Load Balancing Algorithm by Vertical Handover for Integrated Heterogeneous Wireless Networks Mohammad Ali Pourmina* and Navid Mirmotahhary

Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 http://jwcn.eurasipjournals.com/content/2012/1/14

RESEARCH Open Access Load balancing algorithm by vertical handover for integrated heterogeneous wireless networks Mohammad Ali Pourmina* and Navid MirMotahhary

Abstract In this paper, an adaptive resource management scheme for hybrid WWAN/WLAN is proposed. Based on proposed joint velocity and average received power (ARP) estimation algorithms, a novel vertical handoff (VHO) for efficient load balancing in multitier network is developed. Simulation results show that proposed scheme achieves significant improvements over conventional schemes. Keywords: mobility aware vertical handover, load balancing heterogeneous networks, power estimation

1. Introduction based on network selection strategies. An active multi- Future wireless communication systems can be visualized mode MT can also change its connections among different as the integration of different radio access network (RAN) types of IHWN. Such a process is called the vertical hand- technologies, to provide always best connected. Heteroge- off (VHO). Traditional handoff algorithms are based on neous wireless networks (HWN) will give the service pro- link quality or estimate of ARP. However, this measure is vider, a chance to provide sufficient capacity, needed to not sufficient for VHO, and other factors like mobile user support the temporally and spatially fluctuating traffic velocity, network condition, and user preferences should demands generated by mobile users. A practical benefit is be considered. Also because of complex structure of next- that users can be served at lower cost and with the better generation networks, more precise and sophisticated quality of service (QoS). To support freedom of movement method for link measurements is required. In mul-tipath between HWNs and seamless roaming, several VHO man- channel, received signal strength (RSS) is consisted of agement architectures and decision-making algorithms three different phenomena (path loss, shadow fading, and have already been proposed [1]. These will allow full fast fading). Because of MT mobility, multipath effect, and exploitation of flexible HWN infrastructure, resources, shadowing, the RSS has fluctuations, which make raw sig- and services. Although individual radio resource manage- nal strength an unstable criterion for triggering vertical ment (RRM) schemes can be tuned to optimally perform and horizontal handoffs (HHOs). Shadowing, large-scale within their respective RANs, they may not efficiently per- variation in path loss, is caused by obstacles in the propa- form in an HWN if the different RRM schemes are not gation path between the MT and the base station (BS). properly managed. Hence, a major issue is how to jointly The small-scale variation is due to the Doppler shift along utilize the resources of the different RANs in an efficient the different signal paths and the time dispersion caused manner while simultaneously achieving the desired QoS by the multipath propagation delays. As one primary indi- and minimizing the service cost from both user and ser- cator of channel quality, the power of the slowly varying vice provider perspectives. In an integrated heterogeneous shadow component is important for handoff decisions and wireless network (IHWN), a mobile terminal (MT) is power control. Most existing handoff algorithms assume equipped with heterogeneous network interface, which is that multipath fluctuations can be adequately filtered and called the multimode terminal. When a multimode MT base their handoff decisions on local mean power estimates generates or originates a new call in an IHWN, it can [2,3]. Although these variations bring back uncertainty in select connections among different types of the IHWN the act of VHO decision making, they can be utilized to extract precious information about propagation environment and mobility behavior of mobile user [4]. In order to * Correspondence: [email protected] Department of Electrical Engineering, Science and Research Branch, Islamic mitigate these variations in RSS, efficient smoothing Azad University, Tehran, Iran

© 2012 Pourmina and MirMotahhary; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 2 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

techniques must be considered. If the averaging interval is multimodal wireless terminals in a heterogeneous environ- too short, fluctuations may not be effectively removed, or if ment; some preliminary measurement works were done the interval is too long, it may cause delay in handoff pro- mainly between WLANs, general packet radio service cedure, or in non-line of site (NLOS) scenarios, it can aver- (GPRS), and digital video broadcasting for terrestrials age out useful information of corner’s positions. To fully (DVB-T), but the described algorithms were very simple, exploit the capacity of the wireless channel, and to over- and it did not present how such redistribution would be come ping-pong effect, an efficient power estimation performed in detailed steps. Efforts on standardization of method is required [5,6]. The ping-pong effect occurs if the VHO operation can be review on [13-15]. Although factors for VHO decision are changing rapidly and an MT the above network selection strategies have their own performs the handoff as soon as it detects a more suitable advantages, they did not put much attention on system BS. Because of heterogeneity, PHY and MAC layer of dif- performance, such as the blocking probability of originat- ferent IHWN are different, so a unified approach must be ing calls and the forced termination probabilities of hori- taken into consideration for collection of specific measures zontal and VHO calls. They fail to address any ARP and from different networks. As a result, more sophisticated also velocity estimation method in order to perform an VHO algorithm is required to extend the throughput of accurate and seamless VHO. Also these have not consid- multilayer network and to increase efficiency of resource ered corner effect and effect of low SNR in cell bound- management for next generation of HWNs. In this paper, aries. In a homogenous environment, the ping-pong effect utilizing an accurate joint velocity and ARP estimation is a phenomenon that rapidly repeats HHOs between two algorithms, a novel VHO algorithm is proposed which can BSs and can be mitigated by means of dwell timer (DT) or effectively be used for load balancing and internetwork hysteresis margin [16]. In a heterogeneous environment, ping-pong effect reduction in HWNs. Also based on Mar- the ping-pong effect occurs if factors for the VHO deci- kov model, an analytical model for performance evaluation sion are changing rapidly and an MT performs handoff as of the VHO algorithm is proposed. This paper is organized soon as the MT detects the better BS [17]. The DT as follows. Section 2 reviews related work on VHO algo- scheme has been used to avoid such ping-pong effects due rithms. In Section 3, propagation model for an IHWN is to the fact that RSS from HWNs is not comparable to introduced. In Section 4, proposed load balancing algo- each other [5,6]. The ping-pong effect can also occur if the rithm is discussed. VHO algorithm analysis framework is MT’s speed is high or its moving direction is irregular. described in Section 5. The performance of the proposed Therefore, the proposed VHO algorithm balances the traf- VHO algorithm is analyzed through a theoretical model fic load in each network based on efficient mitigation of and simulations based on probability of blocking and prob- inter-network ping-pong effect and also based on MT ability of false network layer assignment in Section 6. mobility behavior. Finally, paper is concluded in Section 7. 3. Propagation and noise model 2. Previous works The propagation model discussed here takes into Early works on VHO considered multitier homogeneous account correlated multipath fading, correlated lognor- networks and used the RSS as the main factor of the mal shadowing, and a distance dependant trend [18]. A hand-off decision-making process [7]. However, the VHO discrete model (with the sampling rate of 1/2BW)for needs to be triggered considering a few more factors [8]. the received signal (RS), g[n], is given by In [9], a VHO algorithm is proposed based on a assumption that a data call is kept in the higher bandwidth net- γ [n]= s[n].r[n]+η[n] (1) work as long as possible and voice calls are vertically handed over as soon as possible to avoid handoff delay. In where r[n] is the complex envelop due to multipath [10], a network selection strategy that only considers propagation and user mobility, which contains the ’ mobile users’ power consumption is introduced. To maxi- mobile s Doppler amplitude information and s[n] is ARP mize the battery life, the mobile user selects the uplink or (local mean) at the MT and h[n]isAWGnoisewith σ 2 downlink that has the lowest power consumption from all zero mean and variance of n which is added to the RS. of the available networks. In [11], a policy-enabled net- r[n], s[n], and h[n] are mutually independent. r[n]is work selection strategy is proposed, which combines sev- defined by [4] eral factors such as bandwidth provision, price, and power 1 K consumption. By setting different weights over different j(2πfd cos(θi)n+φi) r[n]=√ aie (2) factors based on the user’s preference, a mobile user can k i=1 connect to the most desired network. Reference [12] presents a signaling protocol for the exchange of information where fd is the Doppler frequency, θi and ji are between a network management system and intelligent mutually independent random variables uniformly Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 3 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

distributed over (-π, π, ai is the gain of ith scatter and K measured at an MT and second one uses corresponding is the number of independent scatters; usually K =20is propagation times called cell sojourn time (CST) in order sufficient to provide good approximation). The process s to show if user speed is slow, medium, or fast. Both cate- [n] is a wide-sense stationary lognormal random pro- gories are subjected to strong irregular variations caused cess, which contains distance-dependent trend and log- by Rayleigh fading and shadowing [17,20]. Many of fading normal shadowing. We denote its mean and variance by distribution property (FDP)-based methods give an accu- μ σ 2 s and s , respectively. Shadow fading process is rate estimate in noiseless environments, but in noisy envir- assumed to have the exponential correlation function onment, results are unreliable [17,20]. In urban area which proposed by [19] based on the measured autocovariance is modeled as Manhattan structured microcell, speed esti- function of s[n] in urban environments. Path loss, (μs mation is more complicated, due to complexity introduced (d)) which is a mean of s[n], decreases monotonically by severe fading and noise. On the other side, although the with distance from the BS. Let dc be the distance CST-based methods work well in noisy area [17], but these between BS and intersection at which MT makes a turn. algorithms lose their accuracy when they are used on Following [4], dimensionless parameter x0, the distance highly dense urban area with variety of building structures. parameters xc, y0, yc and exponents ζ, h, c are intro- Because CST-based methods calculate MT speed by com- duced. Corner effect could cause ΔS dB signal drop, in paring the CST with a predefined time threshold, a man- y0 meters. P0 is a constant that accounts for transmitted oeuvering user with variable speed might have more (less) power and antenna gain. Path loss for microcellular actual speed than what is estimated based on comparing structure at position d is modeled by CST with predefined threshold. High MT mobility in cell borders is another issue which can result in many cell bor- ⎧ ⎪ d der crossings. The sojourn timer resets every time MT ⎪ P − 20log ⎪ 0 10 x ⎪ 0 crosses the cell border, thus a slow-moving MT that is ⎪ ζ − χ ⎪ 10 d ( 2) repeatedly crosses cell border is considered as a fast- ⎪ − < < ⎪ log10 1+(1+ ,0 d1 dc moving MT by CST-based schemes [17]. In addition, ⎪ x xc ⎪ ⎨ − · CST-based algorithms fail to estimate variable speed. μ S (d) < < s(d)=⎪ PL(d1)10 dc d y0 (3) When variable speed MT is circulating around the cell ⎪ 10y0 ⎪ boundary, CST-based algorithms classify MT as a slow- ⎪ d ⎪ P (d ) − 20log moving MT. CST-based speed estimation algorithms ⎪ L 2 10 ⎪ y0 require estimation and calculation of statistical properties ⎪ η− ⎪ ( 2)χ ⎪ −10 d < of CST in coverage area [17]. In order to calculate prob- ⎩ log10 (1 + 1+ , d2 y0 x yc ability and cumulative distribution functions (PDF and CDF) of CST, while taking into account presence of fast To suppress noise and interference terms, g[n]is fading, shadowing, corner effects, and uncertainty region passed through a unit-gain, square-root raised cosine between neighboring BSs, it is required to perform simpli- lowpass filter with a bandwidth BW >fmax, since we are fications and assumptions, which results in lack of general- only interested in the Doppler power spectrum, which is ity. Hence, an FDP-based method for MT speed estimation narrowband and variable (0 -fmax(Hz)) in microcellular is proposed in this paper. A simple type of window-based structure. fmax is maximum possible Doppler frequency ARP estimators, namely weighted sample average estima- of channel. An example of RSS in a microcellular envir- tors of local mean power, is currently deployed in many onment is plotted in Figure 1, for variable mobile speed commercial communication systems, and various other when long-term SNR is 20 dB. As it is seen, short-term window-based estimators (WBEs) have been proposed in SNR is high near base stations. Long-term SNR is [21]. These WBEs work well under the assumption that plotted for 100 s observation. the shadowing is constant over the duration of the averaging window, and in this case, their performance improves 4. Proposed traffic load balancing algorithm as the window size increases. In practice, however, the sha- Knowledge of MT’s position and velocity plays an impor- dow process varies with time (albeit slowly relative to the tant role on offering efficient network controlling mechan- fast-fading process), and this variation must be considered isms and variety of offered services in IHWNs. Mainly in since both analysis (developed herein) and experiment IHWNs structure, WLANs have less coverage than show that the mean square error (MSE) performance of WWAN, so a reliable mobility tracking algorithm is desir- these WBEs deteriorates severely when the window size able to reduce the number of handoffs and waste of band- increases beyond a certain value. For variable speed, the width due to unnecessary signaling. Researches about MT observation window must be adapted constantly, and speed estimation are divided into two different groups. the rate of adaptation depends not only on the MT speed First one uses statistics of RSS from different BSs but also on the sampling period and shadow fading Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 4 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

50 RSS of BS0 Noisy RSS of BS0 Local Mean of BS0 0 ) −50 dBm (

ain −100 G

−150

−200 0 10 20 30 40 50 60 70 80 90 100 Time (s) Figure 1 Simulated RSS for variable mobile speed, long-term SNR = 20 dB for noisy RSS.

characteristics. In particular, errors in the estimates could − 2πn N1 − propagate due to suboptimal observation windows. A joint j k Vi[k]= wi[n]γ [n]e N (4) velocity and power estimator are proposed in this paper to n=0 calculate mobility behavior of ma-noeuvering MT in dense urban area also to mitigate fluctuations of RSS in order to where wi[n]istheith window with the length Li.An minimize number of VHOs and simultaneously assign dif- estimate of PSD (called periodogram) would be ferent service requests and MTs efficiently to different net- ω ≈ 1 {| |2} works in a IHWN. This in turn can minimize probability PSDi( k) Vi[K] (5) LiF of blocking and probability of false network assignment. 2πK where ωK = for K = 0, 1,..., N -1.Itiswell 4.1. Joint velocity and average received power estimation N In HWNs in order to reduce number of VHOs state of known that fast-moving MTs cause high Doppler spread velocity plays an important role in classification of MTs, while slow-moving MTs cause low Doppler spread. therefore our proposed method in [4] is modified in such Therefore, the shift in local maxima of estimated period- a way that state of velocity is determined in real time for ogram (PSD) is related to maximum Doppler frequency, ˆ act of VHO decision making. Due to time-varying nature which is proportional to the mobile speed (νˆ ∝ fd.λ) in of communication channel, the signal properties include which υˆi is estimated speed under ith window and l is (amplitude, frequencies, and phases) will change with wavelength [4]. time. Thus, we utilized time-dependent Fourier trans- υˆ ∝ arg Max{PSD (ω)} form also referred to as the short-time Fourier transform i ω i (6) to estimate power spectral density (PSD) of RS by using As it is seen in Figure 2, increase in velocity can be DFT of finite-length segments of the RS, obtained by interpreted as a Doppler spread in frequency domain. banks of rectangular filters such that, each filter has dif- Thus, the mobile velocity can be obtained from esti- ferent duration. The N-DFT of segmented RS, g [n], is i mated Doppler spread. First, the estimated PSD is Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 5 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

Internet Firewall

Home Agent Packet Access WWAN Router

WLAN Access Point AAA Server , NMS (AP) Server, ... WWAN

WLAN Foreign Agent Access Point (AP) WWAN

WLAN Mobile Terminal (AP) (MT)

Figure 2 Integrated heterogeneous wireless network.

ˆ − 2 normalized to estimate fd then due PSD symmetry, PSD Li 1 ˆ 1 jω 2 1 is folded (folded PSD is plotted in Figure 2). Bandwidth S ≈ |V (e )| |ω ≈ w [n]P[n] (7) i L tF i =0 L tF i of PSD is detected which is proportional to Doppler i i n=0 spread. In order to find the relative velocity of user, we ŝ Δ ’ where i is the estimated ARP, Li is window length, t classify user s mobility model into two classes, pedes- is sampling interval, and F is normalization factor [4]. trian and fast. As a result, only two segments (subsets) Active smoothing window is switched to another win- of frequency domain of estimated PSD are going to be ˆ dow in which duration is selected proportional to considered as regions of interest, and fd extraction is inverse of estimated velocity for any iteration. The sche- done only in these two segments. In proposed algo- matic of joint ARP and velocity estimator is shown in rithm, maximum is searched only in pedestrian subset Figure 3. Bias and variance of proposed local mean esti- of estimated PSD of RS, which limits search space and mator power are given in Appendix A. as a result increases estimation speed. The ARP (RS local mean) is estimated based on a fact that slow fading 4.2. Load balancing by VHO algorithm and path loss have slow variations while MT is manoeu- As it is mentioned in previous section, due to heteroge- vering in coverage area; therefore, they are present only neity of integrated networks, measurements of each net- in DC component of the estimated PSD of the RS. For work cannot be compared directly to other networks, so manoeuvering MT, the duration of observation window hysteresis method [10,11] cannot be utilized in VHO must be constantly adapted, and the rate of adaptation algorithm. Thus, thresholding technique is considered in is critical on performance of speed and power estima- this paper. In HWN structure shown in Figure 4, each tors [18]. DC component of estimated PSD is adaptively network shall have its own thresholds. Also due to the extracted from different filters fact that requirements of load balancing in each network Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 6 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

1 on i unct

F 0.8 Estimated PSD for v= 0 km/h ty i Estimated PSD for v= 108km/h 0.6 ens D

0.4 ower P

d Doppler Spread ze 0.2 li

orma 0 N 0 100 200 300 400 500 Frequancy (Hz) Figure 3 Folded PSD which shows Doppler spread for different velocities. are different, so proposed algorithm is divided into 2 average of the all the velocity estimates during dwell sections, (1) Downward VHO from WWAN to WLAN time period is considered as a velocity estimate to clas- and (2) Upward VHO from WLAN to WWAN. In sify MT as pedestrian or fast. The idea of utilizing 2 defined scenario, HHOs are only between BSs of thresholds for adding MT to the list of upward VHO WWAN network due to limitations of coverage that candidates solves the problem of lack of accuracy in sce- WLAN access points have. HHO algorithm utilizes joint narios that slow manoeuvering MT are bouncing inside velocity and ARP estimator in the act of HHO decision and outside of cell boundary. Benefits gained from making. Proposed HHO is based on using hysteresis knowledge of user real velocity are to reduce ping-pong margin method [22] in addition to DT which is calcu- effect caused by mobility behavior of MTs, and idea of lated based on inverse of velocity estimates. Block dia- using adaptive DT ((tDT ∝ 1/υˆ)) velocity lack of ability gram of proposed VHO algorithm is shown in Figure 5. to use hysteresis methods for HWNs and in addition to First, velocity and RS local mean are estimated from raw novel proposed ARP method mitigates ping-pong effect RSS. Values and thresholds used in the VHO decision caused by fluctuations and RSS due to fading. making are also calculated and updated periodically. The proposed load balancing algorithm selects a net- 5. VHO algorithm analysis work based on specifications of each network. Algo- Due to the fact that in VHO (HHO) algorithms, deci- rithm 1 illustrates VHO algorithm. According to sion making on target network (cell) is based on present Algorithm 1 in order to reduce the effect of velocity and previous step states, Markov model can be used for estimation error on accuracy of VHO decision making, modeling and calculation of probability of transition in

K[]n Wni[] ^ Max f r[n]s[n] PSDi [] k d FFT - 2 matched filter {.} N piont . M[k]W [] k k0z

^ S PSDi [] k K=0

Figure 4 Block diagram of joint velocity and RS local mean unit. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 7 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

Other Measurments

K[]n wni[]

ˆ Max fˆ r[n]s[n] FFT - PSD[] k d 2 i {.} N piont . k0z ˆ ˆ PSDi [] k S K=0 Vertical Handoff Decision Making Unit

Figure 5 Block diagram of VHO decision making unit.

each state. For the given system model of Figure 4, a Nstate i=0 Psi =1; however, the expressions for the transition user in the system can be in one of the Nstates defined as probabilities remain to be determined; these form the follows topic of discussion in the succeeding sections. − Nnetwork 1 5.1. Service model Nstate =1+ Nnetwork − i (8) i=0 The service model relies on four assumptions.

In case of 2 integrated networks, we have 1. Due to wide coverage that WWAN has, we assume that probability of MT being inside the cov- • State0) The user has no active session in progress erage area of WWAN, PWWAN = 1 and as the cover- and is not occupying any channel (i.e., the user is age area of WLAN is subset of WWAN; it is clear idle), independent of its location. that P <1. • WLAN State1) The user in the WLAN coverage area is 2. New calls arrive in the macrocell and microcell occupying the WWAN resource. according to a Poisson process with mean arrival • State2) The user in the WLAN coverage area is rates lWW and lWL, respectively. A new call is ran- occupying the WLAN resource. domly determined as the real time (RT) and non-RT • State3) The user in theoutofWLANcoverage (NRT) calls with probabilities Prt and Pnrt, respec- area is occupying the WWAN resource. tively. Similarly, a call is also independently determined as a low (high)-bandwidth application with Figure 5 shows the user state transition diagram for probability Pbwl(Pbwh). Clearly, Prt + Pnrt =1and the 2 network system models, where Psi[k]showsith Pbwl + Pbwh =1 steady-state probability at kth moment and Pij [k] denotes the transition probability from state i to state j, Algorithm 1 Proposed VHO algorithm Î i, j 0, 1, 2,..., Nstate, and state transition probability 1: loop matrix P is given by 2: if MSi Î {MSi | Connected to WWAN} then ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ − ˆ ≥ ( ) Ps0 [k] Ps0 [k 1] 3: if SWLAN Tr dB } then P00[k] P01 [k] P02[k] P03[k] W LAN ⎢ ⎥ ⎢ ⎥ ⎢ − ⎥ Î ⎢ Ps1 [k]⎥ P [k] P [k] P [k] P [k] ⎢ Ps1[k 1]⎥ 4: MSi {Downward VHO probability set} ⎢ ⎥ = ⎢ 10 11 12 13 ⎥ · ⎢ ⎥ ⎣ ⎦ ⎣ P [k] P [k] P [k] P [k] ⎦ ⎣ − ⎦ 5: if υˆ ≤ V then Ps2 [k] 20 21 22 23 Ps2 [k 1] (9) th P30[k] P31 [k] P32[k] P33[k] 6: MT Î {Pedestrain Class} and MT Î Ps [k] Ps [k − 1] i i 3 3 P {VHO Candidate set} π[k] π[k−1] 7: Start(tDT){tDT ∝ 1/υˆ } Based on Algorithm 1, a user can change state from 8: if υˆ ≤ Vth untill the timer expires then state0 to any nonzero state when a new connection is 9: at the end of n made. If a session is completed while a user is currently υˆi tDT υˆ = (t)0≤ t ≤ tDT in a nonzero state, the user changes to state0. The Mar- i=1 n kov chain depicted in Figure 5 is irreducible and aperio- 10: MSi Î {VHO Active Set} dic, and all the states are recurrent nonnull, so that the 11: VHO to target Network equilibrium state probabilities can be determined by sol- VHO(targnetwork) ving the (9), subject to the normalization condition 12: else Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 8 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

− − 13: Reset Dwell Timer {Reset (tDT)} PVHO[k]=Ps1 [k 1]P12[k]+Ps2 [k 1]P21 [k] 14: end if (12) + Ps [k − 1]P23[k]+Ps [k − 1]P32[k] 15: else 2 3 16: MSi ∉ {VHO Candidate set} ® According to list of states, each state consists of set of Unbeneficial events (Si)(e.g., each network has Ncelli BSs, so probabil- VHO (MT Stays in Current Serving ity of being in any state can be determined based on Network) probability of being connected to any of cells inside net- 17: end if work coverage area). Hence, 18: end if NCelli 19: else if MTi Î {MT is Connected to WLAN} then Ps [k]= Ps [k] (13) 20: if ˆ ≤ and i il SWLAN TrWLANAdd (dB) l=1 ˆ ≥ SWWAN TrWWAN (dB)then where Si = {Si1, ..., SiN } {∀i, l|i Î {1,... N } and l Î 21: MT Î {Upward VHO probability set} Celli state i {1,..., N }}, and P [k] is probability of occupying 22: Start(t ){t ∝ 1/υˆ } celli sil DT DT resources of tth BS from ith network at the kth 23: if υˆ ≥ Vth untill the timer expires or ˆ moment. State transition probabilities can be defined as SWLAN ≤ Tr (dB)then WLANDrop follows 24: MTi Î {VHO Active Set} 25: VHO to target Network VHO(targ ) Ncell network { | − } { | − } 26: else pij[k]=P Si[k] Sj[k 1] = P Sil[k] Sjl[k 1] (14) l=1 27: Reset Dwell Timer {Reset (tDT)} 28: end if each P{Sil [k]|Sjl[k - 1]} will be determined based on 29: end if predefined VHO algorithm. Before further discussion 30: end if on how to determine conditional probability of transi- 31: end loop tion between events in HWN, it is worth mentioning that based on scenario, some simplifications are possi- 3. Call duration Tcall is exponentially distributed with ble in transition matrix (P) determination. For ameanof1/μ,whereμ is the average call comple- instance, state transition from state3 to state2 is not tion rate. Hence, the call completion (termination) feasible directly, because if a user out of WLAN cover- probability Pterm = P (Tcall ≤ Tth), where Tth is the age area intends to change state to state2 which is time unit for the user state transition diagram, as occupying resources of WLAN, first it must change shown in Figure 5. state to state1 which is entering into coverage area of 4. From Nstate P = 1, it is clear that for scenario WLAN and then it would be feasible to switch to i=0 si Nstate state2 so for any k,wehave depicted in Figure 5. PWWAN = i=0 Psi and PWLAN = Ps0 + Ps1 + Ps2 =1-Ps3. P [k]=P{S [k]|S [k − 1]} 32 21 31 (15) = P{S [k]|S [k − 1]} = P{S [k]|S [k − 1]} = 0 based on the service model, the transition probabilities 22 32 23 33 are P 10 = P20 = P30 = Pterm. For exponentially distributed because in proposed VHO algorithm, upward and l l l interarrival time Tar with a mean of 1/ n( n = WW + downward VHO are different; thus for each scenario, l WL), the new call arrival probability within the next time equations must be calculated separately. VHO criteria ≤ unit is Pnew = P(Tar Tth). Also, it is clear that P10 = Pnew (estimated velocity and ARP) are prepared according to arrival. The probability of a new call arrival in the WLAN Figure 6, and clearly, velocity and ARP estimates are area Pnew WL and the probability of a new call arrival in independent. Event of presence of user in state1 and the WWAN area Pnew WW can be written as follows downward VHO to WLAN at the kth moment is × Pnew WL = Pnew PWLAN (10) S [k]S [k − 1] 2 1 and ˆ = SWLAN[k] > TWLAN, V[k] ≤ Vth|S1[k − 1] Pnew WW = Pnew × PWWAN (11) ˆ = SWLAN[k] > TWLAN, |S1[k − 1] × (16) V[k] ≤ Vth|S1[k − 1] 5.2. State transition probabilities for VHO ˆ As it is shown in Figure 5, VHO probability can be deter- = SWLAN[k] > TWLAN|S1[k − 1] ×{V[k] ≤ Vth} mined by state probabilities crossed by VHO index line Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 9 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

P23

P P 32 P 22 (WLAN) P (WWAN) 33 WWAN& 01 P WLAN 30 WWAN

P10 Idle P03

P21 P02 P13 P20

P12 P31 (WWAN) WWAN& VHO index line WLAN

P11

Figure 6 State transition diagram for Nnetwork =2.

and corresponding state transition probability is as fol- Other transition probabilities can be determined like- lows wise. To calculate a close form for transition probabilities, it is required to calculate joint and conditional P [k]=P S [k]|S [k − 1] 12 2 l PDF of RSS which is given in Appendix B. ˆ = P SWLAN[k] > TWLAN|Sl[k − 1] × P{V[k] ≤ Vth} (17) ˆ 6. Performance evaluation P SWLAN[k] > TWLAN|Sl[k − 1] × { ≤ } = P V[k] Vth This section presents numerical results that demonstrate P{Sl[k − 1]} the network-level performance of an HWN comprising where P{Sl[k - 1]} is given by mobile WIMAX and IEEE 802.11 WLAN RANs. Prob- ability of blockage in WLANs and WWANs and prob- P{S [k − 1]} = l ability of false load balancing based on velocity and ARP ˆ − > ˆ − ≤ P SWWAN[k 1] TrWWAN, SWLAN[k 1] TrWLAN (18) estimates are considered as performance criteria. Users

×P{V[k − 1] > Vth} are distributed uniformly in simulation area (Manhattan area). Mobility behavior of MTs is considered according It should be noted that because RSS from different to mobility profile proposed in [4]. Performance of pro- networks cannot be compared to each other, they can posed ARP estimation algorithm is compared to WBEs, be considered as independent variables. Hence, like sample average (SA), uniformly minimum variance P [k]=P{V[k] ≤ V } unbiased (UMVU) estimator, and Kalman-based method 12 th ˆ ˆ discussed in [21]. As it is seen in Figure 7, proposed P SWLAN[k] > TWLAN, SWLAN[k − 1] ≤ TWLAN (19) × local mean power estimator shows less MSE than win- {ˆ − ≤ } P SWLAN[k 1] TWLAN dow-based methods, although Kalman-based method shows better performance but requires large number of After a few simplifications, upward VHO to WWAN transmitted messages and heavy calculations so that sig- at the kth moment is given by nal strength variations can be filtered out. In Figure 8, ˆ P23[k]=P SWWAN[k] ≥ TWWAN estimated local mean power based on proposed method ⎡ ˆ ˆ is plotted. Performance of proposed load balancing algo- P SWLAN[k] ≤ TAdd,WLAN, SWLAN[k − 1] ≥ TWLAN ⎣ rithm has been investigated in the case that total call ˆ − ≥ P SWLAN[k 1] TWLAN arrival rate and the ratio of the fast to the slow traffic

×P{V[k] > Vth} (20) vary. For example, assume that the total call arrival rate ⎤ P Sˆ [k] ≤ T , Sˆ [k − 1] ≥ T to a WWAN and its embedded WLANs is 1,500 calls/h, WLAN Drop,WLAN WLAN WLAN ⎦ + and the ratio of the fast traffic to the slow traffic is 2:1. P Sˆ [k − 1] ≥ T WLAN WLAN Then, the call arrival rate of fast traffic is 1,000 calls/h × { ≤ } P V[k] Vth and the slow traffic is 500calls/h. The traffic load on the Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 10 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

16 UMVE Sample Average (Temporal Observation Windows ) 14 Proposed Method Kalman Filter 12 ) dB ( 10 E S M 8

4 0 0.5 1 1.5 Temporal Averaging Window Length (s) Figure 7 Local mean power estimation results.

50 Real Local Mean BS0

) Estimated Local Mean BS0 0 dBm ( 0 S

−50

−100 Local Mean B

−150 0 20 40 60 80 100 Time (s) v -1 X σ 2 Figure 8 MSE of local mean estimation versus averaging window length, =20kmh , c =10m,shadowingvariance s =6dB, LOS scenario. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 11 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

WWAN is 140 calls/h, and the load on each WLAN is on proposed method is plotted in Figure 11 and 12 for 136 calls/h, which consists of 86 calls/h for fast and 50 upward and downward VHO, respectively. Because of calls/h for slow. From these assumptions, the actual call robustness of proposed method even in low SNR sce- arrival rates to the WWAN and each WLAN are given narios, load balancing is done effectively. In Figure 13 by and 14, blocking probability is plotted versus different call arrival rate (from 500 calls/h to 2,000 calls/h) for λWW = 140 (1 − PeWL + 860PeWW) each layer with ln =0.4and1/l =120s.Figure13 and shows that blocking probability is effectively decreased in WWANs due to more efficient load balancing, and as λ ( − ) WL = 364PeWL +86 1 PeWW +50 (21) a result, blocking probability is increased in WLAN (Fig- ure 14), which shows more WLAN resource utilization where P is the probability that slow user is allo- eWW due to more efficient load balancing. For better demon- cated to WWAN, which gives arise to shortage in stration, blocking probability in WLAN and WWAN is macrocell capacity, and P is probability that the fast eWL plotted in Figure 15 and 16 versus specific arrival traffic user is allocated to WLAN, which causes increase in with variable ratio of slow traffic, respectively. As it is number of hand-offs. Speed threshold is considered V th shown in Figure 15, when number of slow MTs is = 5 m/s. As it is demonstrated in Figure 9 and 10, in increased, blocking probability is decreased in WWAN both LOS and NLOS scenarios, due to efficient load bal- andasaresultforWLANasitisplottedinFigure16, ancing based on mobility behavior of MTs and network there is a small increase in blocking probability. conditions, probability of false VHO to WWAN and WLAN (i.e., two consecutive VHOs within a short dura- 7. Conclusion tion for a roaming call in the hot-spot area or a very This paper proposed a load balancing scheme that mini- short WLAN session before the user moves out of the mizes the VHO rate while achieving the desired service hot-spot area) is efficiently reduced. Effect of low SNR

0.6 Dwell Timer&ClassicSojournTimeBased−NLOS Scenario Dwell Timer&ClassicSojournTimeBased−LOS 0.5 Proposed Method −LOS scenario Proposed Method − NLOS scenario 0.4

0.3

0.2 Unnesecary Handover to WLAN f 0.1

Probability o −0.1 5 10 15 20 25 30 Velocity (m/s) Figure 9 Probability of false downward VHO. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 12 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

0.5 Proposed Method − LOS Scenario−SNR=inf 0.45 Hystresis & Dwell Timer based (Simulation) 0.4 Dwell Timer&ClassicSojournTime−Based−NLOS Proposed Method −NLOS Scenario−SNR=inf 0.35

0.3

0.25

0.2 Unnesecary Handover to WWAN

f 0.15

0.1

0.05

Probability o 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Velocity (m/s) Figure 10 Probability of false upward VHO.

0.035 Proposed Method − NLOS Scenario− SNR = 20 dB Proposed Method − NLOS Scenario−SNR=inf 0.03 Proposed Method − LOS Scenario−SNR=inf Proposed Method − LOS Scenario− SNR=20dB 0.025

0.02

0.015 Unnesecary Handover to WWAN

f 0.01

0.005

Probability o 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Velocity (m/s) Figure 11 Probability of false upward VHO, SNR = 20 dB. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 13 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

0.025 Proposed Method −LOS Scenario−SNR=inf Proposed Method −NLOS Scenario−SNR=inf Proposed Method −LOS Scenario−SNR=20 dB 0.02 Proposed Method −NLOS Scenario−SNR=20 dB

0.015

0.01 Unnesecary Handover to WLAN f

0.005

Probability o 0 5 10 15 20 25 30 Velocity (m/s) Figure 12 Probability of false downward VHO, SNR = 20 dB.

0.35 Proposed Method 0.3 Classic Sojouron Time Based (LOS) Classic Sojouron Time Based (NLOS) 0.25 WWAN n i

ty 0.2 bili a b

ro 0.15 P ng

ki 0.1 oc Bl 0.05

0 500 1000 1500 2000 Total Call Arrival Rate (Calls/h) Figure 13 Blockage probability in WWAN, LOS and, NLOS scenarios. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 14 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

0.06 Proposed Method (LOS and NLOS scenario) 0.05 Classic Sojouron Time Based (LOS) Classic Sojouron Time Based (NLOS) 0.04

0.03

0.02

0.01

Blocking Probability in WLAN 0

−0.01 500 1000 1500 2000 Total Call Arrival Rate (Calls/h) Figure 14 Blockage probability in WLAN, LOS and NLOS scenarios.

0.35 Proposed Method (LOS and NLOS cenario) 0.3 Classic Sojouron Time Based (NLOS) Classic Sojouron Time Based (LOS)

0.25 WWAN n i

ty 0.2 bili a b

ro 0.15 P ng

ki 0.1 oc Bl 0.05

0 10 20 30 40 50 60 70 80 90 Traffic Rate of pedestrain users (%) Figure 15 Blockage probability in WWAN for different number of pedestrian users in LOS and NLOS scenarios. Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 15 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

−3 x 10 12

AN 10 Proposed Method (LOS and NLOS) L

W Classic Sojouron Time Based (NLOS) n i 9 Classic Sojouron Time Based (LOS) ty bili

a 8 b ro P 7 ng ki

oc 6 Bl 5

4 10 20 30 40 50 60 70 80 90 Traffic Rate of pedestrain users (%) Figure 16 Blockage probability in WLAN for different number of pedestrian users in LOS and NLOS scenarios.

− − quality (i.e., low call blocking probabilities) for highly Li 1 Li 1 ˆ 1 −jω(n−m) dense urban area. The performance of the proposed E[Si]= We E{s[n]s ∗ [m]} Li tF scheme was analyzed via user level Markov chains. n=0 n=0 Numerical results show that the proposed scheme k−1 k−1 (ω θ φ ) − (ω θ φ ) × j d cos in+ i j d cos zm+ z achieves low VHO rate and low call blocking probability E e e in comparison with the currently existing service-based i=0 z=0 ω=0 and sojourn time-based load balancing schemes. Results Considering the fact that shadowing has small varia- show that, under different mobility conditions, the pro- tions over the LTW (W = w[n]w*[m] and E {s[n]s*[m]} = posed scheme exhibits more recourse utilization in inte- s s ), then grated networks while achieving low blocking s − − probabilityinhighlydenseurbanarea.Basedonthese σ Li 1 Li 1 E[Sˆ ]= s lim J ω (n − m) results, it is concluded that the proposed scheme exhi- i →∞ 0 d Li tF Li bits a good service quality and, hence, serves as a viable n=0 n=0 − ω − (23) alternative for practical IHWN deployment. × We j (n m) ω =0 ! 2 Appendix A. Derivation of bias and MSE for = lim Gi(ω) ∗ wi(ω) →∞ ω proposed ARP estimator Li =0

If shadowing is assumed to be constant over the length of where Gi(0) and Wi(0) are DC component of RSS PSD temporal windows (LTW) and also if shadowing and mul- and rectangular window, respectively, and * refers to tipath fading are considered to be independent, from (4) convolution. Equation (23) shows that if LTW approaches to infinitum in time domain, in frequency jω ∗ jω E Vi e · V e δ E[Sˆ ] = lim i (22) domain it approaches to Kronecker delta function [·], i →∞ Li Li tF and as a result, the periodogram estimation error ω=0 approaches to zero. Assume that window magnitude is Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 16 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

normalized (F =1)andletψ = s[n]s*[m]thenfrom(7), autocorrelation function [23]. Let X be square of RSS 2 (ω ) we find a closed form for bias and variance of proposed with ACF equals to J0 dK t [16]. Thus for RSS which ARP estimator, as follows S is a Gaussian process, it can be shown that 2 2 2 2 2 k−1 k−1 k−1 k−1 E X = σ + X for a Gaussian process E X ≥ 2X 1 x ˆ 2 2 Si = therefore E[(Ŝ - E[Ŝ]) ] ≥ E[Ŝi] thus Li t i=0 z=0 n=0 m=0 # $ (ω θ φ ) − (ω θ φ ) ! 2 ψ j d cos in+ i j d cos zm+ z 2 σ W e e E Sˆ − E[Sˆ] = s × − − Li t 1 k 1 k 1 ⎡⎛ ⎞ ⎤ j(φi+φz) 2 = e L−1 k−1 k−1 Li t ω ( θ − θ ) (φ −φ ) ω θ i=0 z=0 E ⎣⎝ ej dn cos i cos z ej i z ej d cos zq⎠ ⎦ − − (24) Li 1 Li 1 n=q i=0 z=0 ω θ − (ω θ ) × Wej( d cos in)e j d cos zm A n=0 m=0 ⎛ ⎡ ⎤⎞ − 2 Li 1 − " A ⎝ ⎣ 1 Li q ⎦⎠ − σs +2 J0 q tωd beginning of period, 0 < q < Li − 1 L L if n − m = q then i q=1 i end of period, − (Li − 1) < q < 0 thus − m ≤ q ≤ L − m − 1 and therefore we have B i σ 2 A = s E p[n] 2 p[n − q] 2 2 2 − − L t Li 1 Li 1 i (28) L −1 A = w[m + q]w ∗ [m]× R| 2| 2 (0) σ 2 i p| p| 2 s 2 2 − − = + Li − q J ωdq t m=0 q= (L 1) L2 t2 L2 t2 0 ω ( θ − θ ) ω θ i i q=1 j d cos i cos z m j dcos iq e e − − Li 1 Li 1 2 2 − − L + q − 2Li q Li 1 Li 1 2 2 i σ B =4σ J q tωd ˆ ∗ ω s 0 L2 E[Si]= w[m + q]w [m]J0 q t d (25) q=0 q=0 i Li s m=0 q=−(L−1) C L −1 L −1 σ i i − − − s ω ∗ Li 1 Li 1 Li 1 2L2 − 3L +1 = J0 q t d w[m + q]w [m] 1 2 − 2 i i Li t C = 1+ q q = q=−(L−1) m=0 L2 L 6L q=0 i q=0 i q=0 i Cww[q] − Li 1 2L2 − 3L +1 σ 2 i i 2 ω B =4 s J0 q t d where CWW[m] is autocorrelation function (ACF) of 6Li rectangular window. Thus, window ACF can be deter- q=0 mined as A lower bound for variance of proposed local mean " power estimator can be determined as follows (from (28)) L − q , q ≤ (L − 1) ⎡ ⎤ Cww[q]= − 0, elsewhere 2 2 − Li 1 R|p| |p| (0) 1 Var(Sˆ) ≤ σ 2 ⎣ + J2 ω q t ⎦ 2 (26) s 2 2 0 d sin ωL/2 Li t jω q=1 then Cww e = ⎛ ⎞ sin ω/2 2 L − q 2 2L2 − 3L +1 ⎝ i − i i ⎠ (29) After substitution in (25), bias can be calculated as fol- Li 3Li lows. L −1 i L − q − i ω − 4 2 J0 dq t Li 1 − L ˆ Li q q=0 i E[Si]=σs J0 q tωd Li q=−(Li−1) ⎡ ⎤ − (27) Appendix B. Derivation of joint and conditional Li 1 − ⎣ 1 Li q ⎦ = σs +2 J0 q tωd PDF of received signal estimates L L Ŝ i q=1 o Due to the fact that RS estimates! dB have Gaussian! ˆ ˆ ˆ ˆ distribution, joint fˆ ˆ Sk−1, Sk and fˆ | ˆ Sk|Sk−1 In order to calculate variance of local mean estimates, Sk−1,Sk Sk ,Sk−1 4th moment of RSS is calculated. When LTW PDF of each event will be Gaussian. Let {ˆ − } μ − {ˆ − } σ {ˆ } μ approaches infinity, the 4th moment of most of stochas- E S[k 1] = sˆ[k 1], Var S[k 1] = Sˆ[k−1], E S[k] = Sˆ[k], tic processes will approach to Gaussian process, and for {ˆ } σ and Var S[k] = Sˆ[k] a Gaussian process, it can be calculated based on Pourmina and MirMotahhary EURASIP Journal on Wireless Communications and Networking 2012, 2012:14 Page 17 of 17 http://jwcn.eurasipjournals.com/content/2012/1/14

TWLAN − μˆ 4. N Mirmotahhary, A Kohansal, H Zamiri-Jafarian, M Mirsalehi, Discrete mobile ˆ SWL [k−1] P SWLAN[k − 1] ≤ TWLAN = Q (30) user tracking algorithm via velocity estimation for microcellular urban σˆ [k − 1] environment. in IEEE Vehicular Technology Conference, Singapore 2631–2635 SWL (May 2008) 5. M Ylianttila, M Pande, J Makela, P Mahonen, Optimization scheme for ! ˆ − μ 2 mobile users performing vertical handoffs between IEEE 802.11 and GPRS/ ˆ ˆ 1 Sk−1 k−1 fˆ ˆ Sk−1, Sk = ) exp EDGE networks, in IEEE Global Telecommunication Conference, San Antonio, Sk−1,Sk σ 2 πσˆ 2 ˆ TX, (December 2001) 2 S − S − k 1 k 1 6. R Hsieh, ZG Zhou, A Senevirante, S-MIP: A seamless handoff architecture for 1 mobile IP, in IEEE International Conference on Computer Communication San ×√ ) 2 Francisco, CA, (April 2003) 2πσˆ 1 − ρˆ ˆ – Sk SS 7. GP Pollini, Trends in handover design. IEEE Commun Mag. 34(3), 82 90 ⎛ ⎞ (31) ! 2 (1996). doi:10.1109/35.486807 σˆ 8. N Mirmotahhary, Y Mafinejad, F Atbaei, A Kouzani, An adaptive policy-based ⎜ ˆ − μ − ρ Sk ˆ − μ ⎟ ⎜ Sk k SˆSˆ Sk−1 k−1 ⎟ σˆ vertical handoff algorithm for heterogeneous wireless networks, in IEEE 8th ⎜ S − ⎟ × exp ⎜ k 1 ! ⎟ International Conference on Computer and Information Technology, Sidney, ⎜ 2 2 ⎟ pp. 188–193 (July 2008) ⎝ 2σ 1 − ρˆ ˆ ⎠ Sk SS 9. Q Zhang, C Guo, Z Guo, W Zhu, Efficient mobility management for vertical handoff between WWAN and WLAN. IEEE Commun Mag. 41(11), 102–108 (2003). doi:10.1109/MCOM.2003.1244929 10. N Nam, N Choi, Y Seok, Y Choi, WISE: energy-efficient interface selection on ! ˆ − μ ˆ ˆ 1 Sk k|k−1 vertical handoff between 3G networks and WLANs. IEEE Int Symp Pers fˆ |ˆ Sk Sk−1 = √ exp − (32) Indoor Mobile Radio Commun 692–698 (July 2004) Sk Sk−1 σ 2 2πσˆ |ˆ 2 ˆ ˆ Sk Sk−1 Sk|Sk−1 11. H Wang, R Katz, J Giese, Policy-enabled handoffs across heterogeneous wireless networks. in IEEE Workshop on Mobile Computing Systems and ! Applications 51–60 (1999) σˆ μ μ ρ Sk ˆ − μ 12. Xiaodong Yang, Thomas OwensJ, Intersystem soft handover for Converged k|k−1 = k + SˆSˆ + Sk−1 k−1 (33) – σˆ DVB-H and UMTS Networks. IEEE Trans Veh Technol. 57, 1887 1898 (2008) Sk−1 13. G Lampropoulos, C Skianis, P Neves, Optimized Fusion of Heterogeneous ! Wireless Networks based on Media Independent Handover Operations. IEEE Wirel Commun Mag. 17(4), 78–87 (2010) 2 2 2 σˆ ˆ = σˆ 1 − ρˆ ˆ (34) 14. N Dimitriou, L Sarakis, D Loukatos, G Kormentzas, C Skianis, Vertical S |S − S SS k k 1 k handover framework for future collaborative wireless networks, Int J Netw # $ Manag, (Wiley) − |υ | − |υ | 15. WF El-Sadek, MN Mikhail, Universal mobility with global identity (UMGI) ρ 1 .tS − .tS SˆSˆ = x0 exp xav exp (35) architecture. IEEE International Conference on Wireless Networks and xav + x0 x0 xav Information Systems, WNIS 09 Los Alamitos389–394 16. N Zhang, J Holtzman, Analysis of handoff algorithms using both absolute where x0 is correlation distance of local mean power and relative measurements. in 44th IEEE Vehicular Technology Conference – and xav is smoothing window length. From above, tran- 82 86 (September 1994) sition probabilities can be determined, for instance p 17. Y Chung, DJ Lee, DH Cho, BC Shin, Macrocell/microcell selection schemes 23 based on a new velocity estimation in multi-tier cellular system. IEEE Trans [k]is Veh Technol. 51(5), 893–903 (2002). doi:10.1109/TVT.2002.801764 18. R Narasimhan, DC Cox, Estimation of mobile speed and average received TWWAN − μWW[k] TWLAN − μWL[k - 1] P [k]=Q /Q power in wireless systems using best basis methods. IEEE Trans Commun. 23 σ σ 49(12), 2172–2183 (2001). doi:10.1109/26.974264 ⎡ WW[k] WL[k - 1] ,∞ - . 19. D Wong, DC Cox, Optimal local mean signal power level estimator for − μ rayleigh fading environments. in IEEE International Conference on ⎣ ˆ TAdd, WLAN k|k−1 ˆ × fˆ (S) 1 − Q dS Information, Communications Signal Processing 1701–1704 (September 1997) Sk−1 ˆ σˆ |S − Sk k 1 20. KDA Appiah, On generalized covariance-based velocity estimation IEEE TWLAN Trans. Veh Technol. 48, 1546–1557 (1999). doi:10.1109/25.790529 × P{V[k] > Vth} 21. T Jaing, ND Sidiropulos, G Giannakis, Kalman filtering for power estimation in mobile communications. IEEE Trans Wirel Commun. 2(1), 151–161 (2003). doi:10.1109/TWC.2002.806386 22. AE Leu, BL Mark, An efficient timer-based hard handoff algorithm for Competing interests cellular networks. in IEEE Wireless Communication and Networking Conference The authors declare that they have no competing interests. 1969–1974 (March 2003) 23. A Papoulis, SU Pillai, Probability, Random Variables and Stochastic Processes, Received: 23 February 2011 Accepted: 16 January 2012 4th edn. (McGraw-Hill, New York, 2002) Published: 16 January 2012 doi:10.1186/1687-1499-2012-14 Cite this article as: Pourmina and MirMotahhary: Load balancing References algorithm by vertical handover for integrated heterogeneous wireless 1. IF Akyildiz, J Xie, S Mohanty, A survey of mobility management in next- networks. EURASIP Journal on Wireless Communications and Networking generation all-IP-based wireless systems. IEEE Trans Wirel Commun. 11(4), 2012 2012:14. 16–28 (2004). doi:10.1109/MWC.2004.1325888 2. SN Enrique, YX Lin, WSW Vincent, An MDP based vertical handoff decision algorithm for heterogeneous wireless networks. IEEE Trans Veh Technol. 57(2), 1243–1254 (2008) 3. W Shen, QA Zeng, Cost-function-based network selection strategy in integrated wireless and mobile networks. IEEE Trans Veh Technol. 57(6), 3778–3788 (2008)