Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1971 A of Cell to Switch Assiget i Mobile Couicatio Networks Usig Algorith Ail Goyal, Shiv Krisha Joshi,Surbhi Gupta Abstract--This paper deals with a desig proble for a etwork of Mobile Couicatio Services (MCN). The goal is to assig cells to switches i a MCS Network i a efficiet aer.it is a NP-Hard proble. We cosider three types of costs. Oe is the cost of hadoff betwee cells. The other is the cost of cablig or trukig betwee a cell ad its associated switch. The third cost is switchig cost which icludes the cost for trasferrig a call to other switch. The proble is costraied by the capacity of switch ad assiget of a cell to a uique switch. algorith is ipleeted i this paper alog with heuristics ethod to solve the proble of assiget of cells to switches ad results are copared with that of Particle Swar Optiizatio ad Algorith. Idex Ters-- Cell to switch assiget, algorith, s, MCS, Particle swar optiizatio, Optiizatio. betwee cell A ad cell B is less because it ivolves oly 1. INTRODUCTION Switch1 ad also the hadoff is siple while hadoff betwee cell A ad cell C is coplex ad the hadoff cost is also ore as it ivolves two switches i.e. Switch1 ad Switch2 Therefore, ice the last decades, there have bee sigificat advaces there are two types of hadoffs, oe ivolves oly oe switch Si the developet of obile couicatio systes. ad the other ivolves two switches. Ituitively, the cells Now a day the obile etworks are igratig towards aog which the hadoff frequecy is high should be broadbad services based o high speed wireless access assiged to the sae switch as far as possible to reduce the techologies [1]. Eve though sigificat iproveet to cost of hadoffs. Merchat [3] gave a coprehesive couicatio ifrastructure has bee aied i the obile descriptio about hadoffs. Switchig cost occurs whe two idustry, the issues cocerig the assiget of cells to user which are couicatig belog to differet MSCs. switches i order to iiize the cablig cost, hadoff cost However, sice the call hadlig capacity of each switch is ad switchig cost i a reasoable tie still reai liited, this should be take as a costrait. Icorporatig the challegig. The sae proble is addressed i this paper. Our cablig cost, hadoff cost ad switchig cost that occurs whe otive is to iiize three costs aely: cablig cost, hadoff a call is coected betwee a cell ad a switch, we have a cost ad switchig cost. Cablig cost ivolves the optiizatio proble[4], called the cell to switch assiget cosuptio of resources while aitaiig couicatio proble. lik betwee two users [2]. The hadoff caused by a subscriber oveet fro oe cell to aother, ivolves ot oly the odificatio of the locatio of the subscriber i the database but also the Ail Goyal is curretly pursuig aster s degree progra i electroics egieerig i PEC Uiversity of Techology, Idia. E-ail: goyal.ail444@gail.co Shiv Krisha Joshi is curretly pursuig aster s degree progra i electroics egieerig i PEC Uiversity of Techology, Idia. E-ail: shivkrishajoshi@gail.co Surbhi Gupta is curretly pursuig aster s degree progra i electroics egieerig i PEC Uiversity of Techology, Idia. E-ail: er surguta@gail co executio of a fairly coplicated protocol betwee switches Switch1 ad Switch2 as show i fig.1.the hadoff cost 2013 This paper presets idea to solve the proble of assiget of cells to switches usig Algorith give I 2008,byXi-She Yag [5] alog with s ethod used by Bhaskar Se Gupta i 1995 [3]. I ext sectio the atheatical forulatio has bee doe for this proble. I the ext sectio it is show how firefly algorith ad ethod ca be ipleeted for this proble. 2. PROBLEM FORMULATION The proble of assiget of cells to switches was first itroduced by Arif Merchat ad Bhaskar Segupta [3] i 1995. The assiget of cell to the switches is a NP-Hard
Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1972 proble, havig a expoetial coplexity ( cells ad switches). He itroduced two types of costs aely hadoff cost ad cablig cost. He also proposed a heuristic ethod to solve this proble. Now i this paper aother cost called Switchig cost [6] is itroduced which is the cost for trasferrig a call for oe switch to aother. Thus i this paper we have a optiizatio proble for iiizig the above costs which is stated as follows: Assig all the cells i a geographical area to the available uber of switches i order to iiize the total cost which is the su of cablig cost, hadoff cost ad switchig cost aitaiig the followig two costraits. 1) Each cell ust be assiged to exactly oe switch ad 2) Each switch has soe liited capacity ad assiget of cells ust be doe i such a way so that the total load o the switch should ot exceed the capacity of the switch. x ik = 1, 1 i (1) k=1 2) Each switch has soe capacity λ i x ik M k, 1 k (2) i=1 3.2 FORMULATION OF COST FUNCTION: 1) Cablig : this is forulated as a fuctio of distace betwee base statio ad switch ad uber of calls that a cell ca hadle per uit tie [8]. c ij (λ j ) isthe cost of Fig1. Hadoff fro B to C is ore expasive tha B to A. 3. MATHEMATICAL MODELING The assiget of cell to the switches is a NP-Hard proble, havig a expoetial coplexity ( cells ad switches) [6]. Let o. of cells be ad o. of switches be h ij hadoff cost betwee cell i ad cell j c ik cablig cost betwee cell i ad switch k d ij distace betwee cell i ad switch (MSC) j M k call hadlig capacity of switch k λ i - No of couicatio i cell i Y ij 1 if cell I ad j are assiged to sae switch ad 0 otherwise. X ik 1 if cell I is assiged to switch k ad 0 otherwise. 3.1 FORMULATION OF CONSTRAINTS: 1) Each cell ust be assiged to exactly oe switch Fig 2: Mappig represetatio for CSA proble[7] cablig per kiloetre which is also odelled as a fuctio of the uber of calls that a cell ca i hadles as: c ij = A ij + B ij λ j (3) 2013
Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1973 c ij (λ j )d ij x ij j=1 for i = 1,2, (4) : So our objective is to iiize the total cost which ca be fored by the suatio of all three costs. The objective fuctio is give by: 2) hadoff cost: we cosider two types of hadoffs, oe which ivolves oly oe switch ad aother which ivolves two switches. The hadoff that occurs betwee cells that belog to the sae switch cosue uch less etwork resources tha what occurs betwee cells that belogs to two differet switches. c ij (λ j )d ij x ij + h ij (1 y ij ) j=1 i=1 j=1 + β i F i (β i ) i=1 (9) h ij (1 y ij ) i=1 j=1 (5) 4. EXISTING METHODOLOGY Assigig cells to switches i cellular obile etwork beig a NP-hard proble ad euerative search ethods are ot appropriate to solve large sized istaces of this proble There are various ethods available for assigig cell to switches like, heuristic approaches, like Geetic Algorith [4] [9], At Coloy Optiizatio [10] ad Particle Swar Optiizatio [11] have bee developed for this kid of proble. All these algoriths cosidered oly cablig cost ad hadoff cost except [6] ad [12]. I this paper Algorith[5] alog with the [3] is ipleeted ad results are copared with Algorith aloe as used i[12] ad with the Particle Swar Optiizatio as used i [11]. 3) Switchig : let βi is the total o of calls MSC i ca hadle per uit tie ad Fi(βi) is the cost fuctio of switchig a call i MSC i. Thus the load at MSC is give by: β i = λ j x ji, for all i = 1 (6) j=1 5. IMPLEMENTATION OF FIREFLY ALGORITHM ALONG WITH HEURISTIC METHOD F i(β i) ivolves both the cost of switchig ad the cost of aitaiig a call at MSC. Thus F i(β i) ca be represeted as: F i (β i ) = α (μ i β i ) β i < μ i (7) Where μ i deote the call switchig capacity of MSC i ad α is a costat. The total switchig cost ivolved is defied by: β i F i (β i ) i=1 (8) 2013 5.1 FIREFLY ALGORITHM algorith is developed by Xi-She Yag [5] i 2008 which is ispired by the utual attractio of fireflies based o the absorptio of light ad distace betwee two fireflies. Algorith cosiders that each firefly has fixed positio i the space ad it always ove towards a greater light source, the is his ow. algorith idealizes soe of the characteristics of the firefly behavior. They follow three rules: 1) All the fireflies are uisex, 2) Each firefly is attracted oly to the fireflies, that are brighter tha itself; stregth of the attractiveess is proportioal to the firefly s brightess, which atteuates over the distace; the brightest firefly oves radoly ad, 3) Brightess of every firefly deteries its quality of solutio; i ost of the cases, it ca be proportioal to the objective fuctio. 5.2 HEURISTIC METHOD
Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1974 is used to fid out the best iitial solutio as give i[3] ad we assig this best solutio to oe firefly ad all other p-1 fireflies are assiged rado values. 5.3ALGORITHM The steps for ipleetatio of algorith are as follows: Step 1 Iitialize the uber of cells (), switches () ad uber of fireflies (p) i the solutio space. Iitialize p-1 fireflies radoly ad assig the iitial best solutio to oe firefly as obtaied by the. Iitialize positio of cells ad switches radoly i the search space. Calculate distace betwee each cell ad switch. Step 2 Geerate the assiged atrix (x ij) for each firefly where each particle is betwee 0 ad 1. The row of the atrix represets switches ad 6.1 COST TABLE colu represets cells. Switches, Cells Step 3 Obtai solutio atrix fro the assiged atrix by akig the largest value of each colu to 1 ad all Step 4 Step 5 other are set to 0. Calculate the total cost based o this solutio atrix. O the basis of this ew cost the brightest firefly is foud which has the iiu cost for the assiget. Now update the positio of all other fireflies based o the attractiveess of best firefly ad also o the basis of distace ad radoess of fireflies. Now update the positio of best firefly radoly. Repeat step 3 to 5 util stoppig criterio is et. 6. EXPERIMENTS AND RESULTS To test the effectiveess of Algorith for the cell assiget proble, we desig ad coduct a series of experiets. All the experiets are doe usig a MATLAB code for various cases of cells ad switches for firefly algorith. Regardig the test probles, we assue that the cells lie o a hexagoal grid of roughly equal diesios i 2 diesios. The paraeters used for firefly algorith are uber of cells (), uber of switches () ad uber of fireflies (p). Values of costats used are as follows: Radoess, α=1 Absorptio coefficiet, β=1 Brightess at source=1 The paraeters used i the iitializatio of proble are: hadoff cost betwee two cells= 0 to 14 per hour costat A used i cablig cost=1 costat B used i cablig cost=0.001 call hadlig capacity of a switch=98000 costat α used i switchig cost=40 uber of couicatio i a cell=0 to 200 per hour ( + ) () () 2, 25 1902 1915 1936 2, 50 7806 7894 7954 2, 100 33312 33414 33528 2, 150 78109 78213 78279 2, 200 133998 134200 134280 2, 250 216366 216370 216410 3, 25 2405 2417 2478 3, 50 10806 10973 11022 3, 100 45169 45208 45290 3, 150 102165 102230 102310 3, 200 181788 181870 181920 3, 250 288010 288090 288160 2013
Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1975 5, 25 2876 2979 3011 5, 50 13576 13642 13735 5, 100 54296 54395 54481 5, 150 124765 124880 124940 5, 200 220005 220030 220160 5, 250 344000 344020 344180 10, 25 3675 3711 3800 10, 50 15165 15273 15411 10, 100 61564 61999 62158 10, 150 137958 138280 139020 10, 200 248643 248710 249360 10, 250 390063 390140 391420 6.2 ANALYSIS OF RESULT 50000 Motio of fireflies is best for the above values of α, β ad γ. For lesser values of these paraeters the chage i 0 the assiget is very low. As the uber of cells ad 2, 25 2, 2, switches is icreased the fial cost value also icreased ad 100 200 with these large proble istaces it is takig ore uber of iteratios ad ore tie. We have coducted experiets to fid the iiu total cost by repeatig the experiets for 5, 10, 15 ties for each set of paraeters. These experiets 200000 reveals that the optiu cost obtaied i each executio is always earer to the average cost. 180000 Table 6.1 shows the iiized cost for differet cases of cells ad switches. It also copare the iiized cost by the three algoriths: alog with s, ad ad fro this list we ca see that coparatively lesser cost is foud usig alog with s ad so it is better i ters of fidig iiu cost. For experiets it is oted that the total iiized cost ca be reduced with larger uber of iteratios ad also with larger uber of fireflies. 7. CONCLUSION Fro the experiets perfored we ca coclude that firefly algorith alog with s ca be ipleeted successfully for the assiget of cells to the switches. The followig coclusios ca be draw: 1. As the uber of fireflies is icreased the probability of fidig the iiu cost ad i less uber of 2013 iteratios is icreased. The CPU tie requireet is less i case of firefly algorith as copared to. 2. As the uber of fireflies is icreased i the solutio space the probability of covergece to the global iia i coparatively lesser uber of iteratios is icreased. But this will icrease the coplexity i the executio ad CPU tie requireet. COST COMPARISON GRAPHS 250000 200000 150000 160000 140000 120000 80000 60000 40000 20000 0 3, 25 3, 50 3, 100 3, 150 3, 200 3, 25
Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1976 400000 [3] Arif Merchat ad BhaskarSegupta, Assiget of cells to switches 350000 300000 250000 200000 150000 i PCS etwork, IEEE Trasectios o Networkig, Vol 3 No 5, pp 521-526, Oct 1995. [4] P. Bhattacharjee, D. Saha, A. Mukherjee, s for Assiget of Cells to Switches i a PCSN: A Coparative Study, Itl. Cof. o 50000 0 5, 25 5, 100 5, 200 Persoal Wireless Couicatios, Jaipur, Idia, 1999, pp. 331 334. [5] Xi-She Yag, Algorith For Multiodal Optiizatio, Luiver Press, 2008. 450000 400000 350000 300000 250000 200000 150000 50000 0 10, 25 10, 100 8. REFRENCES 10, 200 [6] Siba K. Udgata, U. Auradha, G. Pawa Kuar, Gauri K. Udgata, Assiget of Cells to Switches i a Cellular Mobile Eviroet usig Swar Itelligece, IEEE Iteratioal Coferece o Iforatio Techology, 2008, pp 189-194. [7] Cassilda Maria RibeiroAíbal Tavares Azevedo Rodolfo Florece Teixeira Jr., Proble of Assiget Cells to Switches i a Cellular Mobile Network via Bea Search, WSEAS TRANSACTIONS o COMMUNICATIONS,2010. [8] ShxyogJiaShyua, B.M.T. Lib, TsugSheHsiaoa, At coloy optiizatio for the cell assiget proble i PCS etworks, arch, 2005. [1] P. Bhattacharjee, D. Saha, A. Mukherjee, s for assiget of cells to switches i a pcs: a coparative study:, Itl. Cof. o Persoal Wireless Couicatios, Jaipur, Idia,1999, pp. 331-334. [9] T. Shigeyoshi, G. Ashish, Geetic Algorith with a Robust Solutio Searchig Schee,IEEE Trasectios o Evolutioary Coputatio, pp. 201-208, 1997. [2] SyaMeo, Rakesh Gupta, Assigig cells to switches i cellular etwork by icorporatig a pricig echais ito siulated aealig, IEEE Trasetios o syste, e ad cyberetics, Part B, Vol. 34, No. 1, pp. 558-565, Feb 2004. [10] Dorigo M, Maiezzo V, Colori A, The At Syste: Optiizatio by a Coloy of Cooperatig Agets, IEEE Trasactios o Systes, Ma ad Cyberetics-Part B, Vol 26(1), pp. 29-41, 1996. 2013
Iteratioal Joural of Scietific & Egieerig Research, Volue 4, Issue 7, July-2013 1977 [11] Jaes Keedy, Russell Eberhart Particle swar optiizatio, Proc. IEEE It'l. Cof. o Neural Networks (Perth, Australia), IEEE Service Ceter, Piscataway, NJ, 1995, pp.1942-1948. [12] Deepak Shara, Rajesh Kuar ad Shrikat, Assiget of Cellto Switches usig Algorith,Iteratioal Joural of Electroics ad Couicatio Egieerig & Techology (IJECET), October- Deceber (2012), pp. 211-218 2013