availability of limited frequency spectrum makes Quality of Service a challenging task. Therefore, Multi-tier network-ing becomes vital in providnetwork-ing QoS. To improve the spatial reuse of frequency spectrum multi-tier architecture plays an important role. The whole coverage area is covered by two tier of cells, one is macrocells and other is microcells. One macrocell has many microcells. Each cell has base station (BS) which control the cells and transmits signals to mobile terminals. According the transmission power constraints and availability of spectrum, a group of channels are assigned to each cell.

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probabilities are two important Quality of Service measures.

In this paper, we are usingM/M/c/kqueuing model in

microcell for handoff calls with guard channel CAC. We are presenting two-tier cellular networks problem as an optimiza-tion problem with call blocking, call dropping probability in microcell and macrocell and number of microcell covered by a macrocell assumed as an odd integer as constraints and minimizing the implementation cost of the network. We are

using GACN [6] to solve the optimization problem .

The remaining of the paper is as follows. Research work related to two-tier cellular network carried out in the literature is presented in section 2. The mathematical model developed in this work is explained in section 3. Genetic Algorithm used for solving the guard channel CAC optimization problem in Cellular Network (GACN) is presented in section 4. Numer-ical results obtained are discussed in section 5. Finally the work presented in paper is present in the last section.

2. Related Work

It is expected that within time span of 5 year mobile user will be doubled and thus the cellular infrastructure should be

developed accordingly [1]. To satisfy the Quality of service

and manage increasing volume of traffic, Hierarchical Cellular

Network (HCN) may be considered as an solution [2]. In

HCN, tiered networks are designed to provide high coverage and capacity over a given service area. In a two-tier network, macrocell works as upper tier which radius is approximately 1-2 km while microcells works as lower tier whose radius

is upto 1 km. Heterogeneous Cellular Networks considerk

tier model where each tier consists of particular class BSs

such as femtocells or pico-cells [3], Mobile velocity based

bidirectional scheme in HCN is discussed by Shan and Fan

[4]. In mobile velocity based scheme slow mobility user

are directed to microcell while overflow user from microcell, handoff calls and fast mobility users are directed to macrocell. Network design for two tier cellular network based on class

selection strategy is discussed by Ekici and Erosy [5]. Goel

and Lobiyal find minimum cost for two tier cellular network

design using genetic algorithm [6].

Preserving new call blocking probability while reducing handoff probability may be achieved using channel sub-rating

strategy. Xiaolong et al. in their paper [7] proposed a call

ad-mission control scheme for HCN based on channel sub-rating using 1-D Markov process in microcell and 2-D Markov pro-cess in Macrocell. Martin Taranetz evaluated the performance of typical indoor users in urban two-tier heterogeneous mo-bile networks with indoor-deployed small cell base stations (BSs) and normal outdoor BSs. In this indoor and outdoor environments are partitioned by walls with a certain

pene-tration loss [8]. Jain and Rakhee [17] proposed a model in

which guard channel scheme is used and priority is given to

handoff calls. Huang, Kumar and Kuo [18] proposed a model

of three service classes: handoff priority, handoff guarantee and best effort service. An optimal allocation scheme for an integrated wireless cellular model with handoff priority and

handoff guarantee services is designed by Jain and Mittal [9].

The millimeter-wave (mmWave) frequency band is seen as a key enabler of multigigabit wireless access in future cellular networks. MAC tier issues, such as synchronization, random access, handover, channelization, interference management, scheduling, and association for mmWave frequency band are

discussed by Hossein Shokri-Ghadikola et al. [10]. Optimal

channel assignment in mobile communications using Genetic

algorithms is proposed by Wang, Arun Kumaar and Gu [11].

3. Mathematical Model

In this work we divided total no of channels in a cells in two groups one group is known as guard channels which is reserve for handoff calls. Another group with rest of channels used for new call as well as handoff calls. Whole region is divided into microcells covered by macrocells. A macrocell contains odd integer multiple of microcell. Incoming calls are classified in two class one as slow mobility and other as fast mobility. Slow mobility calls arrive in the microcell whereas fast mobility new calls arrive in the macrocell. The blocked calls and dropped handoff calls from microcell are also dealt by the overlayed macrocells. To handle the handoff calls in excess of guard channels in microcell FIFO queue with size

3 is used. M/M/c/kqueuing model is used for modeling

of Markov chain. In designing two tier cellular network, it is important to determine the optimal number of microcells and macrocells to achieve the performance. Therefore, in this paper we have formulated it as an optimization problem to estimate the cost of designing a two tier cellular network.

3.1 Model assumptions

For constructing mathematical model, we have made the following assumptions:

(1) The whole service area is covered by macrocells and a macrocells has odd number of microcells within it.

(2) The radius of a macrocell and a microcell are approxi-mately 600m and 1400m respectively.

(3) Two mobility classes - slow mobility and fast mobility are considered.

(4) Microcell takes slow mobility calls and macrocell takes fast mobility calls as well as overflowed slow mobility calls from microcells.

(5) The mean velocity of fast mobility users(vf)and slow

mobility users(vs)are considered as exponentially

dis-tributed and remain the same for the entire call duration.

(6) All available channels between microcells and macro-cells are randomly distributed.

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(8) When guard channels are not available FIFO queue with size 3 used for handoff calls only.

(9) The time spend by a user in a cell is called dwell time

and calculated as in [12].

(10) λmsandλM f are call arrival rate of slow and fast users

and they follow Poisson distribution.

(11) In a microcell if only guard channels are available all new calls are blocked and overflowed to overlaying macrocell.

(12) In a microcell, if queue is full than handoff calls are blocked and overflowed to overlaying macrocell.

(13) Any call from macrocell to microcell is not allowed in any situation.

3.2 Model formulation and parameter

3.2.1 Performance analysis of microcell

Microcell tier of two-tier cellular network can be modeled

in terms of one-dimensional Markov chain [6]. In this model

usedM/M/c/kqueuing model. In this model we considered

no of serving channels fixed and size of queue also fixed as 3. The mean queue time depends on mean cell dwelling time and

maximum crossover distancem, over the overlapping zone

between two cells. Mean queen time is shown as [16].

Mean queue time_µ1

q

= ₁₀₀M _µ1 ms

The variables used in modeling are defined as follows

λms: slow mobility call arrival rate in microcell

λmsh: slow mobility asymptotic handoff rate in microcell

1/µms: Dwell time of the slow mobility user in Microcell

1/µt: Mean call duration

r: Microcell radius

R: Macrocell radius

vs: Mean speed of slow mobility user

ch1: Number of channels in microcell

G1: Number of Guard channels in microcell

SAm2: Call arrival rate per second perm2for slow mobility

user

Pmb: Microcell call blocking probability

Pmd: Microcell call dropping probability

Where 1/µms=₂rπ_v_s,a=λms+λmsh,b=λmsh,c=µt+µms,

d=µt+µq,ch1=n,G1=m

A Markov chain for a microcell withnchannels,mguard

channel with queue size 3 is presented in Figure 1

Figure 1

In Figure 1, number of calls served by a microcell

corre-sponds to a state. Each microcell consists ofnchannels out of

whichmguard channels and(n−m)channels are available

for new calls as well as handoff calls. If the number of busy

channels are greater than(n−m)channels then new call is

blocked. Blocked new call is transfered to overlayed macro-cell. Further handoff calls are served by guard channels. If

number of busy channels are greater thannthenM/M/k/c

queue of size 3 channels are used by handoff calls only. From

the state diagram in Figure 1 the steady state probabilitiesPi

in microcell is given as follows:

Pi=P0 a

c

i1

i!, 0≤i≤(n−m) (3.1)

Pi=P0 _an−m

ci

_bi−(n−m)

i! , (n−m)<i≤n (3.2)

Pi=P0 _an−m

cn

_bi−n+m

n!πi_j−₌₁n{cn+jd},n<i≤n+3 (3.3)

n+3

∑

i=0

Pi=1 (3.4)

The Asymptotic handoff rate λmsh is calculated iteratively

until difference between two iteration is less than 0.0000005 using the following formula

λmsh(k) =

n+3

∑

i=0

i.Pi.µms (3.5)

The slow new calls in the microcell are blocked after all (n-m) channels are busy and calls are blocked. Therefore, the call blocking probability in microcell can be represent as

Pmb=

n+3

∑

i=n−m

Pi (3.6)

The slow handoff calls in the microcell are dropped, if all channels are busy& queue of size 3 is full. The call blocking

probability,Pmdis given as

Pmd=Pi, wherei=n+3(7) (3.7)

The blocked slow calls in microcells are overflowed to the

macrocell with rateλosand dropped handoff calls overflowed

to the macrocell with rateλosh. The overflow call rateλosand

overflow handoff rateλoshare given as

λos=Nc.λms.Pmb (3.8)

λosh=Nc.λmsh.Pmd (3.9)

Where

Nc=Nc−4+6(c−2), (3.10)

N1=1 and N−1=0

3.2.2 Performance analysis of macrocell

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λM f: Fast mobility call arrival rate in a macrocell

λM f h: Fast mobility asymptotic handoff rate in a Macrocell

λMsh: Slow mobility asymptotic handoff rate once they enter

a macrocell

µMs: Dwell time of the slow mobility user in the Macrocell

µM f: Dwell time of the fast mobility user in the Macrocell

1/µt: Mean call duration

vf: Mean speed of fast mobility user

ch2: Number of channelsna macrocell

G2: Number of guard channels in a macrocell

FAm2: Call arrival rate per second perm2for fast mobility

users

PMb: Call blocking probability in a macrocell

PMd: Call dropping probability in a macrocell

Where 1

µMs =

Rπ 2vs,

1 µM f =

Rπ

2vf,X =λMsh+λosh+λos,Y =

λM f+λM f h,[D=µt+µMs,E=µt+µM f,a=λMsh+λosh,

b=λM f h,ch2=n,G2=n−m.

A Markov chain for a macrocell withnchannels is

pre-sented in Figure 2.

In this figure a state corresponds to the number of fast

usersiand slow users jserved by a macrocell. Using state

transition diagram given in Figure 2, the equilibrium equations can be written as follows:

(X+Y)P0,0=DP0,1+EP1,0 (3.11)

(X+iE+Y)Pi,0=DPi,1+Y Pi−1,0+ (i+1)EPi+1,0,

for 0<i<m (3.12)

(a+iE+b)Pi,0=DPi,1+Y Pi−1,0+ (i+1)EPi+1,0,fori=m

(3.13)

(a+iE+b)Pi,0=DPi,1+bPi−1,0+ (i+1)EPi+1,0,

form<i<n (3.14)

iEPi,0=bPi−1,0, i=m (3.15)

(X+Y+jD)P0,j=X P0,j−1+EP1,j+ (j+1)DP0,j+1,

0<j<m (3.16)

(a+b+jD)P0,j=X P0,j−1+EP1,j+ (j+1)DP0,j+1, j=m

(3.17)

(a+b+jD)P0,j=aP0,j−1+EP1,j+ (j+1)DP0,j+1,

form<j<n (3.18)

jDP0,j=aP0,j−1, j=n (3.19)

(X+jD+iE+Y)Pi,j

=Y Pi−1,j+X Pi,j−1+ (j+1)DPi,j+1+ (i+1)EPi+1,j,

for 0<i+j<m (3.20)

(a+jD+iE+b)Pi,j

=Y Pi−1,j+X Pi,j−1+ (j+1)DPi,j+1+ (i+1)EPi+1,j,

fori+j=m (3.21)

(a+jD+iE+b)Pi,j

=bPi−1,j+aPi,j−1+ (j+1)DPi,j+1+ (i+1)EPi+1,j,

form<i+j<n (3.22)

(jD+iE)Pi,j=bPi−1,j+aPi,j−1,fori+j=n (3.23)

n

∑

i=0

n−i

∑

j=0

Pi,j=1 (3.24)

The Asymptotic handoff rateλMsh andλM f hare calculated

iteratively with accuracy of 0.000005 using the following equations

λMsh(k) = n

∑

i=0

n−i

∑

j=0

(iPi,jD) (3.25)

λM f h(k) =

n

∑

i=0

n−i

∑

j=0

(jPi,jE) (3.26)

The equilibrium equations form 11 to 24 are solved using Gauss Jordon numerical method for calculating the steady

state probabilitiesPi,j.

The call blocking probability,PMbandcall dropping

prob-ability,P_Mdin macrocell is calculated as follows:.

PMb=

∑

i

∑

j

Pi,jandi+j≥(n−m) (3.27)

PMd=

∑

i

∑

j

Pi,jandi+j=n (3.28)

The total call blocking(Pb)and call dropping(Pd)

probabili-ties are calculated using the following equations

Pb=

NcλmsPmbPMb+λM fP_Mb

Ncλms+λM f

(3.29)

Pd=

NcλmsPmdPMd+λM fP_Md

Ncλms+λM f

(3.30)

4. Formulation of Optimization Problem

We have considered a cost minimization problem for two-tier cellular network. The minimum cost problem can be formulated as follows:

MinC=C1N1+C2N2 (4.1)

s.t.

Pb≤Pbmax (4.2)

Pd≤Pdmax (4.3)

πr2N1≤Area (4.4)

πR2N2≤Area (4.5)

R

r =Oddinteger (4.6)

WhereCis total cost of designing a micro-macro cell system.

The cost of designing one unit of microcell and macrocell

areC1andC2respectively. The number of microcells and

macrocells in the system areN1andN2respectively.

The radius of microcell and macrocell are represented by

randRrespectively. P_bmaxandP_dmaxare maximum

accept-able value of call blocking and call dropping probabilities

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Inequality constraints in equation (32) and (33) represent the call blocking and call dropping probabilities which should be less than the given limits. Inequality constraints in equa-tion (34) and (35) represent total coverage area. Inequality constraints in equation (36) represents that there should be integer number of covering microcells in a macrocell. We solved the above optimization problem by using a Genetic Algorithm(GACN).

5. GACN algorithm

The Genetic Algorithm to solve Cellular Network (GACN) optimization problem in this work is given as follows:

Step-1:Initialized population

First we considered genes of 4 cell with field

Ch1 Ch2 G1 G2 r R

Where

• Ch1 is number of channels in a microcell

• Ch2 number of channels in a macrocell

• G1 number of guard channels in a microcell

• G2 number of guard channels in a macrocell

• r radius of a microcell

• R radius of a macrocell

The population is initialized by generating randomly Ch1, Ch2, r and R. For example a gene C1 can be as follows

18 16 5 8 466 398

Using the fitness function population is accepted if R/r is an odd integer; otherwise again new population is generated. We have considered an initial population of 40 chromosomes.

Step-2:Mutation

Select a gene randomly and then select a random position p between 1-6 in the gene

If(p≤4)then

Generate that particular cell accordingly

elseif(5≤p≤6)then

Generate both cell 5 and 6 such that R/r is odd integer For example if random gene is C1 and p=2 then new gene C2 is as

18 15 5 8 466 398

If p=3 or 4 thenrandRboth are generated again such

that ratioR/ris an odd integer

Step-3: Crossover

Select two random population e.g. C1 and C2 as follows.

18 15 5 7 466 398

19 20 1 3 466 398

Select random positionpbetween 1-6 e.g. p=2 then new

genes are

18 20 1 3 466 398

19 15 5 7 466 398

Step-4:Apply the fitness function

Step-5: Evaluate the population

Step-6: Check the stopping criteria

If(stopping criteria is not satisfied) then Go to step no 2

else end

6. Experimentation and Results

The GACN algorithm is used to solve the optimization problem described in 3.2.3 as follows. First an initial popula-tion of 50 is generated. Ch1 and Ch2 are randomly generated between (11,20). G1 and G2 are randomly generated between (0,10). Let the radius of microcell(r) is approximately 0.5 km and the radius of macrocell (R) is between 800-1400 meters.. We apply GACN algorithm for the base problem using the parameters given in Table 1. The results of the experiments are given in table 2.

Table 1.Parameters with their base values

Parameter Base Value

vs 1 m/s

vf 8m/s

SAm2 8×10−8calls per sec perm2

FAm2 2×10−8calls per sec perm2

1/Dt 100 sec

C1 10 cost unit

C2 30 cost unit

A 50000Km2

CS 7

Pb,max 0.01

Pd,max 0.001

Ch_total 150

Table 2.Values of decision parameters for the base problem

Parameter Result of queuing model

C 113210

Ch1 11

Ch2 19

G1 0

G2 4

r 433m

R 1299m

R/r 3

Pb 0.0039

Pd 1.8771x 10−08

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We solve queuing model using GACN algorithm to see convergence around 600 times this algorithm. It is observed that after 200 iterations total cost start decreasing and after 450 iterations the cost remain same. We performed this 600 times and result is shown in Figure 3.

(n-1)E

0,0

2E 1,0 E

Y

_…...

mE

Y b

(m+1)E

…….. b

nE n,0 (n-1),0 b m,0

Y

2E 1,1 E

Y

…...

mE

b b

(m+1)E

…….. b (n-1),1 (n-1)E m,1

Y b b

E 2E

b E

………

…….

………..

Figure 2. Transition diagram for macrocell with n channels & (n-m) guard channels Figure 2

Now we study the effect of some other parameters on the cost. First we study, change of slow mobility call arrival rate

from 5×10−8to 15×10−8calls per sec perm2with a step

size of 1×10−8calls per sec perm2result are shown in figure

4.

0 100 200 300 400 500 600

1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21x 10

5

Number of iteration

T

o

ta

l C

o

s

t

Figure:1 Number of iteration vs Total Cost

Queuing Model with gaurd channel

Figure 3

In Figure 4 it is shown that when slow mobility call arrival rate increase, the system cost increases. In GA algorithm rate of change of cost is more than our proposed queuing model with GACN algorithm.

To examine the effect of fast mobility user arrival rate on the total cost, we considered the fast mobility user arrival rate

from 1×10−8to 5×10−8calls per sec perm2with a step size

of 1×10−8calls per sec perm2. The results are shown in

Figure 5.

4 5 6 7 8 9 10 11 12 13 14

x 10-8

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9x 10

5

slow mobility call arival rate

T

o

ta

l

C

o

s

t

igure:2 slow mobility call arival rate vs total Cost

SA

Queuing model with guard channel

Figure 4

Now, we study change in total cost as we change the average speed of slow mobility user from 0.25m/s to 2.25 m/s taking step size 0.25 m/s and the results shown in figure 6.

1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-8 1.1

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9x 10

5

Fast mobility call arival rate

T

o

ta

l C

o

s

t

Figure:3 Fast mobility call arival rate vs total Cost

queuing model with gaurad channel

Figure 5

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0 0.5 1 1.5 2 2.5 1.1

1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55x 10

5

Slow mobility user speed(m/s)

T

o

ta

l C

o

s

t

Figure:4 Slow mobility user speed(m/s) vs Total Cost

Guard channel with SA Queuing Model with gaurd channel

Figure 6

Similarly, we study the change in total cost as we change the average speed of fast mobility user from 6 m/s to 9 m/s taking step size 0.25 m/s result is shown in figure 5

6 6.5 7 7.5 8 8.5 9

1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.3 1.32x 10

5

High mobility user speed(m/s)

T

o

ta

l C

o

s

t

Figure:5 High mobility user speed(m/s) vs Total Cost

Queuing Model with gaurd channel

Figure 7

7. Conclusion

In this work, we make a model using queuing with guard channel CAC policy and total minimum cost of two-tier cel-lular network calculated using GACN algorithm. We also compared GACN algorithm with SA algorithm Our results show that this queuing model with GASN algorithm gives better results in most of the situation with in comparison to SA.

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ISSN(P):2319-3786

Malaya Journal of Matematik

ISSN(O):2321-5666

Minimizing the cost of two-tier cellular network with queuing handoff calls in microcell using genetic algorithm