Abstract:
Some embodiments provide methods for selecting a serving gateway to service user equipment in communication with a network, including: receiving a message from a base transceiver station including a list of tracking areas handled by the base transceiver station, initiating a domain name system query for at least one tracking area in the list of tracking areas to identify information indicating a serving gateway serving the at least one tracking area, storing, in local memory, the information indicating the serving gateway serving the at least one tracking area, and upon an occurrence of a triggering event, retrieving, from the local memory, the stored information indicating the serving gateway serving the at least one tracking area.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation patent application of, and claims the benefit of the earlier filing date of, U.S. patent application Ser. No. 12/603,698, entitled “Systems and Methods for Selecting Serving Gateways to Service User Equipment,” filed on Oct. 22, 2009, which is hereby expressly incorporated by reference in its entirety. 
     This application is related to U.S. patent application Ser. No. 12/603,704, titled “Systems and Methods for Classifying User Equipment and Selecting Tracking Areas,” to Kamalaraj; U.S. patent application Ser. No. 12/603,710, titled “Systems and Methods for Reduced Latency Tracking Area Selection,” to Dakshayani, filed on Oct. 22, 2009; U.S. patent application Ser. No. 12/603,802, titled “Systems and Methods for Selecting Tracking Areas and Reducing Paging,” to Kamalaraj, filed on Oct. 22, 2009; and U.S. patent application Ser. No. 12/603,712, titled “Systems and Methods for Selecting Tracking Areas and Reducing Tracking Area Updates,” to Kamalaraj, filed on Oct. 22, 2009, each of which is hereby expressly incorporated by reference herein in its entirety. 
    
    
     TECHNICAL FIELD 
     The disclosed subject matter relates to systems and methods for selecting serving gateways and tracking areas to serve user equipment. 
     BACKGROUND 
     Wireless networks are telecommunications networks that use radio waves to carry information from one node in the network to one or more receiving nodes in the network. Wired communication can also be used in portions of a wireless network, such as between cells or access points. Cellular telephony is characterized by the use of radio cells that provide radio coverage for a geographic area, with multiple cells arranged to provide contiguous radio coverage over a larger area. 
     The first generation of wireless telephone technology used analog mobile phones in which analog information signals were transmitted. As technology progressed a second generation (2G) of wireless service was introduced. In 2G systems, digital information signals were used to modulate a carrier. These 2G technologies used time division multiplexed access (TDMA) or code division multiple access (CDMA) technologies to distinguish multiple users. Such networks that were upgraded to handle higher-speed packet data in networks referred to as 2.5G and 3G networks. The 3rd Generation Partnership Project (3GPP) and the 3rd Generation Partnership Project 2 (3GPP2) respectively developed the GSM/UMTS/HSDPA and cdmaOne/CDMA2000 technologies. The next evolution is 4G technology, which is referred to as long term evolution-system architecture evolution (LTE-SAE) and uses orthogonal frequency division multiple access (OFDMA) technology. 
     Other wireless protocols have also developed including WiFi, an implementation of various IEEE 802.11 protocols, WiMAX, an implementation of IEEE 802.16, and HiperMAN, which is based on an ETSI alternative to IEEE 802.16. 
     Wireless communication technologies are used in connection with many applications, including, for example, satellite communications systems, portable digital assistants (PDAs), laptop computers, and user equipment (e.g., cellular telephones, mobile phones equipment). One benefit that users of such applications can obtain is the ability to connect to a network (e.g., the Internet) as long as the user is within range of such a wireless communication technology. 
     SUMMARY 
     Some embodiments of the disclosed subject matter provide reduced latency systems and methods for selecting serving gateways to serve user equipment. Some embodiments of the disclosed subject matter provide reduced latency systems and methods for generating user equipment&#39;s tracking area identity lists. Some embodiments of the disclosed subject matter provide systems and methods for generating user equipment&#39;s tracking area identity lists based on, for example, one or more of the user equipment&#39;s paging load, tracking area update load, and mobility characteristics. 
     Some embodiments provide methods for selecting a serving gateway to service user equipment in communication with a network, including: receiving a message from a base transceiver station including a list of tracking areas handled by the base transceiver station; performing a domain name system query for at least one tracking area in the list of tracking areas to retrieve and store in a local memory information identifying a serving gateway serving the at least one tracking area; receiving an attach request from the base transceiver station identifying the user equipment and a tracking area from which the user equipment is connected to the network; searching the information identifying a serving gateway serving the at least one tracking area stored in the local memory to identify a serving gateway to service the user equipment based on the tracking area from which the user equipment is connected to the network; and sending a message identifying the identified serving gateway to the base transceiver station. 
     Some embodiments provide methods for selecting a serving gateway to service user equipment in communication with a network in which an access gateway receives messages from base transceiver stations including a list of tracking areas handled by the base transceiver station, and wherein the access gateway performs a domain name system query for at least one tracking area in the list of tracking areas to retrieve and store in a local memory information identifying a serving gateway serving the at least one tracking area, the method comprising: receiving an attach request from the base transceiver station identifying the user equipment and a tracking area from which the user equipment is connected to the network; searching the information identifying a serving gateway serving the at least one tracking area stored in the local memory to identify a serving gateway to service the user equipment based on the tracking area from which the user equipment is connected to the network; and sending a message identifying the identified serving gateway to the base transceiver station. 
     Some embodiments provide a mobility management entity in a communication network including a local memory; a first interface which is configured to receive messages from a base transceiver station including a list of tracking areas handled by the base transceiver station, and receive an attach request from the base transceiver station identifying user equipment and a tracking area from which the user equipment is connected to the network; a second interface which configured to perform a domain name system query for at least one tracking area in the list of tracking areas to retrieve information identifying a serving gateway serving the at least one tracking area; the mobility management entity configured to store the retrieve information identifying a serving gateway serving the at least one tracking area in the local memory; and search the information identifying a serving gateway serving the at least one tracking area stored in the local memory to identify a serving gateway to service the user equipment based on the tracking area from which the user equipment is connected to the network; and the first interface further configured to send a message identifying the identified serving gateway to the base transceiver station. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a long term evolution (LTE) network in accordance with some embodiments of the disclosed subject matter. 
         FIG. 2  illustrates relationships between cells, tracking areas, and evolved nodeBs in accordance with some embodiments of the disclosed subject matter. 
         FIG. 3  illustrates a method for selecting a serving gateway to service user equipment in communication with a network in accordance with some embodiments of the disclosed subject matter. 
         FIG. 4  illustrates a graph of nodes representing tracking areas connected by weighted edges representing movement of user equipment between the tracking areas in accordance with some embodiments of the disclosed subject matter. 
         FIG. 5  is an adjacency matrix describing the graph of  FIG. 4   
         FIG. 6  illustrates a method for allocating a tracking area identity list to user equipment based on the graph of  FIG. 4  or matrix of  FIG. 5  in accordance with some embodiments of the disclosed subject matter. 
         FIGS. 7-9  are adjacency matrixes that are generated as the method of  FIG. 6  is applied to the adjacency matrix of  FIG. 5 . 
         FIG. 10  illustrates a table identifying tracking areas, the evolved nodeBs that support those tracking areas, and the tracking area group to which each tracking area belongs in accordance with some embodiments of the disclosed subject matter. 
         FIG. 11  illustrates a directed adjacency matrix for interconnecting the tracking areas of  FIG. 10 . 
         FIG. 12  illustrates a method for allocating a tracking area identity list to user equipment based on the table of  FIG. 10  and matrix of  FIG. 11  in accordance with some embodiments of the disclosed subject matter. 
         FIG. 13  illustrates a method of collecting data describing user equipment related behavior, classifying user equipment based on the behavior, and allocating a tracking area identity list to user equipment based on the classification in accordance with some embodiments of the disclosed subject matter. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a long term evolution (LTE) network and a universal mobile telecommunication system (UMTS) release 8 network. The network diagram of  FIG. 1  includes user equipment (UE)  110 , an evolved nodeB (eNB)  112 , a nodeB  114 , a radio network controller (RNC)  116 , a mobility management entity (MME)/user plane entity (UPE)  118 , a system architecture evolution gateway (SAE GW)  120 , a policy and charging rules function (PCRF)  122 , home subscriber server (HSS)  124 , core IP network  126 , internet  128 , and Serving General packet radio service Support Node (SGSN)  130 . The MME  118 , SAE GW  120 , and SGSN  130  can be implemented in a chassis as described below. The SAE GW  120  can include a serving gateway (S-GW) as well as a packet data network gateway (P-GW). In some embodiments, the S-GW and P-GW can be implemented on separate network devices. 
     MME  118  is a control-node for the LTE access network. The MME  118  is responsible for UE  110  tracking and paging procedures including retransmissions. MME  118  handles the bearer activation/deactivation process and is also responsible for choosing the S-GW for a UE  110  at the initial attach and at time of an intra-LTE handover. The MME  118  authenticates the user by interacting with the HSS  124 . The MME  118  generates and allocates temporary identities to UEs and terminates Non-Access Stratum (NAS) signaling. The MME  118  checks the authorization of the UE  110  to camp on the service provider&#39;s Public Land Mobile Network (PLMN) and enforces UE roaming restrictions. The MME  118  is the termination point in the network for ciphering/integrity protection for NAS signaling and handles the security key management. Lawful interception of signaling is also supported by the MME  118 . The MME also provides the control plane function for mobility between LTE and 2G/3G access networks with the S3 interface terminating at the MME  118  from the SGSN  130 . The MME  118  also terminates the S6a interface towards the home HSS for roaming UEs. 
     The S-GW routes and forwards user data packets, while also acting as the mobility anchor for the user plane during inter-eNB handovers and as the anchor for mobility between LTE and other 3GPP technologies (terminating S4 interface and relaying the traffic between 2G/3G systems and PDN GW). For idle state UEs, the S-GW terminates the down link data path and triggers paging when down link data arrives for the UE  110 . The S-GW manages and stores UE contexts, e.g., parameters of the IP bearer service and network internal routing information. The S-GW also performs replication of the user traffic in case of lawful interception. The P-GW provides connectivity to the UE  110  to external packet data networks by being the point of exit and entry of traffic for the UE  110 . A UE  110  may have simultaneous connectivity with more than one P-GW for accessing multiple packet data networks. The P-GW performs policy enforcement, packet filtering for each user, charging support, lawful interception, and packet screening. The P-GW also provides an anchor for mobility between 3GPP and non-3GPP technologies such as WiMAX and 3GPP2 (CDMA 1X and EvDO). The S-GW or the PGW depending on the embodiment, can be used to provide deep packet inspection and provide advertising to the user on a per subscriber basis as described above on a chassis implementing a S-GW or a PGW. 
     Tracking Area Lists and Paging 
     A radio tower is logically located between user equipment  110  and eNB  112 . One or more such radio towers provide wireless coverage to an area known as a cell. Logical grouping of these cells can form tracking areas, for example, that define a boundaries used for paging, roaming restrictions, etc. Each hexagon of  FIG. 2  represents a cell. 
     Each of the three different fill types of the cells identifies the tracking area in which the cell is located. While each cell is part of only one tracking area, an eNB  112  can serve cells belonging to different tracking areas.  FIG. 2  illustrates nine eNBs  112 , each serving the three cells immediately surrounding a particular eNB  112  (as grouped by the thick black lines). For example, eNB  201  serves cells  211 ,  212 , and  213 . The nine eNBs are located within three tracking areas (tracking areas  221 ,  222 , and  223 ). eNB  201 , for example, has cells belonging only to tracking area  221 . eNB  203 , for example, has cells belonging to all three tracking areas. 
     When eNB  203 , for example, connects to an MME  118 , it sends MME  118  tracking area identities for each of tracking areas  221 ,  222 , and  223 . A tracking area identity (TAI) is used to identify a tracking area, and is constructed from the MCC (Mobile Country Code), MNC (Mobile Network Code), and TAC (Tracking Area Code). A UE  112  can store a list of tracking area identities (“TAI list”) identifying which tracking areas it is served by. The TAI list can be assigned or updated by an MME  118  when, for example, the UE  110  connects to a network, on a periodic basis, or when the UE detects is has entered a tracking area not in its TAI list and sends a tracking area update (“TAU”). 
     A UE  110  can receive a page request, for example, to notify the UE that another device (e.g., another UE, a landline phone, etc) is trying to call the UE or to alert the UE that another device is attempting to send the UE packet data. For example, data can be received at S-GW  120  from a remote device. S-GW  120  can generate and send a page request to MME  118  to locate and establish communications with a UE  110 . In response, MME  118  can send a page to eNBs  112  in the tracking area where the target UE  110  was last known to be located. If the UE  110  receives the page request, the UE can send a paging response to the MME  118  and a process of, e.g., exchanging data or setting up a call, can continue. 
     An MME  118  can assign a TAI list to a UE based on, among other things, for example, the UE&#39;s TAU load and/or paging load. Various embodiments of the disclosed subject matter provide systems and methods for assigning TAI lists to a UE  112 . For low mobility devices, for example, the assigned TAI list can be generated such that the number of associated eNBs  112  is reduced. This can reduce unnecessary paging that can result from, for example, paging too many eNBs even though a low mobility device (e.g., an at-home device) may almost always be serviced by the same eNB  112 . For high mobility, low paged devices, (e.g., in-vehicle security devices), for example, the assigned TAI list can be generated to be associated with a large number of eNBs  112 . Because high mobility, low paged devices are rarely paged, few network resources are wasted by paging a large TAI list. Instead, the focus of assigning a TAI list can be on reducing the number of tracking area updates, which can tend to occur frequently when a high mobility device has a small TAI list. For high mobility, high paged devices, for example, reaching a balance between reducing paging load and reducing tracking area updates can be the focus of assigning a TAI list. In addition, eNBs belonging to a same tracking area typically have connectivity to a same S-GW. Various embodiments of the disclosed subject matter provide systems and methods for selecting an S-GW  120  to serve a UE  110 . 
     Reducing Latency for S-GW Selection 
     An MME  118  is responsible for selecting an S-GW  120  that services the tracking area from which a UE  110  is connecting. For example, when a UE  110  sends an Attach Request to an eNB  112 , the eNB  112  passes this request to an MME  118 , which selects an S-GW  120  to service the UE  110 . 3GPP standards specify that domain name system (DNS) based mechanisms be used to determine which S-GWs can serve a particular tracking area. For example, the list of S-GWs servicing a tracking area can be obtained by performing a DNS resolution using a TAI fully qualified domain name. Some embodiments reduce latency that can be caused by determining which S-GWs can serve a particular tracking area. 
     Referring to  FIG. 3 , when an eNB  112  connection is established to an MME  118 , S1 SETUP messages are exchanged for S1 connection initialization. These messages, exchanged between an eNB  112  and an MME  118 , are illustrated as messages  301 - 306  in  FIG. 3 . S1 Setup Request  306  includes a list of tracking areas handled by eNB  112  (for example, referring to  FIG. 2 , only TA1 if eNB  201 ). The MME  118  can use this list of tracking areas to perform DNS queries to obtain and store TAI to S-GW mappings. Later, the stored mappings can be used for S-GW selection, for example, during a UE Attach procedure, Tracking area update procedure, etc. For example, Attach Request message  307  from UE  110  to eNB  112  results in eNB  112  sending Attach Request  308  to MME  118 . MME  118  can select an S-GW from its locally stored list of S-GWs, handled by this particular eNB  112  and serving the tracking area from which the particular eNB  112  is connected. In addition, to address changes in the DNS server, an MME  118  can use timers to periodically refresh its locally stored TAI to S-GW mappings. 
     Table 1 below illustrates and example structure of TAI to S-GW mappings. 
                                     TABLE 1                           TAI-1   S-GW1               TAI-2   S-GW4   S-GW2           TAI-3   S-GW2           TAI-4   S-GW1   S-GW3                        
The information can be stored in an MME  118  and indicates, for example, that tracking area TAI-2 is served by S-GW4 and S-GW2.
 
     Reducing Latency for TAI List Generation 
     In assigning a TAI list to a UE  110 , the MME can ensure that tracking areas in its assigned TAI list are serviced by the S-GW servicing the UE. Whether a given S-GW services a particular tracking area can be determined by performing a DNS resolution using a TAI fully qualified domain name. However, doing so for every TAI in a TAI list during list allocation can result in undesired latency. For example, to reduce latency for TAI list allocation in an LTE/SAE network, some embodiments perform DNS queries as a result of eNB  112  setup. 
     During processing of an S1 SETUP Request or NAS Attach Request, an MME  118  can perform DNS queries to determine which S-GWs service which tracking areas. The MME  118  can use this information to generate and locally store the list of TAIs serviced by each S-GW. For example, with reference to Table 2, an MME  118  can store information indicating that TAI-1, TAI-2, TAI-3, and TAI-4 are served by S-GW1. 
     
       
         
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
             
             
               
                   
                 S-GW1: 
                 TAI-1 
                 TAI-2 
                 TAI-3 
                 TAI-4 
               
               
                   
                 S-GW2: 
                 TAI-11 
                 TAI-12 
                 TAI-13 
                 TAI-14 
               
               
                   
                   
               
             
          
         
       
     
     When a UE  110  initiates an Attach Request, the list of TAI associated with the same S-GW as the tracking area where the UE is located can be used as the set from which to select the tracking area list to be sent to the UE. For example, when a UE  110  initiates an Attach Request, from, for example, TAI-2, the MME  118  can access the information illustrated in Table 2 to determine that TAI-2 is serviced by S-GW1, and that S-GW-1 also services TA-1, TAI-3, and TAI-4. The TAI&#39;s for the TAI list to be allocated to the UE  112  can be selected from the set of TA-1, TAI-2, TAI-3, and TAI-4, and this can be done without needing to, for example, perform any DNS queries in response to the Attach Request. In addition, to address changes in the DNS server, an MME  118  can use timers to periodically refresh the locally stored information identifying associations between TAI and S-GWs. 
     Some embodiments combine reduced latency for S-GW selection and reduced latency for TAI list allocation. For example, when an MME  118  receives an Attach Request from a UE  110  via an eNB  112 , the MME can use locally stored TAIs to S-GW mappings to select an S-GW serving the tracking area from which the UE is connected, and can use locally stored S-GW to TAI mappings to determine a set of TAIs from which to allocate a tracking area list for the UE, after receiving an attach request. 
     Reducing Tracking Area Updates 
     If the TAI list assigned to a UE was not, for example, generated using appropriate characteristics regarding the UE&#39;s movements, the UE can find itself frequently in tracking areas that are not in its assigned TAI list. This can lead to the UE sending a high number of TAUs and wasting radio resources and UE and network computing power. For example, a cellular phone may move from (referring to  FIG. 2 ) TA-3 to TA-2. If, for example, TA-2 is not in the cellular phone&#39;s tracking area list, the phone can send a tracking area update to an eNB  112 . This tracking update will identify the current tracking area (i.e., TA-2) and the last tracking area visited (i.e., TA-3). To reduce TAUs, some embodiments manage a TAI list by identifying particular tracking areas to which a UE is likely to move. 
     Some embodiments use the identity of last TAI visited, which is included in Attach Requests and TAUs, to predict which tracking area a UE will move to. An MME  118  can maintain a per S-GW serving area graph. An S-GW serving area can be a group of tracking areas that are served by an S-GW. There can be, for example, multiple S-GWs serving an S-GW serving area. The nodes of the graph represent TAIs within the S-GW serving area. A Node(i) is connected to Node(j). When a tracking area update or attach request is received at an MME, the current TAI (j) and Last visited TAI (i) are monitored and an edge (i, j) is given a weight equal to the total number of such requests received. The total number of TAUs and Attach Requests received at each node is also stored. Then the weight of an edge (i,j) is equal to its number of request divided by the total number of request. For example, for a TAI-A: if there were ten total request and five of them were (B,A) then the graph for TAI-A would include an edge between node TAI-A to TAI-B with a weight of 0.5 (i.e., 5/10). 
     A sample graph and corresponding weighed adjacency matrix are shown in  FIGS. 4 and 5 . As shown in the graph and adjacency matrix, for example, the edge between the node for TAI-A and TAI-B has a weight of 0.5 indicating that half of the UEs that moved out of TAI-A, from the S-GW serving area for which  FIG. 4  pertains, moved to TAI-B. Similarly, twenty percent moved to TAI-F and twenty percent moved to TAI-C. In the example of  FIG. 4 , the probability of moving between two nodes in either direction is the same. For example, changes from (1) TAI-A to TAI-B; and (2) TAI-B to TAI-A both have the same probability (i.e., 50%). Other embodiments, for example, can include two oppositely directed edges between each pair of nodes indicating different probabilities based on the direction of movement. 
     A TAI list can be computed using the method illustrated in  FIG. 6 . Starting from the adjacency matrix of  FIG. 5 , the TAI with maximum priority is selected (TAI-B). Then, the weights between all the nodes to which TAI-B is connected are updated. Using W(A,D) as an example, W(A,B), which is 0.5, is multiplied by W(B,D), which is 0.2, to obtain 0.1. Then, 0.1 is added to the current W(A,D), which as shown by node A not being directly connected to node D (or by the adjacency matrix of  FIG. 5 ), is 0; 0+0.1 equals 0.1, hence: {W(A,D)+=0.1 (0.5×0.2), new weight=0.1}}. The updated weights for node A&#39;s remaining neighbors are calculated as: {W(A,F)+=0.15 (0.5×0.3), new weight=0.35}} and {W(D,F)+=0.06 (0.2×0.3), new weight=0.06}. After removing node TAI-B and updating the weights of the various nodes, the adjacency matrix of  FIG. 7  is produced. 
     As shown, the edge between TAI-A and TAI-F has the highest value among the edges from TAI-A. As such, TAI-F is added to the TAI list, and the update weights are calculated: {W(A,C)+=0.07 (0.35×0.2), new weight=0.37}; {W(A,D)+=0.02 (0.35×0.06), new weight=0.12}; {W(A,E)+=0.10 (0.35×0.3), new weight=0.10}; {W(C,D)+=0.01 (0.2×0.06), new weight=0.51}; {W(C,E)+=0.06 (0.2×0.3), new weight=0.06}; and {W(D,E)+=0.01 (0.06×0.3), new weight=0.31}. After removing TAI-F and updating the weights, the adjacency matrix of  FIG. 8  is produced. 
     As shown, the edge between and TAI-A and TAI C has the highest value among the edges from TAI-A. As such, TAI-C is added to the TAI, and the update weights are calculated: {W(A,D)+=0.19 (0.37×0.51), new weight=0.31}; {W(A,E)+=0.02 (0.37×0.06), new weight=0.12}; and {W(D,E)+=0.03 (0.51×0.06), new weight=0.34}. After removing TAI-C and updating the weights, the adjacency matrix of  FIG. 8  is produced. TAI-D and TAI-E can then be added to the TAI list based on their respective weights in relation to TAI-A. 
     In the above example, the total number of TAIs was less than sixteen to begin with, so in some embodiments the entire method would have been skipped. However, for ease of explanation, a graph of only six nodes was used. In addition, various embodiments can use different values for the maximum number of nodes to be added to the TAI list, based on, for example, whether the UE&#39;s characteristics (e.g., high paging, low paging, high mobility, low mobility, etc.). 
     Reducing Paging 
     An MME  118  provides paging to UEs  110 . An MME  118  is specified to send a page to all eNBs in a tracking area where the target UE was last registered. This can lead to a page being sent to a number of eNBs and subsequently being transmitted over the paging channel by a number of eNBs to find the target UE. If a tracking area assigned to a UE is covered by a multitude of eNBs, when the network needs to page the UE, all the eNBs will be paged. This paging can waste radio resources and network computing capacity. To reduce such a waste of resources, some embodiments provide improved paging, through TAI list management, by limiting paging to a reduced set of eNBs. 
     An MME  118  can assign tracking areas to Tracking Area Groups (TAGs). Each tracking area in a TAG can be supported by the same set of eNBs. Edge weighted directed graphs of TAGs can be created, with two edges in opposite directions between two nodes. The edge weight w of an edge from TAG(i) to TAG(j) is the number of EnodeBs in TAG(j) but not in TAG(i). For example, if TAG(A) consisted of EnodeB-1, EnodeB-2, and EnodeB-3; and if TAG(B) consisted of EnodeB-3 and EnodeB-4, then the edge from TAG(A) to TAG(B) would have a weight of one (because TAG(B) includes EnodeB-4, which is not included in TAG(A)). Using the same example, the edge from TAG(B) to TAG(A) would be two (because TAG(A) includes EnodeB-1 and EnodeB-2, which TAG(B) does not). Thus, if the set of eNBs in TAG(i) is a subset of those in TAG(j), the weight from TAG(j) to TAG(i) is set to 0. The minimum weight of any edge is 0. 
     An example table is illustrated in  FIG. 10  including columns of tracking areas  1010 , eNBs supporting those tracking areas  1020 , and tracking area groups  1030 . For example, TAI-1 is supported by eNB-A, eNB-B, and eNB-C, and TAI-1 is in tracking area group TAG-A.  FIG. 11  illustrates the directed adjacency matrix for  FIG. 10 , where the directions of edges go from columns  1110  to rows  1120 . For example, the edge from TAG-A to TAG-B has a weight of zero, and the edge from TAG-B to TAG-A has a weight of two. 
     A TAI list can be computed using the method illustrated in  FIG. 12 . For example, using the data of  FIGS. 10 and 11 , if an ATTACH request is received from a UE  110  in TAI-1, TAI-5 is first added to the UE&#39;s TAI list, because TAI-5 and TAI-1 belong to the same TAG ( 1210  of  FIG. 12 ). Then, the method can enter the while loop, at  1211 . And, TAG-C can be selected, at  1212 , because it has minimal weight (in this example TAG-B and TAG-C have the same weight, so the tracking area with a higher number of TAIs can be selected between the two; in this case TAG-C has two and TAG-B has only one). TAI-3 and TAI-4 are thus added to the TAI list, at  1213  because they the members of TAG-C. Then, TAG-B is selected, adding TAI-2 to the TAI list, then TAG-D is selected and TAI-6 is added. 
     Device Categorization 
     As discussed, an MME  118  can assign a TAI list to a UE based on, among other things, for example, the UE&#39;s tracking area update (“TAU”) load and/or paging load. For example, the method described in  FIG. 6  is related to reducing tracking area updates by reducing the number of TAIs included a UE&#39;s TAI list, and the method described in  FIG. 12  is related to reducing paging load by, for example, reducing the number of eNBs  112  that are paged when a network pages a UE. Also as discussed above, UE&#39;s can be classified into various categories, including (1) low mobility devices; (2) high mobility, low paged devices; and (3) high mobility, high paged devices. Some embodiments can categorize a device into one of these categories, and based on its categorization, select a method or combination of methods to use for generating the UE&#39;s TAI list. 
     At  1310  of  FIG. 13 , for example, an MME  118  can collect data useful for UE categorization. The collected data can include, for example, the number of times the UE&#39;s TAI has changed per unit of time  1311 . This number can be determined based on the 51 messages exchanged between a UE and a network that include the current TAI of the UE. The collected data can also include, for example, the number of times a UE is paged per unit of time. The collected data can be stored in MME as collected data  1320 . 
     Based on collected data  1320 , a UE can be categorized, at  1330 , into for example, one of the three categories described above, and a TAI list can be generated using method  1341 ,  1342 , or  1343 . Regarding, method  1343 , for example, the methods described in  FIGS. 6 and 12  can be combined in various ways, such as, (1) using both and then selecting only TAIs that appear each of the two generated TAI lists; (2) using the output of one method as input to another; (3) using both methods, weighing the results based how mobile and/or how high paging the device is, to select some of the TAIs identified in the two generated lists; (4) various combinations of (1)-(3), etc. 
     Other Example Embodiments 
     The various methods described herein, for example, identify S-GWs or generate TAI lists can be combined with various other methods. For example, the TAI lists generated by the methods described herein are not necessarily the TAI lists allocated to user equipment. Instead, the generated TAI lists can be, for example, used as starting point for other methods to further process before being allocated to user equipment. Accordingly, a tracking area list for a user equipment device, for example, can be, but is not limited to, a tracking area list allocated to a user equipment device, a tracking area list that is used as input to additional methods, a tracking area list that is generated to include a subset of TAIs generated by other methods, or a tracking area list that is not allocated to a user equipment device. 
     Various embodiments of the disclosed subject matter can be implemented using, and combined with, subject matter described in, for example, 3GPP TS 23.401, 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; General Packet Radio Service (GPRS) enhancements for Evolved Universal Terrestrial Radio Access Network (E-UTRAN) access (Release 9), and related specification currently available from the 3rd Generation Partnership Project (3GPP). However, various embodiments can also be implemented using, and combined with, for example, systems, networks, devices, protocols, and standards different than described by these specifications. 
     Although the invention has been described and illustrated in the foregoing illustrative embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the invention can be made without departing from the spirit and scope of the invention, which is limited only by the claims that follow. Features of the disclosed embodiments can be combined and rearranged in various ways within the scope and spirit of the invention.