3G/4G load-balancing optimization for mobile network planning Matthieu CHARDY Orange Labs France, Chatillon Email:
[email protected]
Mariem BEN YAHIA Orange Labs France, Lannion Email:
[email protected]
market factors. In [6], authors conduct a financial analysis for 4G network deployment where they model the operator's cash flow management as a dynamic process and solve it as an optimization problem using dynamic programming. They consider the capital for deployment, the operator's strategical level of coverage and they try to maximize the final cash level. They show that the congestion effect in the 3G network results in a lower total subscription level. In this work, we consider a multi-period 3G/4G load balancing optimization problem, where we aim at designing the best migration scenario. A scenario is a set of possible decisions to take, as the radio resources to add, the number of 3G and 4G sites to intensify for capacity's issues, the need of 4G network expansion, and the number of 4G subscriber's packages to finance. The remainder of the paper is organized as follows. In Section II, we define the multi-period 3G/4G load-balancing decision problem. Section III describes the mathematical framework where we give some details on the resolution approach, a heuristic algorithm and an explicit integer pro grarmning formulation. In Section IV , we report some numer ical comparisons of these approaches based on real instances. Finally, we conclude the paper in Section V .
Abstract-This paper focuses on a multi-period mobile net work planning problem integrating load-balancing mechanisms between the 3G and 4G technologies. This decision problem is
formalized as a joint optimization problem of networks capacity and market shares evolutions over years, triggered respectively by networks investments and marketing subsidies. Two solution methods are proposed:
an empirical sequential methodology
and an exact Integer Linear Programming-based approach. The solution methods are assessed on real-life instances.
multi-period network planning; 3G/4G load balancing; integer linear programming.
Keywords:
I.
IN TRODUC T ION
With the convergence of the fixed Internet and wireless communications, mobile data services are undergoing tremen dous growth. As users increasingly consume data and create an enormous surge in mobile traffic, mobile operators need to focus on the mobile network traffic capacity and on the quality of experience they provide to their users. Broadband network technologies such as 3G, Long Term Evolution (LTE) and advanced LTE are being deployed to meet user expectations for speed in an increasingly mobile wireless environment [1]. In this context, LTE with higher spectrum efficiency than 3G is expected to offer more network traffic capacity [2]. However the transition from 3G to 4G can take several years and mobile operators will need strategies and solutions that will continue to enhance their existing 3G networks, while addressing their 4G deployment requirements. When it comes to decide when and how a business should migrate from 3G to a newer cellular technologies, there is no straight forward answer. Several factors need to be taken into account as 3G and 4G subscribers distribution, 3G/4G coverage and capacity requirements, the cost model and the strategic guidelines (bud get constraints our quality of services ambitions). If not well planned beforehand, operators may experience an unexpected financial cut-off [3], [4]. Few works have studied the 3G to 4G migration consid ering at once the existing heterogeneous infrastructures, the financial constraints and the different subscribers behaviours. In [5], the authors analyze a cellular operators' schedule for network upgrades, considering that can switch both operators and services. They consider a 4G competition market and develops a theoretical game model for studying operator's interactions and choose when to upgrade to 4G regarding the
978-1-4673-8991-4/16/$3l.00 ©2016 IEEE
YuBAO Orange Labs France, Chatillon Email:
[email protected]
II. T HE
MULT I-PERIOD
3G/4G
LOAD-BALANCING
DECISION PROBLEM
We consider a mobile network operator deploying and oper ating both 3G and 4G generations of mobile networks within a territory (a whole country or a sub-region). We assume the geographical area to be already entirely covered by the 3G technology, while the 4G coverage is under extension. This corresponds to a common situation in developed countries for instance. We consider two types of users, owning respectively 3G and 4G devices/subscriptions, and we consider two general services: Voice and Data. Traffic repartition among the differ ent networks is set by the following technical constraints: as illustrated on Figure 1, Voice and Data traffics from 3G users are conveyed only by the 3G network; inversely Data from 4G subscribers can be conveyed by both 3G and 4G networks respectively composed of NodeB and eNodeB (co-located with NodeB). In addition, for user experience motivations, 4G Data services are conveyed by 4G networks when these users are under 4G coverage [7]. From a telecom standpoint, note that
7
•
All these decisions must be seen as different levers to deform and balance 3G and 4G traffics, while ensuring that the networks capacity is sufficient to handle them in a proper way. We thus implicitly consider 3 phases within each time period:
Fig. 1. Comparison between 40 and 30 users behaviors in two cases: (a) presents users under (only-)30 coverage by a pure 30 site (b) presents users under 3&40 coverage by a co-located 3&40 site.
•
several technologies of 3G Data services exist in practice (HSDPA, R99) and that 4G Voice traffic is assigned according to a (CSFB) ratio which characterizes somehow the Voice over IP market penetration (see. [8]): we choose here to leave aside these telecom specificities for the sake of understanding (and simplicity of our further notations and models) as we claim that it does not question the generality of the approach. The main trigger for mobile networks transformations (cov erage extension and capacity upgrade) is the natural traffic growth, which is characterized by an expected growth of the number of users over years on one side and by the one of the Average Usage Per User (AUPU) for all services and technologies on the other side. Considering traffic repartition, we assume the territory to be partitioned into small groups of sites, named blocs, within which 3G traffic (resp 4G traffic) is assumed to be shared between 3G NodeB (resp 4G eNodeB). Note that a bloc is composed of both pure 3G sites and co-located 3&4G sites (see. Figure 4, Left); in addition, we assume the repartition of 3G/4G users among sites to be deterministic and known. This is a clear simplification of the users mobility and sites coverage overlapping phenomena: these hypotheses must therefore be considered as an average static view of the users (traffics) allocation to sites (blocs), which remains relevant at a strategic level. The deployment of a new generation of network (here the 4G technology) is to take years, and an efficient transformation of mobile networks requires the design of multi-annual strategies (also named master plans), involving several types of decisions that we assume here to be taken at discrete time steps (usually each semester for a 5 year time horizon): •
•
marketing campaigns/subsidies: this implies to decide, at each time step, which amount of money to be spent in order to finance devices/subscriptions upgrade (from 3G to 4G). Note that the modelling of human choices is a complex task: in this work, we consider a simple model where the network operator can target any 3G user for upgrading to 4G against a given fixed subside.
•
•
init-phase: update the bloc partitioning of the territory and the estimations of user allocations to sites (notably taking into account marketing trends); decision-phase (during the time step): decide investments and their implications (operate network transformation and users upgrade); end-phase: ensure/check the compliance of the networks capacity with the users traffics.
In addition, let us precise that these decisions are in practice restricted by technical constraints limiting the number of 3G carriers and 4G lOMHz bands per site or per bloc (due to interferences notably). The objective for the network operator is then to design the optimal master plan for the whole time horizon (usually a 5 year time-horizon). Decisions from different time steps are obviously linked together, and should be taken accordingly in order to achieve global optimality of the planning scheme. However, we consider here that the network operator performs a sequential construction of its master plan (decisions are taken time step after time step), see. Figure 2 for the description of this decision process.
network roll-out: this implies to decide, at each time step, how many new sites are built within each (3G and 4G) bloc (intensification) as well as the number of pure 3G sites to be transformed into co-located 3&4G sites (cov erage extension). Note that the systematic deployment of new 4G eNodeB co-located with 3G NodeB is a common assumption, due to the fact that finding new sites is in practice a tricky issue; spectrum capacity dimensioning: this implies to decide, at each time step, the dimensioning of existing sites within each bloc (addition of carriers/lOMHz bands for respectively NodeB/eNodeB);
Fig. 2. Sequential decision process for the multi-period 30/40 load-balancing decision problem.
The following section will be dedicated to the mathe matical modelling and solving of the 3G/4G load-balancing decision problem for a given time period (referred as the single-period 3G/4G load-balancing problem). For the sake of understanding, we conclude this section by illustrating our decision problem on a one-bloc example within the following
8
� ,b {3G; 4G}
sites for each bloc N s G E Bt. With respect to traffics, we ni t denote by nU;',� , g E the estimated numbers of 3G PuVoice and 4G users allocated to each site s E st and by ata puf , g E and the respective average usage per user for the Voice service and Data services under the coverage of each generation of network (see. Figure 1). Note that 3G and 4G users are thus assumed to have the same Voice ,ini '" usage. By extenslOn, we define nUtb,g t . g t �sEsb nUts',ini the initial number of users for each technology and the total number of users (resp. per bloc) is denoted by nut (resp.
simplified framework: (i) any 3G user or 4G user under (only )3G coverage needs one 3G carrier for its traffic, while a 4G user under 4G coverage needs 115 of a 4G 10MHz band (ii) each 3G site owns 3 carriers while each co-located 3&4G site owns 3 carriers (NodeB) and 1 4G lOMhz band (eNodeB). Figure 4 presents a network structured of 3 sites, one of which being a co-located 3&4G site, and an operator's market share composed of 13 users (among which 3 are 4G users). Their distribution among sites leads to a congestion of the 3G network (the 3G network has a cumulative bloc-capacity of 6 carriers while 11 are needed by 3G traffic from both 3G and 4G users in this configuration) while the 4G network proves sufficient in terms of capacity. Then we provide two migration scenarios for this time period, i.e. two feasible solutions for the single-period 3G/4G load-balancing decision problem, described on Figure 5 and 6.
AU
AU
{3G; 4G}
=
'" - '" t,ini tnub nu8, g t). �gE{3G ;4G } �SESt With regards to costs, let us note c�c, g
{3G; 4G}
E the cost of adding one resource capacity unit (adding a 3G carrier or a 4G 10MHz band) to an existing site. In addition, the cost of building a new site is noted cbuild while the cost of deploying the 4G technology on a site is denoted by c�6loy; finally, the unitary subside for upgrading a 3G user's device/subscription to 4G is denoted by C8ub. dd As for decision variables, let us denote by s �,� , g E t E B the number of NodeB/eNodeB to be dd deployed in each bloc during the time period and rc �,� , g E E Bt the number of resource capacity units to be added to existing sites of each technology in each bloc during the time period. Similarly, we respectively note end, S, t end ,g E t,en nUtb,,g E Bt and rCb,g d ,g E , , b,g E Bt the number of users, nodes (NodeB or eNodeB) and resource capacity units of each technology in each bloc at the end of the time period. In addition, we introduce the binary variables X�, s E S�G equal to 1 if the 4G technology is deployed on the existing pure site s during the time period. Finally the number of 3G subscribers of each site whose devices/subscriptions are upgraded to 4G during the time period thanks to a personal marketing subsidy (noted t ' csub) is noted nuts,sub s E s34G
3G
{3G, 4G}, b {3G, 4G}, b Fig. 4. Congestion quantification.
Fig. 3. Example setting.
{3G, 4G}, b
{3G 4G} b
3G
Fig. 5. Migration scenario consist ing in adding two 30 carriers and building one 30 site.
,
Fig. 6. Migration scenario consist ing in deploying one 40 site and upgrading five 30 users to 40.
B. Sequential methodology III. A.
MAT HEMAT ICAL FRAMEWORK
We propose here a sequential methodology to solve the single-period 3G/4G load-balancing decision problem, whose general scheme can be decomposed into 2 phases. First phase is dedicated to the de-saturation of the 3G network, if needed. This first objective is achieved by successively re dimensioning the 3G network and -if not sufficient- extending 4G coverage and 4G market share in order to off-load 4G users traffic on the 4G network. Note that key point of the 3G network re-dimensioning step is that we prioritize existing site capacity upgrading to building new sites (intensification) for cost motivations, while key strategy of the extension step is to deploy the 4G technology on a minimum set of existing pure 3G sites such that the potential off-load of traffic from 4G users (former 4G users that were initially not covered by the 4G technology and former 3G user under 4G coverage that can be financed) ensures the 3G network (for each bloc) to have sufficient capacity to handle the traffic it must conveyed. Second phase is dedicated to the 4G network re-dimensioning, which is similar to the 3G network re-dimensioning step. Note
Notations
We consider a given period t of the planning time horizon Let us denote by st S�G U S�4G the existing sites at the beginning of this time period, where S�G and sites and the 3&4G S�4G respectively represent the pure sites (co-located NodeB and eNodeB). Let Bt denote the bloc partition of the sites and sg the set of sites composing bloc E Bt: by definition we have Bt UbEB,Sg and Vs E st E Bt such that s E SDi For each ni bloc E Bt, let us denote by s�,' � t, g E its number of NodeB and eNodeB (sets are pure 3G and colocated 3&4G sites within bloc are noted sg 3G sg 34G) and by ' rC�' �nit, g E their cumulative numbe of resource , capacity units (i.e. the number of carriers for 3G blocs and the number lOMHz bands for 4G blocs). We then introduce nota tions for technical limitations such as the maximum number of resource capacity units per site for each technology, denoted by Reg, g E as well as the maximum number of 3G T
= LT.
=
3G
b
b
= = 1. {3G, 4G}
I{b
{3G, 4G}
b
�
{3G; 4G}
9
Algorithm 1 S EQUENTIEL for b E Bt do
that 4G intensification is (necessarily) done by deploying 4G on (3G) sites built during the 3G intensification step. This methodology is detailed in Algorithm 1. The cost of this solution is a combination of added resource capacity units related costs, added sites costs and the marketing subsidies as it is specified in indicator costt.
1. 3G BLOC-DIMENSIONING
/*We estimate the 3G Data and Voice traffics based on users allocation to sites and average usage.
TrVoice = AUPuVoice nut F,init ,init Trb,'b3ata G = AU pU3GData( nub,3G + L nus,t 4G ) sESt3G
deploy St,add ) ( build St,b,a3dd cost t = " b,4G G +C4G � C bEE' " crcrct,add + " csubnut,sub +" b,g s � � � sESj4G bEE' gE{3G;4G}
/*We check the bloc's 3G capacity. In n�eded, we first add carriers, and then, we build new 3G sites (intensification).
t,need = ,Tr!:oice +Trf,!tba l > rct,init then if rcb, I 3G 3G b,3G capa . ,need ,init., RC t,init t t t mm rCt,ba3dd [ rCb3G -rCb,3G 3GSb,3G -rCbt,ini ,3G ] G ' end if 'f t,need = rCt,add > 0 then IrCb,3G b,3GLneed t,add r , cb,3' G l,' N s3G] /*3G sites building. i n s b,3G + = m [ I RC3G b ,need - RC st,add /*3G capaclty t . update. rCb3G 3G b 3G end if '
9
C.
_
Integer Linear programming based approach
The single-period 3G/4G load-balancing optimization prob lem (for a given time period t) can be formulated as an integer linear program as follows: ' ml n
S.t
_
)
(
ALGORITHM
" C build St,a3dd +C deploy St,add b, G b,4G 4G � bEE' " crcrct,add + " csubnut,sub +" b£ s 9 � � � sESj4G bEE' gE{3G;4G} end = t,init St,add St,b,g Sb,g + b,g ' b E Bt , 9 E {3G , 4G} (1) t,end t,init +rCt,add +RC9 St,add , rCb,g -rCb, g b,g b,g t b E B , 9 E {3G,4G} (2) t, a dd < N 3G t Sb,3G (3) - S b' b E B ,ini t,add _ < RC t,init t t rCb,g 9 b,g -rCb,g , S b E Bt, 9 E {3G,4G} (4) t,init t sub , b E Bt nUt,b,e3nd nu, (5) s G = nUb,3G sESt3. 4G end t t sub , b E Bt nUt,b,4G nu, = nUb,t,ini (6) s 4G + sESt,34G t,init_ t sub nu, AUPu3GData( nUb, s 3G sESt,34G _" t,init t) +AUPuVoice t nUb � nUs,4G Xs sESjG (7) :s; Capa3GrC�;r;f, b E Bt ,ini ,ini b t t t " ( t t + nu, t su ) + " s nUs,4G � nUs,4G Xs � sESt,34G capa4G tend < ' b Bt ---=-=-:-rc (8) AU PU4GData b,4G ' E t (9) L X�:S; S�,�� , b E B sESjG add_ " t < St,add t St,b,4G (10) � Xs - b,3G , b E B sESjG add end "'T b E Bt , 9 E {3G , 4G} E 1'1, rCt,b,g , rCt,b,g add St,end n t,end St,b,g , b,g , Ub,g E N , b E Bt , 9 E {3G , 4G} nu,s � ub E [..O nu!,��t],S E S�4G; Xs{O; I},S E S�G'
2, 4G COVERAGE & MARKET SHARE EXTEN SION
epl Let S � oy 0 be the set of existing pure 3G sites where 4G will be deployed during period t. Let
=
-----+
Sl'3G
the set of pure 3G sites of bloc b, sorted in
order w.r.t to decreasmg .
off Trbt,3G ' LSEs�ePIOy nu!,�nt),
_
Let
t,init AUPu3GData nus 4G t,int AUPU3GD�ta( nUb 3G
+
of
3G
the
maximum
amout
ep
'
traffic that can be off-loaded, given sg loy. /*We extend the 4G coverage until the maximum amount of traffic potentially off-loaded by 4G device/subscription financing is sufficient to de-saturate the 3G network. W
h'Ile Trb,t,3ofG f
capa3Grcb,t,need 3Cj d l e S P ; oy U = t } {SLG.jistElemenO � t--+ .' t Sb3G = Sb3G\{Sb3G , ·fzstElement()}; X s = 1
rct,initl then if rcb, I capa4G 4G b,4G . dd t,need rC t,init., RC4GS t rC t,init] rCt,ba4G [b - mm rC 4G - b,4G "4G - b4G end if 'f t,need - rCt,add > 0 then IrCb,4G b,4G t,need ,4G l t,add c r , b = s b,4G + /*We install eNodeB. I RC4G t,need C,4G s � �� ; ( b G l] /*We ensure that new s �,�� = max [ RC� ' _
eNodeB are on intensified :5G sites.
end if end for 10
Instance
Sequential meth. obj. value time (sec)
ILP meth. obj. value time (sec)
The cost function is a combination of 3G building sites costs and 4G deploying costs (first term), added resource capacity units on existing sites related costs (second term), and marketing subsidies (third term). Equations (1-2) describe the networks dynamics constrained by the bloc/site related technical limitations ensured by equations (3-4). Then, equations (5-6) capture the users' dynamic within generations of device/subscription. Equations (7-8) ensures the compliance of the 3G and 4G networks bloc-dimensioning (at the end of the time period) with the 3G and 4G traffics (at the end of the time period). Endly, equations (9-10) ensure a proper counting and repartition of the deployed eNodeB (on existing 3G sites or built ones).
lAHLb II COMPARISON OF THE SOLUTION METHODS FOR THE SINGLE PERIOD PROBLEM.
the model is clearly bloc-decomposable. However we choose to present it this way since this canonic problem is in practice enriched with strategic guidelines which often con cern the whole territory and thus lead to coupling constraints (see. paragraph IV-B).
lAHUe. III COMPARISON OF THE SOLUTION METHODS FOR THE MULTI-PERIOD PROBLEM.
Instl Inst2 Inst3 Inst4 Inst5
Instance Instl Inst2 Inst3 Inst4 Inst5
Remark:
IV.
Sequential meth. obj. value time (sec) 3 3 12 38 61
2 3 4 63 240
301 1940 3139 4589 7038
220 1727 2417 3724 5349
lLP meth. obj. value time (sec)
9214 10120 16694 26000 47494
4 8 20 363 605
8108 9310 14858 20540 40370
NUMERICAL EXPERIMEN TAT ION
Test results are presented on a test-bed of 5 real-life in stances derived from the French Pays-de-Loire and Brittany regions. Their main features are given in Table I. Instance
no sites
Instl Inst2 Inst3 Inst4 Inst5
155 310 460 700 1375
no nodes NodeB eNodeB
no users 3G 4G
I
155 310 460 700 1375
40 100 120 177 430
increase of the computation time (a rough ratio of ten for the two larger instances); however we can conclude that this method remains tractable, even for large instances. Note that is quite the same for single-period and multi-period problems, which could be expected as we proceed with a sequential solving of single-problems for the multi-period ones. From a cost perspective, these results clearly show the benefit of using an exact method for single-period problems solving. In the single-period framework this solution method is an exact solution method and leads to an average decrease of of the solution cost. Note that this benefit appears slighly lower in the multi-period framework with an average saving of
108300 216670 325000 600624 1201250
I
2683 5 53670 80500 107500 215000
20.8%
TABLE I INSTANCES DESCRIPTION.
A.
I
1 6 9 27
13.4%.
Comparison of the solution methods
B. Impact illustration of strategic guidelines
In this paragraph, we compare the two solution methods presented in Section III, referred respectively as "Sequential Meth" and "ILP meth" when the sequential methodology described in III-B or the Integer Linear Program (ILP) de scribed in III-C is used for solving a single-period 3G/4G load-balancing problem. Note that integer linear programs are solved with the branch-and-bound algorithm from GLPK, a non-commercial solver [9], used with its default setting. We provide tests results for two versions of the problem: a 5 year multi-period planning problem (time horizon is 20162020) with yearly time periods (see. III) and the single-period problem (see. II). For each problem and solution method, we report for the objective value for the solution found noted "obj. value" and the computation time in seconds, noted "time (sec)". Note that the solution found by the ILP approach for the single-period problem is an optimal one provided the branch and-bound converges, which always proves to be the case in our tests. Two main observations can be drawn from these numerical results. From a computational point of view, solving single period problems with the IPL method leads to an important
The design of master plans is often constrained, not only by technical constraints, but also by budget arbitrages as well as quality of service (QoS) ambitions. This paragraph aims at illustrating the impact of such strategic guidelines. We consider here two types of constraints: first a budget constraint meant to control investments on the 3G network, which is straight forward formulated as follows: � �
bEE'
, , t add t add Crc 3Grcb,3G + C build Sb,3G
