Optimal Location Area Planning for Mobile Cellular ...

3 downloads 498 Views 2MB Size Report
Mar 26, 2015 - MIS Group, Indian Institute of Management Calcutta, Joka, Kolkata 700 104, India. ...... strategy consulting and implementation of application.
IETE Journal of Research

ISSN: 0377-2063 (Print) 0974-780X (Online) Journal homepage: http://www.tandfonline.com/loi/tijr20

Optimal Location Area Planning for Mobile Cellular Network using Evolutionary Computing Methods Madhubanti Maitra, Ranjan Kumar Pradhan, Debashis Saha & Amitava Mukherjee To cite this article: Madhubanti Maitra, Ranjan Kumar Pradhan, Debashis Saha & Amitava Mukherjee (2005) Optimal Location Area Planning for Mobile Cellular Network using Evolutionary Computing Methods, IETE Journal of Research, 51:3, 235-244, DOI: 10.1080/03772063.2005.11416399 To link to this article: http://dx.doi.org/10.1080/03772063.2005.11416399

Published online: 26 Mar 2015.

Submit your article to this journal

Article views: 1

View related articles

Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tijr20 Download by: [New York University]

Date: 23 April 2016, At: 03:08

JETE Journal of Research Vol 51, No.3, May-June, 2005, pp 235-244

Optimal Location Area Planning for Mobile .Cellular Network using Evolutionary Computing Methods MADHUBANTI MAITRA, RANJAN KUMAR PRADHAN Department of Electrical Engineering, Jadavpur University, Kolkata 700 032, India. e-mail: [email protected] DEBASHIS SAHA MIS Group, Indian Institute of Management Calcutta, Joka, Kolkata 700 104, India. e-mail: [email protected] AND

IETE Journal of Research 2005.51:235-244.

AMITAVA MUKHERJEE IBM Global Services, Sector 5, Salt Lake, Kolkata 700 091, India. e-mail: [email protected]

In a mobile wireless cellular network the size of a location area (LA) could vary from one single cell to the entire service area under a Mobile Switching Center. These two situations depict two extreme possibilities. For the first case paging cost would be minimal whereas location update (LU) cost will be significantly high. For the latter possibility, the situation will just be the reverse. This work addresses the problem of designing an optimum LA within available spectrum such that total network cost, comprising of LU cost and cost for paging, can be minimized by resolving the inherent trade-off between these two cost components. We .have formulated a constrained cost optimization problem to find out the optimal LA size. Since the optimization problem is combinatorial in nature, as solution methodologies we have presented two heuristics, based on Simulated Annealing and Genetic Algorithm. The quality of the solutions obtained proves that in near future these two evolutionary methods will be strong contenders for solving NP-Hard problems. Indexing terms: Location Update (LU), Blanket paging, 2-D random walk, Movement threshold, Simulated Annealing (SA), Genetic Algorithm (GA).

1. INTRODUCTION N contrast to a landline telephonic network, mobile wireless cellular network (MWCN) accommodates dynamically re-locatable service users with whom location uncertainty is always associated. To reduce this location uncertainty, each mobile terminal has to report its location information in regular interval, which is called an LU procedure. In dynamic LU scheme, the frequency of LU performed by a mobile terminal (MT) depends upon a stochastic phenomenon, which is user's movement behavior [1-6].

I

Upon the arrival of a mobile-terminated call, it is the responsibility of the network to search for the terminal for delivering the call successfully. This search is an iterative process, which continues until the terminal is successfully located. The frequency of paging to be performed by the network, per user, depends upon another stochastic phenomenon, which is incoming call arrival process for each user [7]. Since LU and paging process, both consume sufficient Paper No 131-A; Copyright© 2005 by the JETE.

amount of radio resource, cost is incurred for performing an LU as well as for paging. Both these processes are coupled in a sense that there is an inherent trade-off between these two cost components, and these two together determine the total network cost. The size of the LA, in particular, affects the signaling load generated due to paging and LU. From a designer's point of view, it is required to find out an optimum size of LA such that the desired cost effectiveness can be achieved. The present work falls into the class of location area planning (LAP) problem [8,9]. For developing the analytical model we assume microscopic mobility pattern of mobile users whose movement is restricted in a sense that it can be described as random walk [10-12]. Moreover the blanket paging scheme has been chosen to consider a pessimistic design view though several paging schemes are already existent in the literature [7-13]. Under this scheme, all the cells in an LA are polled simultaneously and the polling cycle is bound to one. Also, various LU schemes are proposed in the literature [ 1-6]. In this present work we have adopted movement based LU scheme [6]. Though several attempts have been made to design LAs using evolutionary computing methods [ 14,15], the contribution of this work is 235

236

JETE JOURNAL OF RESEARCH, Vol 51, No 3, 2005

IETE Journal of Research 2005.51:235-244.

three-fold. First of all, the idea of movement based LU scheme is borrowed from [6] to formulate an LAP problem. To the best of our knowledge, the scheme was proposed to reduce the signaling load generated for each LU. However, this potentially rich scheme has not been exploited exhaustively to form an effective LAP problem. Secondly, the per user basis model, proposed in [6], has been extended to accommodate a moderate population of mobile users. Thirdly, an effort has been put to study the efficacy and robustness of evolutionary computing methods, which loom to be effective search techniques for solving hard constrained combinatorial optimization problems with multitude of complexities. For hexagonal cell configuration, we have tried to find out optimum movement threshold value, which would, in effect determine the number of cells, which collectively could be considered as a dynamic optimal LA (as it depends upon two stochastic phenomena viz call arrival pattern and microscopic behavioral pattern of terminal mobility). Due to the uniqueness of our design considerations and problem formulation, we have developed two random search heuristics; SA based and GA based to find an optimal solution of the above problem and have compared the quality of solutions found by each for different inputs. The rest of the paper is organized as follows. In section 2, we describe the system as well as our proposed model. In section 3, constrained cost optimization problem for LA planning is formulated. In section 4.1, we discuss the SA technique in general and then we propose an algorithm based on SA technique for solving the formulated problem. In section 4.2, we present our GA based heuristic. In section 5, some representative results are presented. Section 6 concludes the present work.

2.

SYSTEM AND MODEL DESCRIPTION

2.1. System Description Figure I shows that the cellular network coverage area is comprised of hexagonal shaped cells. The entire coverage area is partitioned into rings of cells. The center cell is defined to be the cell where an MT has performed the last LU. An MT resides in each cell, it enters, for a generally distributed time interval, and then it can move to any of the neighboring cells. The movement of an MT is assumed to be simple random walk [12]. The next LUis performed by the MT, when the number of cell boundary crossings, since the last LU, equals a threshold value d. It is also assumed that MTs move in a radial direction as shown in Fig 1.

If an MT makes say d movements in one particular radial direction, as shown in Fig 1, then the LA will be defined as the area within (d- 1) rings from the center cell. If d assumes an optimum value then the corresponding LA will be an optimum LA [10].

Fig I Hexagonal cell configuration

If the LA consists of D rings then, D=(d-1)

(1)

The number of cells within the LA, L 0 , will be:

N (D)= 3*(D + 1) * D + I

(2)

The perimeter L(D) of the LA L 0 , can be calculated as L(D)=(l2D+6) * R

(3)

where, R denotes the radius of the circle inscribing a hexagonal cell and the area of each cell is (6....J314) * R2 and

(4)

d=2...J3R The areaS (D) of the LA L 0 , is

S(D) = [3D* (D + I)+ 1] * (2.6) * R

(5)

Next it is assumed that the incoming call arrivals to each MT follow a Poisson process. The paging area is the entire LA that is the area within (d- 1) rings from the center cell.

2.2 Analytical Model Let a (k) be the probability that there are K boundary crossings performed by an MT between two successive call arrivals. If the probability density function of cell residence time tm has the Laplace-Stieltjes transform Fni(s) MT and mean 11Aw the call arrival to each terminal follows Poisson process with rate A.c. Based on these assumptions the expression of a (k) can be derived as follows [6]. Here, () is the call-to-mobility ratio (CMR), where CMR is

A.

,

defined as-f- [6]. m

K=O, K>O;

(6) Considering that cell residence time tm follows a Gamma distribution, we get [6]

(7)

237

MADHUBANTI MAITRA et al: OPTICAL LocATION AREA PLANNING

Let f3 (k, K) denote the probability that the MT is k rings away from the center cell, given that the mobile user has already performed K number of cell boundary crossings. To depict the mobility pattern of an MT, 2-D Random Walk model is considered. Let us assume that PK denotes the K x K state transition matrix, where an element Pi.j.k in PK gives us the probability that a mobile terminal moves from one ith ring cell to one jth ring cell in single step. Then the probability j3(k, K) comes out to be [6]

PK; single step state transition matrix j3(k, K) = {

..

.

P"J Pkn-l); n step transitiOn matnx

(8)

Since we want to find out the optimum value of d, we express LU cost C11 as a function of d and the expression is as follows (detail derivation is given in [ 17]) :

U* IETE Journal of Research 2005.51:235-244.

C 11(d) = - - - - - - - : - : : : - - - - (1 _ [ F,~ (A.J] d)2

(9)

Similarly, we derive paging cost Cv as a function of d and it is as follows (detail derivation is in [ 17]):

there are qk switches. This number must be greater than or equal to the total number of attached mobile users. In this constraint Nk denotes population size within the LA. The maximum radius of a cell should be less than maximum allowable radius so that the constraint on system power budget is not violated equation (16).

4. SOLUTION METHODOLOGY Evolutionary computing [18] has introduced two such robust yet random search techniques, which are SA based search [19] and GA [20]. The high complexity associated with the optimization problem (P), necessitates computationally efficient and robust tools. Our earlier efforts using traditional techniques (gradient search, IP, LP etc.) were not fruitful due to the complexity involved in the problem. This motivated us to develop two heuristics which are based on SA and GA and are presented in the next section. However, the quality of solution (compared to classical optimization techniques) is often traded off against computation time, and one can always reach to a nearoptimal solution within bounded computation time.

4.1.

Simulated Annealing

d-l

Cv(d)= V*

L

p_kN(k);rf/Jk

(10)

k=O

where Yis the number ofMT attached to the network within the LA and U and V are respective cost coefficients for performing an LU and paging and f/Jk is the probability of finding the MT within the LA, Lk, the density of the MT in that area is denoted by Pk. So, the total cost is (11)

In this section we discuss fundamental concepts of simulated annealing [ 19] as a solution methodology for combinatorial optimization problem.

4.1.1. Simulated Annealing Fundamentals The design of the algorithm based on SA consists of four important elements. (1) A set of allowed system configurations (Configuration

or

space) (2) A cost function (3) A set of feasible moves (Generation or Perturbation mechanism) d-l

+V

L

P-kN(k)f/Jk

k=O

(4) A cooling schedule (12)

3. PROBLEM FORMULATION The constained optimization problem can be stated mathematically as (13)

•

Configuration Space

In our LAP problem, a feasible solution is a topology, where N (D) number of neighboring cells, are grouped together to form an LA. So, we define, the configuration space as the set of feasible movements made by an MT after which an LU will occur. Let us define the configuration space as

Subject to: 3 d; is integer O