Performance Evaluation of Location
Management in UMTS
Shun-Ren Yang and Yi-Bing Lin, Fellow, IEEE
Abstract— The universal mobile telecommunications system uti-lizes a three-level location-management strategy to reduce the net costs of location update and paging in the packet-switched service domain. Within a communication session, a mobile station (MS) is tracked at the cell level during packet transmission. In the idle period of an ongoing session, the MS is tracked at the UTRAN registration area (URA) level to avoid frequent cell updates while still keeping the radio connection. If the MS is not in any com-munication session, the MS is tracked at the routing-area (RA) level. The inactivity counter mechanism was proposed in 3GPP 25.331 to determine when to switch between the three location-tracking modes. In this mechanism, two inactivity counters are used to count the numbers of cell and URA updates in an idle pe-riod between two packet transmissions. If the number of cell up-dates reaches a threshold 1, the MS is switched from cell tracking to URA tracking. After that, if the number of URA updates reaches a threshold 2, the MS is tracked at the RA level. This paper pro-poses analytical and simulation models to investigate the perfor-mance of the inactivity counter mechanism. Our study provides guidelines for 1 and 2 selection to achieve lower net costs of location update and paging.
Index Terms—Mobile network, mobility management, universal mobile telecommunications system (UMTS), wireless data.
I. INTRODUCTION
E
XISTING second-generation (2G) mobile-communi-cations systems [such as global system for mobile communications (GSM)] are designed for voice services, which only have limited capabilities for offering data services. On the other hand, the third-generation (3G) systems [such as universal mobile telecommunications system (UMTS)] [10] support mobile multimedia applications with high data-trans-mission rates. As shown in Fig. 1, the UMTS infrastructure includes the core network (CN) and the UMTS terrestrial radio-access network (UTRAN). The CN is responsible for switching/routing calls and data connections to the external networks, while the UTRAN handles all radio-related func-tionalities. The CN consists of two service domains: theManuscript received September 26, 2002; revised February 7, 2003. The work of S.-R. Yang was supported by the MediaTek Fellowship. The work of Y.-B. Lin was supported in part by the MOE Program for Promoting Academic Excellence of Universities under Grant 89-E-FA04-1-4, Chair Professorship of Providence University, IIS/Academia Sinica, FarEastone, CCL/ITRI, and the Lee and MTI Center for Networking Research/NCTU. This paper was presented in part at the International Conference on Information Networking 2003, Jeju Island, Korea, February 2003.
S.-R. Yang is with the Department of Computer Science and Information En-gineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. (e-mail: sjyoun@csie.nctu.edu.tw).
Y.-B. Lin is with Institute of Information Science, Academia Sinica, Taiwan, R.O.C. (e-mail: liny@csie.nctu.edu.tw)
Digital Object Identifier 10.1109/TVT.2003.819616
circuit-switched (CS) service domain and the packet-switched (PS) service domain. The CS domain provides access to the PSTN/ISDN, while the PS domain provides access to the IP-based networks. In the remainder of this paper, we will focus on the UMTS packet-switching mechanism. In the PS domain of the CN, the packet data services of a mobile station [MS; see Fig. 1(a)] are provided by the serving GPRS support node [SGSN; see Fig. 1(d)] and the gateway GPRS support node [GGSN; see Fig. 1(e)]. The SGSN connects the MS to the external data network through the GGSN. The UTRAN consists of Node Bs [the 3G term for base stations; see Fig. 1(b)] and radio network controllers [RNCs; see Fig. 1(c)] connected by an asynchronous transfer mode (ATM) network. The connection between the UTRAN and the CN is achieved via the ATM links between the RNCs and SGSNs. The MS communicates with Node Bs through the radio interface based on the wide-band CDMA (WCDMA) technology.
The cells (i.e., radio coverages of Node Bs) in a UMTS ser-vice area are partitioned into several groups. To deliver serser-vices to an MS, the cells in the group covering the MS will page the MS to establish the radio connection. The location change of an MS is detected as follows. The cells periodically broadcast their cell identities. The MS listens to the broadcast cell identity and compares it with the cell identity stored in the MS’s buffer. If the comparison indicates that the location has been changed, then the MS sends the location-update message to the network. In the UMTS PS domain, the cells are grouped into routing areas (RAs). The RA of an MS is tracked by the SGSN. The cells in an RA are further grouped into UTRAN registration areas (URAs). The URA and the cell of an MS are tracked by the UTRAN. Fig. 2 illustrates an example layout of cells, URAs, and RAs.
In UMTS, the mobility-management activities for an MS are characterized by two finite state machines: mobility manage-ment (MM) and radio resource control (RRC). The packet MM (PMM) state machine for the UMTS PS domain is exercised between the SGSN and the MS for CN-level tracking, while the RRC state machine is executed between the UTRAN and the MS for UTRAN-level tracking. Incomplete state diagrams for these two machines are illustrated in Fig. 3. Specifically, the figure only considers the states after the MS has attached to the PS do-main. The PMM state diagram in the MS is slightly different from that in the SGSN. To simplify the presentation, we only show the common portions of the MS and the SGSN state tran-sitions that are used in this paper. The state diagrams in Fig. 3 are described as follows. After an MS is attached to the PS service domain, the PMM state machine will be in one of the two states: PMM idle and PMM connected. In the RRC state machine, there are three states: RRC idle mode, RRC cell-connected mode, and
Fig. 1. Simplified network architecture for the UMTS PS domain.
Fig. 2. Cells, URAs, and RAs.
Fig. 3. State diagrams for UMTS mobility management. (a) Incomplete PMM state diagram for PS domain. (b) Simplified RRC state diagram.
RRC URA connected mode. We will briefly elaborate on the PMM and RRC state transitions. See [1] and [2] for complete descriptions of the PMM and RRC state machines.
When there is no data transmission between the MS and the core network, the MS is in the PMM idle state and RRC idle mode. In this case, UTRAN has no information about the idle MS and the MS is tracked by the SGSN at the RA level.
When a PS signaling connection is established between the MS and the SGSN (possibly in response to a page from the SGSN), the MS enters the PMM connected state [see T1 in Fig. 3(a)]. Since the establishment of the PS signaling connection triggers the establishment of the RRC connection between the MS and its serving RNC, the RRC state of the MS is switched to RRC cell-connected mode [see T1 in Fig. 3(b)]. In this case, the SGSN tracks the MS with accuracy of the
serving RNC and the serving RNC is responsible for tracking the cell where the MS resides. Packets can only be delivered in this state.
In the PMM connected/RRC cell-connected mode, if the MS has not transmitted/received packets for a period, the RRC state of the MS is switched to RRC URA connected mode [see T2 in Fig. 3(b)]. In this case, the RRC connection is still maintained, while the URA of the MS is tracked by the serving RNC. In this transition, the PMM state of the MS remains unchanged, i.e., the state is PMM connected.
In the PMM connected/RRC URA connected mode, if the MS transmits/receives a packet, the RRC state is moved back to RRC cell-connected mode [see T3 in Fig. 3(b)]. On the other hand, if the PS signaling connection and the RRC connection are released (e.g., a communication session is completed) or if
TABLE I
UMTS LOCATION-UPDATECOSTS
no packet is transmitted for a long time, the RRC state is first switched to RRC cell-connected mode and then to RRC idle mode [see T3 and T4 in Fig. 3(b)]. In this case, the PMM state is also changed to PMM idle [see T4 in Fig. 3(a)].
The above three-level location-management strategy is de-signed to reduce the net costs of location update and paging. Within a communication session (i.e., the MS is in the RRC cell-connected mode and the PMM connected state), the MS ex-pects to continuously transmit/receive packets. In this case, the MS performs a location update whenever it moves to a new cell. With a cell update, no cell is paged if there are dedicated chan-nels allocated to the MS. If the MS has no dedicated channel, the currently visited cell is requested to page the MS for packet delivery. Without loss of generality, we assume one cell-paging cost in this paper. On the other hand, during an ongoing ses-sion, there may exist some idle periods where no packets are delivered. To avoid frequent cell updates while still keeping the RRC connection in this situation, the MS is switched to RRC URA connected mode to perform a URA update for every URA crossing. When the communication session between the MS and the SGSN is completed, the MS will not transmit/receive any packet for a long period. In this case, the RRC connection should be released for efficient wireless bandwidth utilization. In addi-tion, the MS should be tracked at the RA level because cell- or URA-level tracking is too expensive in terms of signaling over-head and power consumption. Therefore, the RRC and PMM states are switched to RRC idle mode and PMM idle state, re-spectively, and the MS is tracked at the RA level. Based on the above description, the costs of the three location-update modes are summarized in Table I.
In the PMM and RRC state machines, the mechanism that triggers transitions T2 and T4 has significant impacts on the signaling traffic of the UMTS system. This mechanism can be implemented by two approaches. The first makes use of two inactivity timers and . At the end of a packet transmission, timer is set to a predefined threshold value and is decremented as time elapses. Transition T2 occurs if the MS does not transmit/receive any packets before timer expires. When timer expires, the second timer is set to a predefined threshold value and is decremented. Timer is used to determine the time when transition T4 occurs. In the second approach, two inactivity counters and are employed. Counter counts the number of cell updates in the idle period between two packet transmissions. If the number of cell updates reaches a threshold , then the MS is switched to perform URA updates through transition T2. After T2 has occurred, counter is used to count the number of URA updates in the observed idle period. If the number of URA updates reaches a threshold , then the MS is switched to perform RA updates (i.e., transition T4 occurs).
As noted in our previous work [12], the timer approach may have a synchronization problem. That is, the peer-state machines in the MS and the UTRAN or the SGSN may stay in different states at the same time due to the errors of the clock rates. Besides, the counter approach may significantly outper-form the timer approach because the timer approach uses two timers of fix-length thresholds. When the mobility rate and/or packet-transmission patterns change, the fixed thresholds of the timers do not adapt to the changes. On the other hand, the thresholds and of the counter approach always capture the th cell update and the th URA update of an MS no matter how the mobility rate and packet-transmission patterns change. Therefore, this paper will not elaborate on the inactivity timer approach and will focus only on the inactivity counter mechanism. In the following sections, we propose analytical and simulation models to investigate the performance of the inactivity counter mechanism. Specifically, given any mobility and traffic patterns, we determine the net costs of location update and paging under various and threshold values. Our study provides guidelines for and selection that results in lower net costs.
II. ANALYTICALMODEL FOR INACTIVITY
COUNTERMECHANISM
This section proposes an analytical model to study the UMTS inactivity counter mechanism. We first describe a two-dimen-sional (2-D) random walk model for user movement based on a hexagonal cellular configuration. We then show how to use this model to investigate the performance of the UMTS inactivity counter mechanism. For specific thresholds and , we de-rive the expected number of location updates (including cell, URA, and RA updates) performed in the idle period between two packet transmissions and the expected number of cells that need to be paged for packet delivery.
A. Random Walk Model
For demonstration purposes, we consider the hexagonal cell layout in Fig. 4. In this configuration, the cells are clustered into several URAs, which are in turn clustered into several RAs.
An -layer URA covers cells. Fig. 4
illustrates a three-layer URA. The cell at the center of the URA is referred to as the layer-0 cell. The cells surrounding layer
cells are referred to as the layer- cells. There are cells in layer except for layer 0, which contains exactly one cell. An -layer URA consists of cells from layer 0 to . The structure of an -layer RA is similar to that of an -layer URA, except that the basic elements are URAs instead of cells. Therefore, an -layer RA covers URAs. Fig. 4 illustrates seven two-layer RAs (A, B, C, D, E, F, and G). Each consists of seven three-layer URAs. Based on this RA/URA/cell structure, we derive the number of cells and URAs that are visited before a user moves out of an RA.
In [3], we proposed a cell-type classification algorithm based on the random walk model. The work showed that an -layer hexagonal cellular network can be modeled by a state transition diagram with states. Based on our model, Tseng et
Fig. 4. Cell/URA/RA layout in a UMTS network.
Fig. 5. Type classification for a six-layer UTRAN registration area.
al. [16] further reduced the number of states to , where for
is odd is even.
(1)
According to the type-classification algorithm in [3] and [16], we classify the cells in a URA into several cell types. For and , a cell type is of the form , where repre-sents that the cell is in layer and represents the th type in layer . Cells of the same type are indistinguishable in terms of movement pattern, because they are at the symmetrical po-sitions (with respect to the solid and dashed lines in Fig. 5) on the hexagonal URA. Based on the derivation in [16], Fig. 5 la-bels the types of cells for a six-layer URA. In this example, the
cell in layer 0 is of the type . The six cells in layer 1 are grouped together and assigned to the same type . A layer–2 cell may have three or two neighbors in layer 3 and is assigned to types and , respectively.
Based on the above cell labeling, we compute the number of movements an MS will take to cross the boundary of an -layer URA. A state of this random walk is of the form . For
and , the state is transient,
which represents that the MS is in one of the cells of type .
For and , the state is
absorbing, which represents that the MS crosses the boundary of the URA from a cell of type . Details of the random walk and derivation of its steady-state probabilities are given in [3]. The results are summarized as follows. Let
be the one-step transition probability from state to state , i.e., the probability that the MS moves from a cell to a cell in one step. The transition probability matrix
of the random walk is
..
. ... ... ... ... . .. ... ... ...
(2)
As an example, the element in matrix represents that the MS moves from a cell to a cell in one step with probability 1/6. Define as
for
Fig. 6. Timing diagram for cell, URA, and RA updates.
An element in is the probability that the random walk moves from state to state with steps [it is possible that state is revisited several times during these steps]. Let be the probability that an MS initially stays at state and takes its first entrance into state at the th step. Then, is expressed as
for
for (4)
which can be solved by using the transition probability matrices (2) and (3). Equation (4) gives the probability that an MS will move out of a URA at the th cell crossing. Note that the number of URA movements before the user leaves an RA can also be derived using the same approach where the cells are replaced by the URAs.
B. Location Update and Paging Costs
Fig. 6 shows the timing diagram of the location-update ac-tivities for an MS in an idle period between two packet trans-missions. Suppose that the previous packet transmission of the MS ends at time and the next packet transmission begins at time . Let . Consider the execution of the inac-tivity counter mechanism with specific thresholds and . For the first cell crossings during period , the MS performs a cell update for each of the cell crossings. After the th cell update, the MS will not perform any cell updates and begins per-forming the URA updates. After the th URA update, the MS will not perform any URA updates and begins performing the RA updates. Assume that the th cell update occurs at time and that the first URA update occurs at time . Based on the equal-routing probability assumption of the random walk at time , the MS will stay at any cell of the visited URA with equal probability. On the other hand, after any URA update, the MS will only stay at one of the boundary cells of the visited URA. Thus, to derive the number of URA updates in , we need to consider the following two cases.
Case I. Starting from an arbitrary cell, we compute the
number of cell crossings before the MS moves out of the URA [i.e., the number of cell crossings in in Fig. 6]. As we mentioned before, at time , the MS can be in any cell of the URA with the same probability. Therefore, at
, the MS is at the cell with probability , at
a cell of type with probability ,
at a cell of type with
probability and at a cell of type ( ,
) with probability , where
(5)
is the number of cells covered by an -layer URA. Con-sider a six-layer URA that covers cells (see Fig. 5). Since there are six cells of type and 12 cells of type in the URA, the MS is in a cell of type with probability 6/91 and in a cell of type with prob-ability 12/91. Let be the probability that after , the MS will leave the -layer URA at the th cell move-ment. Then
(6)
Case II. Starting from a boundary cell of an URA at time
, we compute the number of cell crossings before the MS moves out of the URA. In [13], we showed that after en-tering the URA, the MS is in a boundary cell with proba-bility proportional to the number of boundary edges for that boundary cell. Under the condition that an MS is moving into a boundary cell, the MS enters a type cell with probability , enters a type
cell (when is odd) with probability , and enters
a type cell with
proba-bility , where is the
for a six-layer URA. In this example, there are three boundary edges for each of the six cells and the MS enters a boundary cell of type with proba-bility 18/66. Similarly, there are two boundary edges for each of the 12 cells and the MS enters a boundary cell of type with probability 24/66. Let be the probability that after an MS enters an -layer URA, it moves out of the URA at the th cell movement. If is odd, then
(7)
If is even, then
(8)
Suppose that an MS is in an arbitrary cell of an -layer URA. Let be the probability that after cell move-ments, the MS crosses URA boundaries. Similarly, consider an MS initially residing at a boundary cell of an -layer URA. Let be the probability that after cell move-ments, the MS crosses URA boundaries. From (6)-(8), we have
(9) Four cases are considered in (9).
Case I: . If there is no cell movement during an idle period, there will be no URA boundary crossing
during this period and .
Case II: , Assume that the MS crosses the first URA boundary at the th cell movement [with
probability ]. For , if (i.e., the MS
does not cross any URA boundary during these cell movements), must be larger than . Therefore, in this
case, .
Case III: , . In this case, there are URA boundary crossings during the cell move-ments. If the MS crosses the first URA boundary at the th cell movement [with probability ], then the MS must cross the remaining URA bound-aries during the subsequent cell movements
[with probability ]. Therefore,
.
Case IV: . During an idle period, it is impossible that the number of URA boundary crossings is larger than the number of cell movements. Thus, in this case.
Similarly, we have
(10) Equations (9) and (10) can be effectively computed by using the dynamic programming technique [14]. Note that (6)–(10) can also be used to derive the number of RA boundary crossings for an -layer RA layout, given that the number of URA movements is known.
With (9) and (10), we derive the number of cell/URA/RA up-dates in the idle period between two packet transmissions as fol-lows. Assume that in Fig. 6 has a general distribu-tion with the density funcdistribu-tion , the expected value , and the Laplace transform
For the inactivity counter mechanism with specific thresholds and , let be the number of location updates (including the cell, URA, and RA updates) during period . Based on the aforementioned random walk model, the distribution of can be derived as follows. Suppose that the cell residence time has an Erlang distribution with mean , variance
, and density function
for (11)
where . We select the Erlang distribution because this distribution can be easily extended into a hyper-Erlang distribution, which has been proven to be a good
approximation to many other distributions as well as measured data [7], [8], [11].
Since the cell crossings of an MS can be modeled as an equi-librium Erlang-renewal process [15], the probability mass func-tion of the number of cell crossings within is
for . For , we have
(12)
Consider a UMTS network with -layer URA and -layer RA structure. From (9), (10), and (12), the probability mass function for is shown in (13) at bottom of the page. Equation (13) is explained as follows.
Case I: . In this case, the MS only performs cell updates in the idle period. Therefore, the probability of location updates is equal to the probability of cell crossings.
Case II: . In this case, there are cell crossings in the idle period (with probability ). Note that . Therefore, during these cell crossings, the MS performs cell updates for the first cell crossings (with probability 1). After the MS enters the URA update mode, the MS performs URA updates during the subsequent cell crossings [with
probability ].
Case III: . Similar to Case II, represents the number of cell crossings in the idle period, where
. The MS first performs cell updates for the first cell crossings. Then, it enters the URA update mode, where there are URA crossings in the remaining cell crossings with probability ,
for
for
for
TABLE II
COMPARISONBETWEEN THEANALYTICAL ANDSIMULATIONRESULTS
where . During these URA crossings, the MS performs URA updates for the first URA crossings (with probability 1). Then the MS performs
RA updates in the subsequent URA crossings with
probability , where .
Based on (13), we derive the net cost of location update and paging during the expected period . Assume that the cost for performing a location update is and that the cost for paging at one cell is . Let be the expected location-update cost during . From (13), we have
(14)
For the paging operation, there are three possibilities.
• If the MS stays at the cell-update mode, then only one cell needs to page the MS.
• If the MS stays at the URA update mode, then all cells of the URA should page the MS.
• If the MS stays at the RA update mode, then all cells of the RA should page the MS.
Let be the expected paging cost during . Based on (13), we have
(15)
From (14) and (15), the net cost for location update and paging during is
(16)
The analytical analysis has been validated by a discrete event-simulation model. The event-simulation simulates the movement of an MS on the hexagonal plane, where the UMTS network consists of two-layer URAs and RAs. The interval is exponentially distributed and the cell residence times have the Erlang distri-bution given in (11). Note that our models can be applied to gen-eral distributions and that we only show the exponential case for demonstration. Table II compares the analytical and simu-lation results. The parameters , , and used in Table II will be explained in detail later. The table indicates that the er-rors between the analytical and simulation models are within
1%. Also, the errors for the , , , and
values are less than 1% in most cases. Details of these results will not be presented. It is clear that the analytical analysis is consistent with the simulation results.
III. NUMERICALEXAMPLES
Based on the simulation validated by the analytical model de-scribed in the previous section, this section investigates the per-formance of the UMTS inactivity counter mechanism. The ex-periment settings in this study are similar to that of our previous study on the GPRS ready-counter mechanism [12]. We combine the ETSI packet data model [6] with theON/OFFsource model (also known as a packet train model) [4]. As shown in Fig. 7, we assume that the packet data traffic consists of communica-tion sessions. Within a communicacommunica-tion session, packet traffic is characterized byON/OFFperiods. In anONperiod, a burst of data
packets are transmitted. In anOFFperiod, no packets are deliv-ered. Other assumptions are summarized as follows.
• The OFFperiod is drawn from a Pareto distribution with mean and infinite variance. It has been shown that the Pareto distribution with infinite variance can match with the actual data traffic measurements very well [17]. A Pareto distribution has two parameters, and , where describes the “heaviness” of the tail of the distribution. The probability density function is and the expected value
Fig. 7. Packet data traffic.
Fig. 8. Effects ofK , K , and onC , C , and C (solid: = (1=200) ; dashed: = (1=600) ; = (1=10) , V = (1= ),
V = (1= ), (U=V ) = 4, and = 0:7).
variance for the distribution becomes infinite. The typical parameter values obtained in [17] are s and
forOFFperiods. Our study uses the above and values.
• The idle period between two consecutive communica-tion sessions has a Gamma distribucommunica-tion with mean and variance . The Gamma distribution with shape pa-rameter and scale parameter (i.e., mean
and variance ) has the following density func-tion:
for
where is the Gamma function.
It has been shown that the distribution of any positive random variable can be approximated by a mixture of Gamma distributions ([11], see Lemma 3.9). In this paper, we use the Gamma distribution to investigate the impact of variance for intersession idle periods.
• Following the ETSI packet data model, the number ofOFF
periods in a session has a geometric distribution with mean where . In other words, an ON
period is followed by anOFFperiod with probability and
is followed by an intersession idle period with probability .
• The cell-residence times have a Gamma distribution with the mean and variance . The Gamma distribution was employed to model MS movement in many studies [5], [8], [9] and is used in this paper to investigate the impact of variance for cell-residence times.
To simplify our discussion, we consider the two-layer URA and the two-layer RA cell layout. The effects of the input parameters are investigated as follows.
Fig. 8 shows how affects , , and . For a fixed , it is clear that if increases, the location-update (LU) cost increases while the paging cost decreases. When is very large, the MS always performs cell updates and no URA or RA update is executed. In this case, the and costs are not affected by the change of [see the and curves in Figs. 8(a) and (b), where ]. In Fig. 8(c), the
is computed directly from the and using (16), where . For the input parameters selected in Fig. 8(c), the lowest costs are observed when or 2. The selection of is affected by and , which are described in the following two cases.
Case I: Since theOFF periods are short [specifically in Fig. 8], there are few cell updates
TABLE III
C ANDC COSTS IN At PERIOD( = 10 ; COSTSARE
NORMALIZED BYONELU COST)
during and the paging cost dominates the cost. Therefore, to maintain low cost (i.e., to ensure that only one cell is paged for the next packet delivery), the MS should stay at the cell-update mode. For all experi-ments considered in this paper, the probability that there are less than two cell crossings during is larger than 99%. Therefore, if is selected, then it is likely that the MS will stay at the cell-update mode in the period.
Case II: On the other hand, the MS crosses many cell
boundaries during an intersession idle period . For ex-ample, the average number of cell crossings is 20 for
and 60 for . Consider the case where . Table III lists and normalized by one
LU cost. When 1 and ,2 the cost
is 20.25 LUs. When and , the cost
is 10.8 LUs. Based on the above discussion, we have (17) Since Theorem 1 in the Appendix indicates that the lowest value occurs when or , (17) implies that is the optimal threshold value in a period. To obtain low values by considering both Cases I and II, it is appropriate to select or 2.
Figs. 8 and 9 show how affects , , and . The effects of on the location update cost and paging cost are similar to that of : given a value, the cost is an increasing function of while the cost is a decreasing function of . Fig. 8 also indicates that when is large, and are not affected by the change of . Fig. 9 shows that if is small, is an increasing function of . On the other hand, if is large, is a decreasing function of . This phenomenon is explained in the following two cases.
Case I: (the period is long). When and , Table III indicates that the cost is 28 LUs. When and , the cost is 23.9 LUs. Thus
(18) From Theorem 1, the lowest value occurs when
or , and (18) implies that the lowest cost is expected when .
Case II: (the period is short). The
cost is 10.8 LUs when and and
1In computer simulation, it is impossible to generate an infinite number. Thus, k is defined as a number larger than the number of cell crossings in any idle
period.
2k is an arbitrary integer number.
is 16.1 LUs when and . In this case,
Theorem 1 indicates that the lowest cost is observed
when .
In a real mobile-communications network, the mobility and traffic patterns of a mobile user usually change dynamically. To obtain lower cost in such an environment, it is required to consider both high (i.e., large ) and low (i.e., small ) packet-arrival patterns. Fig. 10 illustrates the discrepancies of for various values when . The discrepancy is defined as
where is the cost for and is
the lowest cost. Under a given value, Fig. 9 indicates that there exists an optimal value that results in the lowest . Fig. 10 plots the curves for various . When , Fig. 9 shows that the optimal is and that the corresponding is 14.46. Since is 20.76,
the discrepancy is
.
Fig. 10 indicates that when , is an in-creasing function of . In this case, the discrepancies
for are less than 10%. On the other hand, when , is a decreasing function of . In this case,
are less than 10% for . Therefore, for all values considered in our experiments, if we want to
main-tain reasonably low values such that ,
the value should be selected from the range [20,30].
Effects of . Fig. 8 plots the , , and curves for
and . The figures show
that , , and increase as decreases. A small implies a long intersession idle period and more cell movements during this period. Therefore, the location-update cost will increase accordingly. For fixed and values, increasing the number of cell movements implies increasing the probability that the MS will enter the URA update mode or even the RA update mode when the next packet arrives. Thus, a high paging cost is expected. We also notice that when both and are large, increasing only has an insignificant effect on . This phenomenon is explained as follows. For large and , it is likely that is larger than the number of cell crossings during the idle period. Therefore, the MS will only perform cell updates and increasing only insignificantly increases the value.
Effects of . A smaller implies more intersession idle pe-riods. Since more cell crossings are observed in an intersession idle period than in theOFFperiods of a session, increases as decreases. Similar to the discussion for the interaction be-tween and , is more sensitive to the change of for a small than a large .
Effects of variance . Fig. 11 plots the curves where the cell-residence times have a Gamma distribution with the mean and the variance . This figure indicates that is a decreasing function of . When increases, more short and long cell-residence times are observed. Long cell-residence times imply a small number of cell crossings , which result in a small . On the contrary, short cell-residence times imply
Fig. 9. Effects ofK on C (K = 2, = (1=10) , V = 1= , V = 1= , (U=V ) = 4, and = 0:7).
Fig. 10. DiscrepancyD(K = j) of C (K = 2, = (1=10) , V = 1= , V = 1= , (U=V ) = 4, and = 0:7).
large number of cell crossings , which increases . We ob-serve that when , the numbers of URA and RA cross-ings do not increase as quickly as does. The result is that the negative effect of short cell-residence times are not as significant as the positive effect of long cell-residence times. Therefore, the combined effect is that decreases as increases. Fig. 11 also indicates that is not sensitive to the change of when
.
Effects of variance . Fig. 12 plots as a function of , where is the variance of the intersession idle periods . This figure shows that decreases as increases. When increases, more long and short periods are observed. For a short , few cell movements occur during this period (i.e., is small) and a small is expected. On the other hand, for a long , many cell movements occur during this period (i.e.,
Fig. 12. Effects ofV onC (K = 2, K = 5, = (1=200) ,
V = (1= ), (U=V ) = 4, and = 0:7).
, the numbers of URA and RA crossings do not increase as rapidly as does. Consequently, the net effect is that decreases as increases.
IV. CONCLUSION
This paper investigated the location-management strategy for UMTS PS service domain. When an MS is not in any communi-cation session, the system tracks the RA where the MS resides. Within a communication session, the MS is tracked at the cell level during packet transmission. In the idle period of an on-going session, the MS is tracked at the URA level to avoid fre-quent cell updates while still keeping the radio connection. The inactivity counter mechanism was proposed in 3GPP 25.331 [1] to determine when to switch between the three location-tracking modes (cell, URA, or RA). In this mechanism, two inactivity counters are used to count the numbers of cell and URA up-dates in an idle period between two packet transmissions. If the number of cell updates reaches a threshold , the MS is switched from the cell tracking to the URA tracking. After that, if the number of URA updates reaches a threshold , the MS is tracked at the RA level. We utilized analytical and sim-ulation models to investigate the performance of the inactivity counter mechanism. It is clear that as and increase, the location-update cost increases while the paging cost decreases. There exists optimal and that minimize the net cost of location update and paging. For the input parameters con-sidered in this paper, the lowest costs are observed when
or 2. If the intersession idle periods are long, is an increasing function of . On the other hand, if the are short, is a decreasing function of . We quantitatively showed how increases as intersession idle periods and user mobility increase. In addition, both the variances of cell-res-idence times and of intersession idle periods affect . Our study indicated that as and increase, decreases.
APPENDIX
PROOF FORTHEOREM1
Consider an idle period where no packet is delivered. Let be the number of cell crossings in this idle period. In the inactivity counter algorithm, let be the net cost
of location update and paging in the idle period with cell-up-date threshold and URA-update threshold . Let
be the optimal threshold value pair that minimizes the net cost . Define as a number larger than the value in the idle period. Let be an arbitrary integer number.
Theorem 1: For an idle period, , or (1,0).
Proof: Let and be the numbers of URA and RA crossings between the st cell crossing and the th cell crossing, respectively. It is clear that . We consider three cases.
Case I: . In this case, there are no URA and RA updates during the idle period and the net cost is not affected by the value of . Therefore, for an arbitrary value , we have
(19)
Case II: and . In this case, there are no RA updates during the idle period. The net cost is
(20) where is the number of cells in an URA [e.g., in (5) for an -layer URA layout]. Note that the number of URA crossings between the second and the th cell
crossing is . Since the number of URA
crossings is no more than the number of cell crossings in the same time period, we have
or
(21) From (20) and (21), we have
(22)
Case III: and . Let the th
URA update correspond to the th cell crossing in this idle period; then, is the number of RA updates and the net cost is
(23) where is the number of cells in an RA. The number of RA crossings between the second and the th cell crossing is . Similar to the derivation of (21)
(24) From (23) and (24), we have
From (19), (22), and (25), for all and values, we have
In other words, , , or (1,0).
ACKNOWLEDGMENT
The authors would like to thank the anonymous reviewers. Their comments have significantly improved the quality of this paper.
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Shun-Ren Yang received the B.S. and M.S. degrees
in computer science and information engineering from National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in 1998 and 1999, respec-tively. He is currently pursuing the Ph.D. degree at NCTU.
His research interests include the design and anal-ysis of personal communications services networks, computer telephony integration, mobile computing, and performance modeling.
Yi-Bing Lin (M’95–SM’95–F’03) received the
B.S.E.E. degree from National Cheng Kung Univer-sity, Tainan, Taiwn, R.O.C., in 1983 and the Ph.D. degree in computer science from the University of Washington, Seattle, in 1990.
From 1990 to 1995, he was with the Applied Research Area, Bell Communications Research (Bellcore), Morristown, NJ. In 1995, he was ap-pointed Professor, Department of Computer Science and Information Engineering (CSIE), National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C. In 1996, he was appointed Deputy Director of the Microelectronics and Information Systems Research Center at NCTU. From 1997 to 1999, he was elected Chairman of CSIE at NCTU. He has published over 150 journal articles and more than 200 conference papers. He is the author of the book Wireless and Mobile Network
Architecture (coauthored with Imrich Chlamtac; Wiley: New York, 2001). His
current research interests include the design and analysis of personal com-munication-services networks, mobile computing, distributed simulation, and performance modeling. He serves as a consultant to many telecommunications companies, including FarEasTone and Chung Hwa Telecom.
Dr. Lin is a Senior Technical Editor of IEEE NETWORK. He is an Editor of IEEE TRANSACTIONS ON WIRELESSCOMMUNICATIONS, IEEE PERSONAL
COMMUNICATIONS MAGAZINE, Computer Networks, International Journal
of Communications Systems, ACM/Baltzer Wireless Networks, Computer Simulation Modeling and Analysis, and Journal of Information Science and Engineering. He is an Associate Editor of IEEE TRANSACTIONS ONVEHICULAR
TECHNOLOGYand IEEE COMMUNICATIONSSURVEY ANDTUTORIALS. He is an Area Editor of ACM Mobile Computing and Communication Review and a Columnist for ACM Simulation Digest. He has been a Guest Editor for the
ACM/Baltzer MONET special issue on personal communications, the IEEE
TRANSACTIONS ONCOMPUTERSspecial issue on mobile computing, the IEEE TRANSACTIONS ONCOMPUTERSspecial issue on wireless internet, and the IEEE COMMUNICATIONS MAGAZINE special issue on active, programmable, and mobile code networking. He served as Program Chair for the Eighth Workshop on Distributed and Parallel Simulation and for the Second International Mobile Computing Conference. He also served as General Chair for the Ninth Workshop on Distributed and Parallel Simulation. He received the 1998, 2000, and 2002 Outstanding Research Awards from the National Science Council, R.O.C., and the 1998 Outstanding Youth Electrical Engineer Award from the Chinese Institute of Electrical Engineering (CIEE), R.O.C. He also received the NCTU Outstanding Teaching Award in 2002. He is an Adjunct Research Fellow of Academia Sinica and is Chair Professor at Providence University, Taichung, Taiwan, R.O.C.
