research article modeling and performance analysis of an

Research ArticleModeling and Performance Analysis ofan Improved Movement-Based Location Management Schemefor Packet-Switched Mobile Communication Systems

Yun Won Chung,1 Jae Kyun Kwon,2 and Suwon Park3

1 School of Electronic Engineering, Soongsil University, 369 Sangdoro, Dongjak-gu, Seoul 156-743, Republic of Korea2Department of Electronic Engineering, Yeungnam University, 280 Daehak-ro Gyeongsan, Gyeongbuk 712-749, Republic of Korea3 Department of Electronics and Communications Engineering, Kwangwoon University, 20 Gwangun-ro, Nowon-gu,Seoul 139-701, Republic of Korea

Correspondence should be addressed to Suwon Park; [email protected]

Received 28 October 2013; Accepted 9 January 2014; Published 9 March 2014

Academic Editors: A. Manikas and H. Wymeersch

Copyright © 2014 Yun Won Chung et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

One of the key technologies to support mobility of mobile station (MS) in mobile communication systems is location managementwhich consists of location update and paging. In this paper, an improved movement-based location management scheme with twomovement thresholds is proposed, considering bursty data traffic characteristics of packet-switched (PS) services. The analyticalmodeling for location update and paging signaling loads of the proposed scheme is developed thoroughly and the performanceof the proposed scheme is compared with that of the conventional scheme. We show that the proposed scheme outperforms theconventional scheme in terms of total signaling load with an appropriate selection of movement thresholds.

1. Introduction

One of the key technologies to support mobility of mobilestation (MS) in mobile communication systems is locationmanagement which consists of location update and paging.In location update, an MS informs network of its currentlocation information whenever it changes its location area(LA) [1]. Then, if there is an incoming call for an MS, thelocation information of the MS is retrieved and networksends paging requests to all the base stations within theretrieved LA to find the current cell of the called MS. Toperform location update and paging, however, signaling loadis generated and this depends on the size of LA. If the sizeof LA is small, an MS updates its location frequently. Then,location update signaling load is high and paging signalingload is low. On the other hand, if the size of LA is large,location update signaling load is low and paging signalingload is high. Therefore, there is a tradeoff between locationupdate signaling load and paging signaling load, from theaspect of LA size.

In most mobile communication systems, such as GSM,GPRS, UMTS, and LTE, zone-based location update schemeis widely used, where an MS updates its location whenever itchanges its current zone which is defined as a fixed group ofcells. InGSM [2], LA is defined as a zone. InGPRS [1], routingarea (RA) is defined as a zone for packet-switched (PS) dataservice and the size of RA is generally smaller than that ofLA. In UMTS [1], URA (UTRAN registration area), which issmaller than RA, is defined as a zone for a more fine-grainedlocation management of MSs. In LTE [3], tracking area (TA)is defined as a zone. For efficient location management TAlist (TAL) is also defined in LTE, where there is no locationupdate if anMSmoves within TAs belonging to the sameTALassigned to the MS.

Current LA, RA, URA, and TA, however, are generally offixed size for all MSs and they do not accommodate diversetraffic and mobility characteristics of MSs. For example, ifan MS has high call-to-mobility ratio (CMR), small LA, RA,URA, and TA are more appropriate. On the other hand,if an MS has low CMR, large LA, RA, URA, and TA are

Hindawi Publishing Corporatione Scientific World JournalVolume 2014, Article ID 812657, 12 pageshttp://dx.doi.org/10.1155/2014/812657

2 The Scientific World Journal

more appropriate. Thus, there is no fixed size of LA, RA,URA, and TA appropriate for all MSs with diverse trafficand mobility characteristics. In order to solve this prob-lem, dynamic location update schemes have been proposed.Distance-based [4, 5], timer-based [6, 7], and movement-based [8–13] schemes are representative examples of dynamiclocation update. In these schemes, the condition for loca-tion update is adaptively configured to individual MSs toaccommodate different traffic and mobility characteristicsof MSs. In distance-based location update scheme [4, 5],an MS updates its location whenever the distance from thelast updated cell reaches a predefined distance threshold. Intimer-based location update scheme [6, 7], an MS performsa location update whenever the predefined time threshold iselapsed from last updated time. Finally, in movement-basedlocation update scheme, an MS performs a location updatewhenever the number of cell crossings from the last updatedcell reaches a predefined movement threshold [8–13]. Inthis paper, movement-based location management scheme isconsidered, which combines the strength of both distance-based and timer-based schemes, that is, good performanceand easy implementation.

Lots of works on movement-based location managementscheme have been carried out [8–13]. In [8], a movement-based location update scheme with selective paging wasproposed and the performance was analyzed. In movement-based location update, there is a movement counter whichkeeps the number of cells visited since the last locationupdate. An MS updates its location whenever the counterreaches a predefined value, that is, movement threshold𝑑, and then resets the counter value to 0. If there is anincoming call to an MS, network pages all the cells whichcan be reached within a movement threshold 𝑑 movementsfrom the last updated cell. Selective paging scheme basedon a shortest-distance-first (SDF) scheme is used to reducepaging signaling load. In [10], cell-level location of MSs ispredicted based on the assumption that themovement ofMSsfollows routine trajectories and selective polling strategy isused to reduce signaling load. In [11], the performance ofmovement-based location management scheme with homelocation register/visitor location register (HLR/VLR) archi-tecture is thoroughly analyzed using mathematical analysis,by relaxing a simple exponential distribution assumption ofcell and LA residence times. In [12], an optimal sequentialpaging scheme for movement-based location managementwas proposed using optimal movement threshold based onMSs’ movement statistics. In [13], a shape of TAL is proposedbased on movement-based location management. Then, theperformance of the proposed TAL scheme is analyzed inLTE femtocells. In [9], the authors developed an embed-ded Markov chain model to investigate the performanceof movement-based location management scheme, derivedclosed-form analytical formulas for the signaling costs, andanalyzed the effects of various parameters on the signalingcost.

In PS systems, a conventional movement-based schemewith single movement threshold, however, is not appropriate,since MSs in PS systems have bursty data traffic characteris-tics. Since there are short idle period between data packets

in a session and long idle period between data sessions [14],small and large movement thresholds may be more appro-priate for a short and long idle periods, respectively. In thispaper, an improved movement-based location managementscheme with two movement thresholds, that is, a smallmovement threshold 𝑑

1for a short idle period between data

packets in a session and a large movement threshold 𝑑2for

a long idle period between data sessions, is proposed. Theanalytical modeling for location update and paging costsof the proposed scheme is developed thoroughly and theperformance of the proposed scheme is compared with thoseof the conventional scheme. We note that the concept of theproposed improved movement-based location managementscheme was introduced in our preliminary work in [15] but itdid not contain neither detailed algorithm nor performanceanalysis results. Also, although the idea of using multiplemovement thresholds is similar to using multiple timerthresholds in our previous work for an improved timer-basedlocation management [7], this work provides significantextensions from that in [7]. Firstly, a new location updatecriterion of movement-based location management schemeis considered, instead of simple timer-based location updatecriterion, and a detailed algorithm for the proposed schemeis presented. Also, a new analytical modeling consideringlocation update criterion of movement-based location man-agement is developed thoroughly. Finally, the effect of cellresidence time variance on signaling load is newly analyzed.

The remainder of this paper is organized as follows.Section 2 proposes an improved movement-based locationmanagement scheme. The performance of the proposedscheme is analyzed in Section 3 by developing an analyticalmethodology. In Section 4 numerical examples are provided.Conclusion and future work are presented in Section 5.

2. An Improved Movement-BasedLocation Management Scheme

In PS systems,MS states aremanaged in networks for efficientuse of radio resources and signaling networks. InGPRS, readyand standby states are defined. In ready sate, an MS is morelikely to receive or transmit data packets in short time andupdates its location for every cell change. If a session betweenan MS and a network is completed and there is no packetexchange until the expiration of ready timer, it is more likelythat the MS does not send or receive a new data packet forsome time and the MSmoves to the standby state, where RA-based location information is managed. The ready timer isreset and restarted when there is a packet exchange betweenan MS and a network. In UMTS, cell-connected, URA-connected, and PMM-idle states are defined, and cell-, URA-,and RA-based location information is managed, respectively.Inactivity timer and periodic URA update timer are usedto control MS state transitions. In LTE, cell- and TA-basedlocation information is managed in active and idle states.

In this paper, two MS states are defined based on thetraffic characteristics of MSs, as in GPRS and LTE, and thesetwo state are denoted as ready and standby, for notationalconvenience. Two movement thresholds 𝑑

1and 𝑑

2(𝑑1≤ 𝑑2)

The Scientific World Journal 3

Begin

d = d1

Cm = 0

Ready state

MS movesinto new cell

Cm = Cm + 1

CI = CI + 1

CI ≥ dI?

d = d2

Yes

No

Standby state

MS movesinto new cell

Cm = Cm + 1

Cm ≥ d2?

Yes

No

Packet arrival

Incomingpacket?

Yes

Page cells withind1 rings from the last

registered cell

Packet transmit orreceive

Packet arrival

Incomingpacket?

Yes

Page cells withind2 rings from the last

registered cellPacket transmit or

receive

No

No

CI = 0

Cm ≥ d1?

No

Yes

Location update

Location update

Cm = 0

Figure 1: Flow chart for an improved movement-based location management scheme.

are proposed for ready and standby, respectively. However,the analytical methodology developed in this paper can beextended to any PS systems which have more MS states. Inthis paper, state transitions between MS states are controlledby inactivity counter which counts the number of cellscrossed since the last location update. An inactivity counter isreset whenever there is data packet exchange betweenMS andnetwork. If there is no data packet exchange betweenMS andnetwork until the inactivity counter is expired, an MS movesfrom ready state to standby state. We note that the signalingpacket exchange does not reset the inactivity counter.

Figure 1 illustrates the flowchart for the proposed scheme.If an MS attaches to the network, the sate of the MS is setat ready state and the movement threshold 𝑑 is initialized to𝑑1. The value of an inactivity counter 𝐶

𝐼and the value of

movement counter 𝐶𝑚are initialized to 0. Inactivity counter

is used to control the transition between ready and standbystates. Movement counter is used to track the number ofcells crossed since the last location update. The MS in theready state moves into one of two cases according to thenext events. If the MS moves into a new cell, the values ofmovement counter and inactivity counter are increased by 1


(𝐶𝑚

= 𝐶𝑚+1 and𝐶

𝐼= 𝐶𝐼+1) and the inactivity counter value

is compared with the value of inactivity movement threshold,𝑑𝐼. If𝐶𝐼≥ 𝑑𝐼, movement threshold 𝑑 is changed to 𝑑

2and the

state is changed from ready state to standby state. Otherwise,a movement counter value is compared with 𝑑

1. If 𝐶𝑚

≥ 𝑑1,

location update is performed and movement counter valueis reset to 0. If 𝐶

𝑚< 𝑑1, there is no location update and

the MS just returns back to the ready state and waits forthe next event. If there is any packet arrival, it is processedappropriately according to whether it is an incoming or anoutgoing packet. If it is an incoming packet, network pagescells within 𝑑

1rings of cells from the last registered cell.

Otherwise, an outgoing packet is transmitted. After receivingor transmitting packets, the values of movement counter andinactivity counter are initialized to 0.

In standby state, the MS moves into one of two casesaccording to the next events. If the MS moves into a newcell, the value of movement counter is increased by 1 (𝐶

𝑚=

𝐶𝑚

+ 1) and the movement counter value is compared withthe value of movement threshold in the standby state, 𝑑

2. If

𝐶𝑚

≥ 𝑑2, location update is performed and it returns back

to standby state. The value of movement counter is reset to 0.Otherwise, theMS just returns back to standby state andwaitsfor the next event. If there is any packet arrival, it is processedappropriately according to whether it is an incoming or anoutgoing packet. If it is an incoming packet, networks pagecells within 𝑑

2rings of cells from the last registered cell.

Otherwise, an outgoing packet is transmitted. After receivingor transmitting packets, movement threshold is changed to𝑑1, the values ofmovement counter and inactivity counter are

initialized to 0, and the MS state changes to ready state.

3. Performance Analysis ofthe Proposed Scheme

In this section, we develop an analytical methodology to inv-estigate the performance of the proposed scheme. Firstly, wedescribe mobility and trafficmodels considered in this paper.Based on these models, the number of location updates andthe number of paged cells are derived. Finally, total signalingload is obtained as a weighted sum of the number of locationupdates and the number of paged cells.

3.1. Mobility and Traffic Models. Figure 2 shows a timingdiagram for the proposed movement-based scheme withdata traffic modeling based on ETSI packet model withan ON/OFF source, which is adopted from [14]. A sessionduration consists of alternating ON/OFF periods, where aburst of data packets is generated during ON period and nopacket is transmitted during OFF period [14]. The 𝑑

1, 𝑑2,

and 𝑑𝐼are movement threshold in ready state, movement

threshold in standby state, and inactivity movement thresh-old, respectively. If the value of movement counter is largerthan inactivitymovement threshold, themovement thresholdvalue is changed to 𝑑

2. There are two idle periods, that

is, intersession idle period 𝑡𝑝1

and intrasession idle period𝑡𝑝2. It is assumed that the intersession idle period 𝑡

𝑝1has a

gamma distribution with mean 1/𝜆𝑝1

and variance 𝑉𝑝1

[14].

The gammadistributionwithmean 1/𝜆𝑝1

= 𝜂/𝜆 and variance𝑉𝑝1

= 𝜂/𝜆2 has the following probability density function:

𝑓𝑡𝑝1

(𝑡) =𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂), (1)

where Γ(𝜂) = ∫∞

𝑧=0𝑧𝜂−1

𝑒−𝑧𝑑𝑧 is the gamma function, and 𝜂

and 𝜆 denote the shape parameter and the scale parameter,respectively. The intrasession idle period 𝑡

𝑝2, that is, OFF

period, is assumed to follow a Pareto distribution with mean1/𝜆𝑝2

and infinite variance, which is widely used to modelactual packet data traffic [14]. The Pareto distribution has thefollowing density function:

𝑓𝑡𝑝2

(𝑡) =

{{

{{

{

(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

if 𝑡 ≥ 𝑙

0 if 𝑡 < 𝑙,

(2)

where 𝛽 describes the heaviness of the tail of the distributionand 𝑙 is theminimumvalue that the distribution can have.Theexpectation of the Pareto distribution is 𝐸[𝑡

𝑝2] = (𝛽𝑙/(𝛽−1)).

The number of OFF periods in a communication session isassumed to follow a geometric distribution with mean 𝛼/(1−

𝛼) (0 ≤ 𝛼 < 1) based on the ETSI data traffic model [14].In conventional movement-based scheme, only one

movement threshold value 𝑑0is generally used. In the

proposed scheme, however, two movement threshold valuesare assumed. An MS initially updates its location for every𝑑1unit of movement during idle period. Inactivity counter

𝑑𝐼starts at the beginning of the idle period and it is reset

whenever there is a data packet exchange. It is assumed thatthe interarrival time of packets during ON period is veryshort and there is no inactivity counter expiration duringON period. If there is no data packet transmission duringthe inactivity counter, the inactivity counter expires and anew movement threshold 𝑑

2is used for location update. If

both 𝑑1and 𝑑

𝐼expire at the same time, we assume that only

the expiration of 𝑑𝐼is valid and a new threshold 𝑑

2is used

for location update, that is, the next location update occurs(𝑑2− 𝑑1)movements later.

Cell residence time𝑇𝐶𝑖at the 𝑖th cell is assumed to have an

independently and identically distributed Erlang distributionwith mean 1/𝜆

𝑚= 𝑚/𝜆

𝑐and variance 𝑉

𝑚= 𝑚/𝜆

2

𝑐, and the

PDF is given by

𝑓𝑇𝐶𝑖

(𝑡) =𝜆𝑚

𝑐𝑡𝑚−1

(𝑚 − 1)!𝑒−𝜆𝑐𝑡 for 𝑡 ≥ 0, (3)

where 𝑚 = 1, 2, 3, . . .. Erlang distribution is selected becauseit can be easily extended into hyper-Erlang distribution,which has been proven as a good approximation to manyother distributions as well as measured data [16]. In order toderive the number of movements, we use the property thatthe sum of𝑚 random variables with exponential distributionwith mean 1/𝜆

𝑐follows an Erlang distribution with mean

1/𝜆𝑚

= 𝑚/𝜆𝑐and variance 𝑉

𝑚= 𝑚/𝜆

2

𝑐. Thus, an Erlang dis-

tribution consists of 𝑚 Poisson arrivals with rate 𝜆𝑐. Thus,


d1d1 d1

d1

d1 d1 d2 d2

On On On On OnOff Off Off

Intersession idle periodSession duration

Intrasessionidle period

Location update

Figure 2: Timing diagram for the proposed movement-based scheme and data traffic modeling.

the probability that the number of movements during time𝑡 is 𝑖 is given by

𝑃𝑁move

(𝑖; 𝑡) =

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

𝑃𝑁𝑝

(𝑗; 𝑡) , (4)

where 𝑃𝑁𝑝

(𝑗; 𝑡) is the probability that the number of Poissonarrivals during time 𝑡 is 𝑗 and is expressed by

𝑃𝑁𝑝

(𝑗; 𝑡) =(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!. (5)

3.2. Derivation of the Number of Location Updates. For con-ventional scheme, the number of location updates duringtime 𝑡 is derived as

𝑁conv𝑢

(𝑡) =

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋𝑃𝑁move

(𝑖; 𝑡)

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!.

(6)

The total numbers of location updates during 𝑡𝑝1

and 𝑡𝑝2

ofconventional scheme are calculated as

𝑁conv𝑢1

= ∫

∞

0

𝑁conv𝑢

(𝑡) 𝑓𝑡𝑝1

(𝑡) 𝑑𝑡

= ∫

∞

0

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

∫

∞

0

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

1

𝑗! ⋅ Γ (𝜂)

× ∫

∞

0

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡𝜆𝑒

−𝜆𝑡(𝜆𝑡)𝜂−1

𝑑𝑡

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

1

𝑗! ⋅ Γ (𝜂)

(𝜆𝑐)𝑗

(𝜆)𝜂

(𝜆𝑐+ 𝜆)𝑗+𝜂

× ∫

∞

0

((𝜆𝑐+ 𝜆) 𝑡)

𝑗+𝜂−1

𝑒−(𝜆𝑐+𝜆)𝑡𝑑 ((𝜆

𝑐+ 𝜆) 𝑡)

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐)𝑗

(𝜆)𝜂


Γ (𝑗 + 𝜂)

𝑗! ⋅ Γ (𝜂)

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐)𝑗

(𝜆)𝜂


Γ (𝑗 + 𝜂)

Γ (𝑗 + 1) Γ (𝜂)

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐)𝑗

(𝜆)𝜂


Γ (𝑗 + 𝜂)

𝑗Γ (𝑗) Γ (𝜂)

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐)𝑗

(𝜆)𝜂


1

𝑗 ⋅ 𝐵 (𝑗, 𝜂)

= (𝜆

𝜆𝑐+ 𝜆

)

𝜂 ∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐

𝜆𝑐+ 𝜆

)

𝑗1

𝑗 ⋅ 𝐵 (𝑗, 𝜂),

(7)

where 𝐵(𝑗, 𝜂) is the beta function,

𝑁conv𝑢2

= ∫

∞

0

𝑁conv𝑢


(𝑡) 𝑑𝑡

= ∫

∞

𝑙

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

∫

∞

𝑙

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

𝛽 ⋅ (𝜆𝑐𝑙)𝛽

𝑗!

× ∫

∞

𝑙

(𝜆𝑐𝑡)𝑗−𝛽−1

𝑒−𝜆𝑐𝑡𝑑 (𝜆

𝑐𝑡)


=

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

𝛽 ⋅ (𝜆𝑐𝑙)𝛽

𝑗!Γ (𝑗 − 𝛽, 𝜆

𝑐𝑙)

= 𝛽 ⋅ (𝜆𝑐𝑙)𝛽

∞

∑

𝑖=0

⌊𝑖

𝑑0

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

Γ (𝑗 − 𝛽, 𝜆𝑐𝑙)

𝑗!,

(8)

where Γ(𝑗 − 𝛽, 𝜆𝑐𝑙) is the incomplete gamma function.

For proposed scheme, the number of location updatesduring time 𝑡 is derived as

𝑁prop𝑢

(𝑡) =

𝑑∗

∑

𝑖=0

⌊𝑖

𝑑1

⌋𝑃𝑁move

(𝑖; 𝑡)

+

∞

∑

𝑖=𝑑∗+1

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)𝑃𝑁move

(𝑖; 𝑡)

=

𝑑∗

∑

𝑖=0

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

+

∞

∑

𝑖=𝑑∗+1

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!,

(9)

where 𝑑∗ is defined as 𝑑∗ = (⌈𝑑

𝐼/𝑑1⌉ − 1)𝑑

1. The total num-

bers of location updates during 𝑡𝑝1

and 𝑡𝑝2

of the proposedscheme are calculated as

𝑁prop𝑢1

= ∫

∞

0

𝑁prop𝑢


(𝑡) 𝑑𝑡

= ∫

∞

0

𝑑∗

∑

𝑖=0

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

+ ∫

∞

0

∞

∑

𝑖=𝑑∗+1

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

×

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

=

𝑑∗

∑

𝑖=0

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

∫

∞

0

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

+

∞

∑

𝑖=𝑑∗+1

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

×

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

∫

∞

0

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

= (𝜆

𝜆𝑐+ 𝜆

)

𝜂

×

𝑑∗

∑

𝑖=0

{

{

{

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐

𝜆𝑐+ 𝜆

)

𝑗1

𝑗 ⋅ 𝐵 (𝑗, 𝜂)

}

}

}

+ (𝜆

𝜆𝑐+ 𝜆

)

𝜂

×

∞

∑

𝑖=𝑑∗+1

{

{

{

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

×

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐

𝜆𝑐+ 𝜆

)

𝑗1

𝑗 ⋅ 𝐵 (𝑗, 𝜂)

}

}

}

,

(10)

𝑁prop𝑢2

= ∫

∞

0

𝑁prop𝑢


(𝑡) 𝑑𝑡

= ∫

∞

𝑙

𝑑∗

∑

𝑖=0

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

+ ∫

∞

𝑙

∞

∑

𝑖=𝑑∗+1

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

×

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

=

𝑑∗

∑

𝑖=0

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

∫

∞

𝑙

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

+

∞

∑

𝑖=𝑑∗+1

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

×

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖

∫

∞

𝑙

(𝜆𝑐𝑡)𝑗

𝑒−𝜆𝑐𝑡

𝑗!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

= 𝛽(𝜆𝑐𝑙)𝛽

[

𝑑∗

∑

𝑖=0

{

{

{

⌊𝑖

𝑑1

⌋

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖


𝑗!

}

}

}

+

∞

∑

𝑖=𝑑∗+1

{

{

{

(𝑑∗

𝑑1

+ ⌊𝑖 − 𝑑∗

𝑑2

⌋)

×

𝑚𝑖+𝑚−1

∑

𝑗=𝑚𝑖


𝑗!

}

}

}

]

]

.

(11)

3.3. Derivation of the Number of Paged Cells. Paging is per-formed at the beginning of each ON period. It is assumedthat no paging is needed at the packet intervals during theON period because the intervals are too short and thus,the location of an MS can be tracked at cell level implicitlyby data packet transmission. The number of paged cellsdepends on themovement threshold value usedwhen theONperiod begins. In this paper, hexagonal cell is assumed formathematical tractability. We use a selective paging scheme[8] to find the current cell of the called MS, where networkpages the called MS starting from the cell where the MS


updated its location lastly and outwards, in a shortest distancefirst order until the called MS is found [8].

For conventional scheme, the number of cells pagedduring time 𝑡 is derived as

𝑁convV (𝑡) =

∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

𝑁𝑐(𝑘) 𝛿 (𝑘, 𝑗%𝑑

0) 𝑃𝑁move

(𝑗; 𝑡)

=

∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

0)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!,

(12)

where 𝑁𝑐(𝑘) is the number of cells from the center cell to

the 𝑘th ring and 𝛿(𝑘, 𝑗%𝑑0) is the probability that after 𝑗%𝑑

0

movements, the distance between the current and the centercells is 𝑘 [8], where % is modular operation.

The total numbers of cells paged during 𝑡𝑝1and 𝑡𝑝2of con-

ventional scheme are calculated as

𝑁convV1

= ∫

∞

0

𝑁convV (𝑡) 𝑓

𝑡𝑝1(𝑡) 𝑑𝑡

= ∫

∞

0

∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

0)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

= (𝜆

𝜆𝑐+ 𝜆

)

𝜂 ∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

0)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐

𝜆𝑐+ 𝜆

)

𝑖1

𝑖 ⋅ 𝐵 (𝑖, 𝜂),

(13)

𝑁convV2

= ∫

∞

0

𝑁convV (𝑡) 𝑓


= ∫

∞

𝑙

∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

0)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

=

∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

0)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

∫

∞

𝑙

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

= 𝛽 ⋅ (𝜆𝑐𝑙)𝛽

∞

∑

𝑗=0

𝑗%𝑑0∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

0)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

Γ (𝑖 − 𝛽, 𝜆𝑐𝑙)

𝑖!.

(14)

For proposed scheme, the number of cells paged during time𝑡 is derived as

𝑁propV (𝑡) =

𝑑∗−1

∑

𝑗=0

𝑗%𝑑1∑

𝑘=0

𝑁𝑐(𝑘) 𝛿 (𝑘, 𝑗%𝑑

1) 𝑃𝑁move

(𝑗; 𝑡)

+

∞

∑

𝑗=𝑑∗

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

𝑁𝑐(𝑘) 𝛿 (𝑘, (𝑗 − 𝑑

∗)%𝑑2)

× 𝑃𝑁move

(𝑗; 𝑡)

=

𝑑∗−1

∑

𝑗=0

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!

+

∞

∑

𝑗=𝑑∗

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, (𝑗 − 𝑑

∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!.

(15)

The total numbers of cells paged during 𝑡𝑝1

and 𝑡𝑝2

ofproposed scheme are calculated as

𝑁propV1

= ∫

∞

0

𝑁propV (𝑡) 𝑓


= ∫

∞

0

𝑑∗−1

∑

𝑗=0

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

+ ∫

∞

0

∞

∑

𝑗=𝑑∗

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡


=

𝑑∗−1

∑

𝑗=0

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

∫

∞

0

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

+

∞

∑

𝑗=𝑑∗

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

∫

∞

0

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!

𝜆𝑒−𝜆𝑡

(𝜆𝑡)𝜂−1

Γ (𝜂)𝑑𝑡

= (𝜆

𝜆𝑐+ 𝜆

)

𝜂

×{

{

{

𝑑∗−1

∑

𝑗=0

{

{

{

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐

𝜆𝑐+ 𝜆

)

𝑖1

𝑖 ⋅ 𝐵 (𝑖, 𝜂)

}

}

}

+

∞

∑

𝑗=𝑑∗

{

{

{

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐

𝜆𝑐+ 𝜆

)

𝑖

×1

𝑖 ⋅ 𝐵 (𝑖, 𝜂)

}

}

}

}

}

}

,

(16)

𝑁propV2

= ∫

∞

0

𝑁propV (𝑡) 𝑓


= ∫

∞

𝑙

𝑑∗−1

∑

𝑗=0

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

+ ∫

∞

𝑙

∞

∑

𝑗=𝑑∗

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

=

𝑑∗−1

∑

𝑗=0

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2) 𝛿 (𝑘, 𝑗%𝑑

1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

∫

∞

𝑙

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

+

∞

∑

𝑗=𝑑∗

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗

∫

∞

𝑙

(𝜆𝑐𝑡)𝑖

𝑒−𝜆𝑐𝑡

𝑖!(𝛽

𝑙)(

𝑙

𝑡)

𝛽+1

𝑑𝑡

= 𝛽 ⋅ (𝜆𝑐𝑙)𝛽{

{

{

𝑑∗−1

∑

𝑗=0

{

{

{

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, 𝑗%𝑑1)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗


𝑖!

}

}

}

+

∞

∑

𝑗=𝑑∗

{

{

{

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)

×

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗


𝑖!

}

}

}

}

}

}

= 𝛽 ⋅ (𝜆𝑐𝑙)𝛽{

{

{

𝑑∗−1

∑

𝑗=0

{

{

{

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗


𝑖!

×

𝑗%𝑑1∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, 𝑗%𝑑1)}

}

}

+

∞

∑

𝑗=𝑑∗

{

{

{

𝑚𝑗+𝑚−1

∑

𝑖=𝑚𝑗


𝑖!

×

(𝑗−𝑑∗)%𝑑2

∑

𝑘=0

(1 + 3𝑘 + 3𝑘2)

× 𝛿 (𝑘, (𝑗 − 𝑑∗)%𝑑2)}

}

}

}

}

}

.

(17)


3.4. Signaling Load. For signaling load analysis, it is assumedthat the weight for performing a location update is 𝑈 andthe weight for paging at one cell is 𝑉. Location updatesignaling load and paging signaling load of the conventionalscheme during a cycle of consecutive communication sessionand intersession idle period are obtained based on thegeometric distribution of the number of OFF periods in acommunication session [14] as follows:

𝑈conv = 𝑈(𝑁conv𝑢1

+𝛼

1 − 𝛼𝑁

conv𝑢2

) , (18)

𝑃conv = 𝑉(𝑁convV1

+𝛼

1 − 𝛼𝑁

convV2

) . (19)

From (18) and (19), the total signaling load for location updateand paging of the conventional scheme is

𝑇conv = 𝑈conv + 𝑃conv. (20)

Likewise, location update signaling load and pagingsignaling load of the proposed scheme during a cycle ofconsecutive communication session and intersession idleperiod are obtained as follows:

𝑈prop = 𝑈(𝑁prop𝑢1

+𝛼

1 − 𝛼𝑁

prop𝑢2

) , (21)

𝑃prop = 𝑉(𝑁propV1

+𝛼

1 − 𝛼𝑁

propV2

) . (22)

From (21) and (22), the total signaling load for locationupdate and paging of the conventional scheme is

𝑇prop = 𝑈prop + 𝑃prop. (23)

4. Numerical Examples

4.1. Signaling Load Comparison. In numerical examples, wecompare the signaling load of the conventional and proposedschemes for varying mobility and intersession idle period.Figure 3 shows signaling load for varying the value of move-ment threshold in conventional scheme, that is, 𝑑

0, with four

different sets of movement threshold values, as shown inTable 1 for𝑈 = 2,𝑉 = 1, 𝜂 = 1, 𝑏 = 1.2,𝑚 = 1,𝛼 = 0.8, 1/𝜆

𝑐=

10.5 ∗ 20/3600(ℎ) (low mobility), 1/𝜆 = 10.5 ∗ 100/3600(ℎ)

(short intersession idle period), and 𝑙 = (𝑏 − 1)/𝑏 ∗ 𝜆𝑐. The

location update signaling load of the conventional schemedecreases as𝑑

0increases. On the other hand, paging signaling

load of the conventional scheme increases as 𝑑0increases.

Thus, the total signaling load of the conventional schemefollows a convex shape with optimal movement threshold𝑑0= 2. Since the total signaling load of the proposed scheme

does not depend on 𝑑0, it has a constant value. The proposed

schemes with Sets 1 and 2, that is, smaller values of 𝑑1and 𝑑

2,

have less signaling load than those with Sets 3 and 4, that is,higher values of 𝑑

1and 𝑑

2. The proposed schemes with Sets 1

and 2 have smaller signaling load than conventional schemefor most values of 𝑑

0. Also, the proposed schemes with Sets 3

and 4 have smaller signaling load than conventional schemeif the value of 𝑑

0is large.

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12 14 16 18 20

Sign

alin

g lo

ad

d0

UconvPconvTconvTprop (set 1)

Tprop (set 2)Tprop (set 3)Tprop (set 4)

Figure 3: Signaling load for 1/𝜆𝑐= 10.5∗20/3600(ℎ) (lowmobility),

1/𝜆 = 10.5 ∗ 100/3600(ℎ) (short intersession idle period).

Table 1: Sets of movement threshold values.

𝑑1

𝑑2

𝑑𝐼

Set 1 3 6 6Set 2 3 6 12Set 3 6 12 12Set 4 6 12 24

Figure 4 shows signaling load for varying the value of𝑑0with four different sets of movement threshold values, as

shown in Table 1 for 𝑈 = 2, 𝑉 = 1, 𝜂 = 1, 𝑏 = 1.2, 𝑚 = 1,𝛼 = 0.8, 1/𝜆

𝑐= 10.5 ∗ 20/3600(ℎ) (low mobility), 1/𝜆 =

10.5∗600/3600(ℎ) (long intersession idle period), and 𝑙 = (𝑏−

1)/𝑏∗𝜆𝑐.The total signaling load of the conventional scheme

follows a convex shape with optimal movement threshold𝑑0= 5. Similar to Figure 3, the proposed schemes with Sets 1

and 2 have less signaling load than thosewith Sets 3 and 4.Theproposed schemes with Sets 1 and 2 have smaller signalingload than conventional scheme for all values of 𝑑

0. Also, the

proposed schemes with Sets 3 and 4 have smaller signalingload than conventional scheme if the value of 𝑑

0is very small

or large.Figure 5 shows signaling load for varying the value of

𝑑0with four different sets of movement threshold values,

as shown in Table 1 for 𝑈 = 2, 𝑉 = 1, 𝜂 = 1, 𝑏 =

1.2, 𝛼 = 0.8, 1/𝜆𝑐

= 10.5 ∗ 2/3600(ℎ) (high mobility),1/𝜆 = 10.5 ∗ 100/3600(ℎ) (short intersession idle period),and 𝑙 = (𝑏 − 1)/𝑏 ∗ 𝜆

𝑐, 𝑚 = 1. The total signaling load of

the conventional scheme follows a convex shape with optimalmovement threshold 𝑑

0= 6. Similar to Figures 3 and 4, the

proposed schemes with Sets 1 and 2 have less signaling loadthan thosewith Sets 3 and 4. Similar to Figure 4, the proposedschemes with Sets 1 and 2 have smaller signaling load thanconventional scheme for all values of 𝑑

0. Also, the proposed


0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20

Sign

alin

g lo

ad

d0



Figure 4: Signaling load for 1/𝜆𝑐= 10.5 ∗ 20/3600(ℎ) (low mobil-

ity), 1/𝜆 = 10.5 ∗ 600/3600(ℎ) (long inter-session idle period).

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16 18 20

Sign

alin

g lo

ad

d0



Figure 5: Signaling load for 1/𝜆𝑐= 10.5∗2/3600(ℎ) (highmobility),

1/𝜆 = 10.5 ∗ 100/3600(ℎ) (short intersession idle period).

schemes with Sets 3 and 4 have smaller signaling load thanconventional scheme if the value of 𝑑

0is very small or large.

Figure 6 shows signaling load for varying the value of𝑑0with four different sets of movement threshold values,

as shown in Table 1 for 𝑈 = 2, 𝑉 = 1, 𝜂 = 1, 𝑏 = 1.2,𝛼 = 0.8, 1/𝜆

𝑐= 10.5 ∗ 2/3600(ℎ) (high mobility), 1/𝜆 =

10.5 ∗ 600/3600(ℎ) (long intersession idle period), and 𝑙 =

(𝑏 − 1)/𝑏 ∗ 𝜆𝑐, 𝑚 = 1. The total signaling load of the

conventional scheme follows a convex shape with optimalmovement threshold 𝑑

0= 11. Contrary to Figures 3, 4, and 5,

the proposed schemes with Sets 1 and 2 have more signalingload than those with Sets 3 and 4.The proposed scheme with

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14 16 18 20

Sign

alin

g lo

ad

d0



Figure 6: Signaling load for 1/𝜆𝑐= 10.5∗2/3600(ℎ) (highmobility),

1/𝜆 = 10.5 ∗ 600/3600(ℎ) (long intersession idle period).

Set 4 has smaller signaling load than conventional scheme forall values of 𝑑

0. Also, the proposed schemes with Sets 1, 2, and

3 have smaller signaling load than conventional scheme if thevalue of 𝑑

0is very small.

From the results of Figures 3, 4, 5, and 6, it is concludedthat the optimal movement threshold value of the conven-tional scheme varies for different combinations of mobilityand traffic environments of an MS, and the signaling loadof the conventional scheme rapidly increases if movementthreshold value is far from the optimal movement thresholdvalue. On the other hand, the proposed scheme with Sets1 and 2 performs better than the conventional scheme formost combinations of mobility and traffic environments ofan MS with stable performance, except for high mobility andhigh intersession idle period. For high mobility and highintersession idle period, the proposed scheme with Set 4performs better than the conventional scheme.Therefore, theproposed scheme outperforms the conventional scheme withan appropriate selection of movement threshold values.

4.2. Effect of Cell Residence Time Variance on Signaling Load.Figure 7 shows signaling load for varying the value of move-ment threshold in conventional scheme with three differentsets of𝑚 values in order to show the effect of variance on cellresidence time, for𝑈 = 2,𝑉 = 1, 𝜂 = 1, 𝑏 = 1.2, 1/𝜆

𝑐= 10.5∗

2/3600(ℎ) (high mobility), and 1/𝜆 = 10.5 ∗ 100/3600(ℎ)

(short intersession idle period), 𝑙 = (𝑏−1)/𝑏∗𝜆𝑐, and 𝛼 = 0.8

with Set 1 in Table 1. As can be seen in Figure 7, signaling loadin both the conventional and proposed schemes decreasesas the values of 𝑚 increases, that is, the variance increases.That is, it is shown that higher variance on cell residencetime results in less signaling load. Also, for small values of𝑚,the signaling load of the proposed scheme is always smallerthan that of the conventional scheme. It is concluded that


10

20

30

40

50

60

70

80

90

100

110

0 2 4 6 8 10 12 14 16 18 20

Sign

alin

g lo

ad

d0

Tconv (m = 1)Tconv (m = 2)Tconv (m = 3)

Tprop (m = 1)Tprop (m = 2)Tprop (m = 3)

Figure 7: Effect of cell residence time variance on signaling load(1/𝜆𝑐= 10.5 ∗ 2/3600(ℎ) (high mobility), 1/𝜆 = 10.5 ∗ 100/3600(ℎ)

(short intersession idle period)).

the proposed scheme works well irrespective of cell residencetime variance.

5. Conclusion and Future Work

In this paper, an improved movement-based location man-agement scheme with two movement thresholds is proposedto accommodate bursty data traffic characteristics of PSservices. The analytical modeling for location update andpaging signaling loads of the proposed schemewas developedthoroughly and the performance of the proposed scheme wascompared with that of the conventional scheme in detail,for varying the mobility and traffic characteristics of MSs.We show that the proposed scheme outperforms the con-ventional scheme with an appropriate selection of movementthresholds, irrespective of cell residence time variance. Inour future work, we will develop an adaptive selection ofan appropriate set of movement thresholds depending onmobility and traffic characteristics of an MS, based on theanalysis results of this paper.

Disclosure

The abstract of this paper was presented at the poster sessionof Wireless Telecommunications Symposium 2012 with thetitle of “An enhancedmovement-based locationmanagementscheme in wireless communication networks.”

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

The research of Suwon Park was supported by Basic ScienceResearch Program through the National Research Founda-tion of Korea (NRF) funded by the Ministry of Education(NRF-2010-0025509).

References

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[2] M. Mouly and M. B. Pautet, The GSM System For Mobile Com-munications, Telecom Publishing, 1992.

[3] R. Liou, Y. B. Lin, and S. Tsai, “An investigation on LTEmobilitymanagement,” IEEE Transactions on Mobile Computing, vol. 12,no. 1, pp. 166–176, 2013.

[4] V. W. S. Wong and V. C. M. Leung, “An adaptive distance-basedlocation update algorithm for next-generation PCS networks,”IEEE Journal on Selected Areas in Communications, vol. 19, no.10, pp. 1942–1952, 2001.

[5] Y. Zhu and V. C. M. Leung, “Optimization of distance-basedlocation management for PCS networks,” IEEE Transactions onWireless Communications, vol. 7, no. 9, pp. 3507–3516, 2008.

[6] C. Rose, “Minimizing the average cost of paging and registra-tion: a timer-basedmethod,”ACMWireless Networks, vol. 2, no.2, pp. 109–116, 1996.

[7] Y. W. Chung, J. K. Kwon, Y. J. Kim, and D. K. Sung, “An imp-roved timer-based location management scheme for packet-switched (PS) mobile communication systems,” IEICE Transac-tions on Communications, vol. 88, no. 6, pp. 2650–2653, 2005.

[8] I. F. Akyildiz, J. S. M. Ho, and Y. B. Lin, “Movement-based loca-tion update and selective paging for PCS networks,” IEEE/ACMTransactions on Networking, vol. 4, no. 4, pp. 629–638, 1996.

[9] X. Wang, X. Lei, P. Fan, R. Hu, and S. Horng, “Cost analysisof movement-based location management in PCS networks:an embedded Markov chain approach,” IEEE Transactions onVehicular Technology, 2013.

[10] V. C. Giner and P. G. Escalle, “A lookahead strategy for mov-ement-based location update in wireless cellular networks,” inProceedings of the 6th International Conference on InformationTechnology: New Generations (ITNG ’09), pp. 1171–1177, LasVegas, Nev, USA, April 2009.

[11] X.Wang, P. Fan, J. Li, and Y. Pan, “Modeling and cost analysis ofmovement-based location management for PCS networks withHLR/VLR architecture, general location area and cell residencetime distributions,” IEEE Transactions on Vehicular Technology,vol. 57, no. 6, pp. 3815–3831, 2008.

[12] Y. H. Zhu and V. C. M. Leung, “Optimization of sequential pag-ing in movement-based location management based on move-ment statistics,” IEEE Transactions on Vehicular Technology, vol.56, no. 2, pp. 955–964, 2007.

[13] J. Ferragut and J. M. Bafalluy, “A self-organized tracking arealist mechanism for large-scale networks of femtocells,” in IEEEInternational Conference on Communications (ICC ’12), pp.5129–5134, Ottawa, Canada, June 2012.

[14] S. R. Yang and Y. B. Lin, “Performance evaluation of locationmanagement in UMTS,” IEEE Transactions on Vehicular Tech-nology, vol. 52, no. 6, pp. 1603–1615, 2003.


[15] Y.W. Chung, J. K. Kwon, and S. Park, “An enhancedmovement-based locationmanagement scheme inwireless communicationnetworks,” in Proceedings of the Wireless TelecommunicationsSymposium (WTS ’12), London, UK, April 2012.

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