IMS Network Deployment Cost Optimization Based on Flow-Based Traffic Model

Transcription

1 IMS Network Deloyment Cost Otimization Based on Flow-Based Traffic Model Jie Xiao, Changcheng Huang and James Yan Deartment of Systems and Comuter Engineering, Carleton University, Ottawa, Canada {jiexiao, Abstract The IP Multimedia Subsystem (IMS) is envisioned as the next-generation IP-based multimedia system that integrates data, seech, and video network services over both wireless and wireline networks. Modeling and design of IMS network has been an imortant area to both researchers and network roviders. Our interest is in the area of develoing efficient design models and otimization methods for IMS networks. In this aer, we focus on otimizing the cost of SIP server deloyment in an IMS network. To reflect the traffic loads on the servers, a flow-based model is used to characterize the SIP traffic. Formulated as a linear rogramming roblem, the cost otimization involves maing a logical IMS core network toology into a hysical network toology. Three otential maing strategies are roosed. Each strategy s secific constraints are incororated into the mathematical formulation of the roblem. A numerical examle of each strategy is resented, and the discussion on the formulations is rovided. Index Terms IP Multimedia Subsystem, CSCF Server, SIP signaling Traffic, Cost Otimization, Maing Strategy 1. INTRODUCTION IMS is envisioned as the next generation IP-based multimedia communication system that integrates data, seech, and video network technology and covers wireless and wireline networks. The IMS [1][1], as a new core network domain, was first introduced by the Third Generation Partnershi Project (3GPP) in two hases (release 5 and release 6) [2] for Universal Mobile Telecommunications System (UMTS) networks. 3GPP2 further defined an IP multimedia framework, which finally harmonized with the IMS. Figure 1 illustrates a simlified IMS core network architecture. IMS based networks consist of distinct Call/Session Control Function (CSCF) servers and Home Subscriber Server (HSS). There are three tyes of CSCF servers, the Proxy-, Interrogating- and Server-Call/Session Control Function servers (P-CSCF, I-CSCF, S-CSCF, resectively [1]). This aer only focuses on the network entities illustrated. Based on IP technology, IMS rovides a multimedia session control service that allows mobile users to access new multimedia and multisession alications as well as to establish synchronous multimedia sessions across fixed and mobile terminals Error! Reference source not found.[3][4]. Since the service creation interfaces are standardized by IMS, they allow for the develoment of new multimedia and multi-session alications. IMS offers this session control to the alications by Session Initiation Protocol (SIP) [5][6]. Figure 1: Simlified IMS Core Network Architecture SIP, as an alication layer control rotocol, is defined by Internet Engineering Task Force (IETF) [6]. SIP lies at the core of IMS architecture and lays the role of session establishment, modification, and termination between two or more end users. Each CSCF server is actually a secialized SIP server. Modeling and design of IMS network have always been an imortant area to both researchers and network roviders. Our interest is in the area of develoing efficient design models and otimization methods for IMS network. In our research, we focus on IMS network deloyment cost otimization to roduce a good network design otentially caable of securing considerable saving. In this aer, the mathematical modeling and the alication of efficient otimization methods are alied. We, as designers, have to make selective use of various available theoretical models and different aroximations, such as hysical node caacity and hysical link bandwidth. Also we consider various ractical constraints in secific models. In a real IMS network, the logical IMS network can be maed to different IMS hysical networks with different maing strategies, where the logical CSCF servers are maed into the hysical node(s). In this aer, three otential maing strategies are roosed. Then, each maing strategy can be formulated as cost otimization issue, in a linear rogramming roblem. Each strategy s secific constraints are incororated into the mathematical formulation of the roblem. In order to better understand how to formulate the cost otimization in a secific strategy, an examle for each maing strategy is rovided, including the detailed rocedures. The discussion on the formulations is rovided at the end. The challenge for studying IMS is the comlexity of its signaling rocedures. There are numerous signaling rocedures

2 defined in IMS [3]. Each user agent (UA) may trigger a secific signaling rocedure at a secific time deending on its secific call scenario at that moment. Estimating server loads based on individual signaling rocedures is therefore not scalable. We roosed a flow-based traffic model that allows redicting the loads of IMS CSCF servers in a scalable way by utilizing the characteristics of IMS messages in [8]. A flow is an aggregation of signaling messages that traverse the same ath in an IMS network. In [8] we demonstrated that all signaling rocedures can be aggregated into 17 flows, as shown in Table 1. The flow concet has significantly simlified the rocess to estimate the loads of various CSCF servers while the correlation structure across the loads of these servers is still catured. For more details about the flow concet, readers are referred to [8]. In this aer, we assume that all signaling rocedures have been aggregated into 17 flows that traverse various CSCF servers. We therefore focus on the issue of maing CSCF servers to hysical server nodes. Table 1: Summary of 17 flows Flows Flow Path 1 P S --- S P 2 S P 3 P S 4 I S P --- P S I 5 S P --- P S 6 P S I S I S --- S I 9 S I P P I S I P 12 I S I 13 I S P 14 I S 15 HSS I 16 HSS S 17 S HSS Moreover, each maing strategy has its own advantages and disadvantages. Network roviders select a maing strategy with the best erformance results according to their needs and actual network conditions, including the number of users, the caacity of hysical nodes, the budget lan, and so forth. This requires the roviders to consider both advantages and disadvantages of each maing strategy, in order to determine the one that is satisfied by themselves and their users. In the following sections, we start with a generic maing strategy, and then focus on two secial maing strategies, which can be widely used in the ublic domain. 2.1 Generic Maing Strategy The Generic Maing Strategy is a method that allows for the maing of a logical CSCF server into any hysical node. The uer art of Figure 2 illustrates a logical IMS core network toology, which is the way that the IMS messages ass through the network from one logical server to the next without regard to the hysical interconnection of the hysical nodes. The loads of each logical server can be redicted by alying the flow-based traffic model [8]. However, in the hysical structure of the IMS network, also called hysical IMS network toology, which is deicted in the lower art of Figure 2, the loads of each hysical node can be estimated according to the different maing strategies, each determining how the logical servers are maed into the hysical node(s).. Figure 2 shows the Generic Strategy of maing logical servers in the IMS core network into hysical nodes interconnected through a network. In this case, any hysical node can host one or more logical server(s). On the other hand, two or more hysical nodes can host one or more identical logical servers. Any two or more hysical nodes can be identical, which means that they can host the same logical servers. The Generic Maing Strategy includes all ossible maing ways. Most of IMS-related research work currently has concentrated on IMS architecture and SIP rotocol develoment [4], network erformance evaluation under varying network arameters [3][9], and the Quality of Service (QoS) issue [10]. To our best knowledge, there is no such reference that rovides the formulation on IMS network deloyment cost otimization roblem utilizing the flow-based traffic model. 2. MAPPING STRATEGY The IMS servers (P/S/I-CSCF and HSS) illustrated in Figure 1 are all logical entities. In a real network, all logical servers need to be imlemented on hysical node(s). How to ma logical servers located in a logical IMS core network toology to hysical node(s) located in hysical IMS network toology is not standardized, but is of great interest to the network roviders. Network roviders may choose different maing strategies to achieve their own objectives. On the other hand, an industry-leading network rovider may want a maing strategy that rovides high reliability and high exandability. Figure 2: A Generic Maing Strategy

3 Although the maing strategy is called generic, certain constraint is necessary to minimize the search for the otimal solution. The constraint is related to the flow concet. All flows listed in Table 1 can be classified into two tyes: round tri flow and single tri flow. The round tri flow is defined as a flow that traverses the involved logical servers twice: one in the forward direction and one in the reverse direction. The single tri flow asses the involved logical servers only once. The selection of hysical nodes for erforming both directions in a round tri flow should be identical. This is because the hysical nodes chosen in the forwarding direction may hold some information regarding the end users. It will minimize the information to be dulicated on different hysical nodes by choosing the reverse ath to be the same hysical nodes excet the order is reversed Notations for Network Modeling As you will see, a good mathematical notation can reresent a secific design roblem in a comact and unambiguous way. It hels us to understand the formulation better. Physical Node, Logical Server, and Flow The four different logical servers in logical IMS network are labeled with the generic label v, where v 1, 2, 3, 4, and the hysical nodes are denoted as y, where y 1, 2,, Y, and Y is the number of hysical nodes in the network. A flow is denoted as f, where f 1, 2,, 17. A direct hysical link connects its hysical end nodes directly. Flow Demand, Physical Path Flow demand volume is denoted as h f, and it reresents the traffic volume (number of messages) in a given unit of time. For flow f, the total number of available hysical aths is denoted by P f, and they are labeled with from the first hysical ath to the total number of hysical aths, i.e. 1, 2,, Pf. This sequence is called the list of candidate hysical aths. Each hysical ath connects the hysical end nodes of flow f, and it is described as the set of hysical links of which the hysical ath is comosed of. In this aer, we assume the candidate aths for a flow are known to the carrier. A carrier may decide the candidate aths based on its own olicy. Figure 3 deicts an examle of maing the logical servers into four hysical nodes, which are hosting the corresonding logical servers, as shown in the bracket. A list of hysical aths that can carry flow 3 (flow ath: PS; f = 3) is drawn in the lower art of Figure 3. Table 2 lists the candidate hysical aths for flow 3 under the network toology in Figure 3. Moreover, for hysical ath 5, hysical node #3 can handle flow 3 alone. Now, flow demand volume is assigned to the available hysical aths. The loads assigned to hysical ath, a candidate hysical ath of flow f are denoted by w f, as shown in Table 2. Since the demand volume of flow f needs to be realized by the traffic on all the candidate hysical aths, we can write the following equation: w 31 w32 w33 w34 w35 w36 h3 (1) It leads to the demand constraint, which can be written in a general form as follows: P f 1 Logical Toology Flow 3, f=3 Physical Toology Node #2 (P) P-CSCF Node #1 (P) w f h f HSS h3 Path 4. w34 S-CSCF Internet Cloud Path 1, w31 Path 3, w33 Path 2, w32 I-CSCF Path 5,w35 Node #3 (P/I/S) Path 6, w36 Node #4 (S/HSS) Figure 3: An Examle of Maing, 6 Available Physical Paths for Flow 3 (Flow Path: PS) Table 2: A List of Candidate Physical Paths for Flow 3, under the Network Toology in Figure 3 Candidate hysical aths for flow 3 (flow ath: PS) w f 1 Physical node #1 #3 w 31 2 Physical node #1 #4 w 32 3 Physical node #2 #3 w 33 4 Physical node #2 #4 w 34 5 Physical node #3 w 35 6 Physical node #3 #4 w 36 Indicator Two indicators are defined for formulating the design roblem. The first indicator, denoted by fyv, indicates the relationshi among hysical node y, logical server v, hysical ath, and flow f. It is defined as: fvy 1, if hysical node y hosts logical server v along fvy hysical ath of flow f (3) 0, otherwise. is constant and obtained from the analysis erformed on network toology assuming that the carrier knows all candidate aths for each flow based on its olicy. The second indicator determines the number of times that logical server v is involved in flow f, and it is denoted by. (2) fv

4 As discussed, there are two tyes of flow, which are the round tri flow and the single tri flow as summarized in Table 3. The ath of each flow is rovided in Table 1. The logical servers along a round tri flow are involved twice. And, the logical servers along a single tri flow are involved once. However, flow 11 and flow 12 are secial cases due to the flow traverses logical S-CSCF server only once although they look like a round tri flow. is written as follows: fv 2, 1,if 2,if 2,if 1,if 2,if 1,if 0, otherwise. fv if logical server v is involved in flow f, and flow f is a round tri logical server v is involved in flow f, and flow f is a single tri logical server v is P - CSCF, for flow 11 logical server v is I - CSCF, for flow 11 logical server v is S - CSCF, for flow 11 logical server v is I - CSCF, for flow 12 logical server v is S - CSCF, for flow 12 Table 3: The Tyes of Flows Tyes of flow Flow Single tri flow #2, #3, #6, #7, #9, #10, #13, #14, #15, #16, #17 Round tri flow #1, #4, #5, #8 Secial flow #11, #12 Load, Rate, Caacity The cost of a hysical node mainly deends on its caacity. Thus, the loads of hysical node are redicted in order to determine the best choice for the caacity of a hysical node. The loads on each hysical node indicate the number of actual IMS messages rocessed in a given unit of time, and we denote these loads as l y for hysical node y. As we can see in Figure 3, the loads of a hysical node are calculated as the summary of the loads of the flows that traverse the node. l w y (4) f v fv fvy f (5) In secific, this equation can be divided into three stes. Ste a: fvyw f, accumulates the loads allocated to each available hysical ath of the flow f, with a given logical server v and hysical node y. Ste b: v fv fvyw f, reresents the total loads on hysical node y, for flow f. Ste c: f v fv fvyw f, sums u the loads for all the involved flows. Our goal is to find the caacity of a hysical node that can satisfy the loads requirement. Let cy reresents the rocessing caability of a hysical node. c y can be in various units that are related to the cost of the server. For examle, c y can be the number of certain CPUs the server carries. Since in IMS network, each logical server has different message functions to be rocessed, we need to decide how much caacity is required to rocess messages for each tye of logical server. This caacity coefficient is denoted as for v logical server v. v is in the unit of time-caacity roduct. For examle, v =2 can mean that a message requires two time units for a logical server with a single CPU or one time unit for a logical server with two CPUs. Here we assume the overhead associated with multile CPUs is negligible to simlify the analysis. However our analysis can be generalized to include those overheads. It should be noted that messages rocessed by the same logical server do not necessarily take the same amount rocessing time due to their different tyes. To simlify our analysis, we take v as the statistical mean of the caacity required by all tyes of messages rocessed by the logical server. Equation (5 calculates the loads of hysical node y, which reresent a sum of the loads on logical server v that is hosted in a hysical node y. Hereby, the caacity of hysical node y should be greater than the accumulation of the loads of logical server v times v, for all ossible logical server v that the hysical node y hosts. This is a second set of constraints that can be generally written as: f v v fv fvyw f c y (6) Furthermore, in the design roblem, we aim to minimize the hysical node caacity cost. Therefore, a rate y is introduced and it reresents the cost er unit rocessing caability for hysical node y Formulation of Cost Otimization Problem IMS network deloyment cost otimization issue is considered with a set of given flow demand volumes. A comlete version of formulating the cost otimization issue as a linear rogramming roblem for a Generic Maing Strategy is rovided below. When the hysical network construction is given, the formulation can be formed. - Indices: f =1, 2,, 17, flow v = 1, 2, 3, 4, logical server =1, 2, P f, candidate hysical ath for flow f y=1, 2, Y, hysical node - Constants: fyv : =1, if hysical node y hosts logical server v along hysical ath that is one available hysical ath of flow f; 0, otherwise. fv : number of times that logical server v is involved in flow f. h f : flow demand volume for flow f. v : caacity coefficient in time-caacity roduct unit for logical server v. y : cost coefficient er unit rocessing caacity for hysical node y. - Variables: w f : loads allocated to hysical ath of flow f.

5 - Objective: Minimize total network hysical nodes cost. F (7) - Constraints: Demand Constraints: y y c y w (8) f h f Caacity Constraints: f v v fv fvyw f c Constraints on variables, w 0 (continuous, non - negative) f y (9) c y 0 (continuous, non - negative) (10) (11) According to Equation 8 and 9, the cost otimization issue can be formulated as a linear rogramming roblem. In the otimal solution of this roblem, all constraints resented in Equation 9 are binding, i.e., the hysical node loads are equal to the hysical nodes caacities; however, the caacity of the hysical node may not come in continuous value. To reduce the unused caacity, we can set c y to integer. Then the roblem becomes an integer rogramming roblem which is more difficult to solve Examle An examle to show the formulation of the cost otimization roblem is rovided. The simle network is shown in Figure 4, with 5 hysical nodes connected through a network. Each hysical node is hosting one or more logical server(s), as shown in the bracket after the name of hysical node. The assumtions are made as follows: 1. There are 3 flows involved; they are flow 11, 15, 16, i.e. f 11,15, 16. The corresonding hysical aths are extracted from Figure 4 for each flow. 2. It is easy to see that the number of otential aths that can be used as candidate aths is large. To simlify the examle, we assume only the aths listed in Table 4 are the candidate aths. Figure 4: An Examle of Formulating Cost Otimization Problem, with 3 Flows Involved, for a Generic Maing Strategy Table 4: The Candidate Physical Paths, Reference to Figure 4 The choice of Candidate hysical aths hysical nodes for 3 flows P I S HSS Flow 11 (PISIP) 1 #1 #4 #2 #1(P) #4 (I) #2 (S) #4 (I) #1(P) 2 #1 #4 #3 #1(P) #4(I) #3 (S) #4(I) #1(P) Flow 15 (HSSI) 1 #4 #5 #5 (HSS) #4 (I) Flow 16 (HSSS) 1 #2 #5 #5 (HSS) #2 (S) 2 #3 #5 #5 (HSS) #3 (S) The given information is rovided as follows: a) Flow demand volume, 400, f 11 f 250, f , f 16 b) Caacity coefficient for logical server v, 2, v 1 1, v 2 v 5, v 3 2, v 4 c) Cost coefficient for hysical node y, 5, y 1 10, y 2 y 10, y 3 5, y 4 5, y 5 h (12) (13) (14) The objective function can be written as: Minimize F Subject to: a) Demand Constraints: w 5c1 10c2 10c3 5c4 5c5 (15) w 11,1 11,2 h (16) w 15,1 h (17) w 16,1 w16,2 h (18) b) Caacity Constraints: 2 2 ( w w c 11,1 11,2 ) 1 (19) 5 ( w11,1 ) 5 ( w16,1 ) c2 (20) 5 ( w11,2 ) 5 ( w16,2 ) c3 (21) 2 ( w11 1, w11,2 ) ( w15,1 ) c4 (22) ( w1 5,1 ) 2 ( w16,1 w16,2 ) 5 (23) 2 c c) Constraints on variables: 1, 2, for f 11 0, for 1, for f 15 1, 2, for f 16 w f (24)

6 2.2 Customized Maing Strategy 1 Four logical servers (P/I/S-CSCF, HSS) that we concentrated on lay different roles in IMS system. When using Customized Maing Strategy 1 to ma these logical servers to the hysical nodes, each hysical node only hosts one logical server, and it focuses on erforming one tye of tasks. The tasks on each hysical node are clearly demarcated. This maing strategy is desired when the loads of two or more logical servers exceed the caacity of a hysical node. This is often the case for the network roviders with a large number of users. Overall, there are three advantages by using this maing strategy. First, it is easier to create a backu hysical node and ugrade caacity for the future. Second, this strategy brings a small imact to the system when the failure occurs on the hysical nodes, because each hysical node only takes care of one tye of tasks. Third, it is easy to imlement and maintain the hysical nodes. The main disadvantage of this maing strategy is cost. The remaining caacity of the hysical nodes which host one tye of logical server can not be allocated to other logical servers and therefore will be wasted. Figure 5 deicts this maing strategy, where each hysical node hosts only one logical server. Multile hysical nodes, which host the same tye of logical server, can then erform a load balance. Logical Toology P-CSCF IMS CORE NETWORK I-CSCF SIP Diameter S-CSCF HSS - Indices: f =1, 2,, 17, flow v = 1, 2, 3, 4, logical server y v =1, 2, Y v, hysical node that hosts logical server v - Constants: : =1, if flow f traverses logical server v; =0, otherwise. fv fv : number of times that logical server v is involved in flow f. h : flow demand volume for flow f. f v : caacity coefficient in time-caacity roduct unit for logical server v. vy : cost coefficient er unit rocessing caacity for hysical node y that hosts logical server v. - Variables: w fvy v : loads allocated to hysical node y of flow f for logical server v. - Objective: Minimize total hysical nodes cost for logical server v. F c (25) v - Constraints: Demand Constraints: yv yv vyv vyv w (26) fvy h v f Caacity Constraints: w fv c f v fv fv fvyv vy v (27) Constraints on variables, w 0 (continuous, non - negative) fvy v c vy v 0 (continuous, non - negative) (28) (29) Physical Toology P #1 P #m I #1 Internet Cloud I #mi HSS #1 HSS #mhss Examle An examle is rovided to formulate the cost otimization roblem when using maing strategy 1. The network toology illustrated in Figure 6 is the toology shown in Figure 4 with the relocation of logical servers in 5 hysical nodes. The assumtions and given information remain the same as rovided in Section In this case, only Nodes #2 and #3 need to be otimized for logical server S-CSCF. S #ms S #1 Figure 5: Customized Maing Strategy Formulation of Cost Otimization Problem In this maing strategy, it is easy to see that the hysical nodes that suort one logical server lay loads balance among themselves. Because there is no sharing of residual caacities among different logical servers, the hysical nodes that suort different tyes of logical servers can be otimized searately. This can significantly simlify the otimization rocess because the number of variables to be otimized only deends on the number of hysical nodes hosting the same logical server rather than the number of candidate aths. The otimization roblem described in the last section can be reformulated as follows. Figure 6: An Examle of Formulating the Network Cost Otimization Problem, with 3 Flows Involved, for Customized Maing Strategy 1

7 The objective function can be written as: Minimize F3 10c3,2 10c Subject to: - Demand Constraints: w h 400 3,3 (30) w 11,3,2 11,3,3 11 (31) w 16,3,2 w16,3,3 h (32) - Caacity Constraints: 5 ( w11,3,2 w16,3,3 ) c3,2 (33) 5 ( w11,3,2 w16,3,2 ) c3,3 (34) - Constraints on variables: w, w 0 (35) 11,3,2 0 11,3, 3 w 16,3,2 0, w16,3, 3 0 (36) In this examle, each hysical node hosts only one logical server. It reduces the comlexity of the roblem formulation. Moreover, it carries a small number of variables so that it requires the less comutation time to solve the roblem, comared with the generic maing strategy. 2.3 Customized Maing Strategy 2 While the Customized Maing Strategy 1 discussed in the last section fits large carriers with numerous users, the maing strategy discussed in this section fits small carriers who try to act different logical servers into the same hysical nodes to save footrint and cost. The Customized Maing Strategy 2 is illustrated in Figure 7. In this strategy, hysical nodes are divided into different grous. One logical server can be hosted by the hysical nodes located in one grou only. One grou of hysical nodes can host one or more than one logical servers. Furthermore, we assume that a message that traverses the logical servers that belong to the same grou will be rocessed by one hysical node only in the grou. This constraint can reduce the traveling time within a grou. In the extreme case, if each grou hosts only one logical server, this becomes the customized maing strategy 1. The Customized Maing Strategy 2 allows a hysical node to host two or more logical servers. For many network roviders, the caacity of one hysical node may be more than the loads of one logical server. This maing strategy is more ractical than the revious strategy for this tye of carriers. In general, there are two main advantages of using this maing strategy over the first one. First, maing more than one logical server to a hysical node can utilize the existing hysical node caacity, thus reduce costs. Second, this method can reduce the messages traveling time. The main disadvantage of this maing strategy over the revious one is the comlexity involved. When a hysical node hosts more than one logical server, the hysical node has to handle more tyes of tasks which may interfere with each other. The maintenance cost will clearly be higher Formulation of Cost Otimization Problem In this maing strategy, the grou concet is introduced. A grou of hysical nodes is denoted as g, where g 1,2,3,...,G and G is the total number of grous we have in the network toology. In a grou, the hysical nodes host the same logical servers. Every hysical node y belongs to one grou. Because the residual caacities of the hysical nodes can only be shared among the hysical nodes in the same grou, the otimization can be decomosed into the otimization of each grou of hysical nodes. It can be formulated as the follows. - Indices: f =1, 2,, 17, flow v = 1, 2, 3, 4, logical server g=1,2,3,,g, grou number y g =1, 2, Y g, hysical node located in grou g. - Constants: fg : =1, if flow f traverses grou g. fvg : =1, if flow f traverses logical server v maed to grou g. fv : number of times that logical server v is involved in flow f. h : flow demand volume for flow f. f v : caacity coefficient in time-caacity roduct unit for each logical server v. gy : cost coefficient er unit rocessing caacity for hysical node y in grou g. - Variables: w fgy g : loads of flow f allocated to hysical node y in grou g. - Objective: Minimize total hysical nodes cost for grou g. F c (37) g yv gyg gyg - Constraints: Demand Constraints: w fgy h g f fg (38) yv Figure 7: Customized Maing Strategy 2

8 Caacity Constraints: f v v fv fvg w fgy c g gy g (39) Constraints on variables, w 0 (continuous, non - negative) fgy g c gy g 0 (continuous, non - negative) (40) (41) Examle The network toology illustrated in Figure 8 is rovided to show the formulation of cost otimization roblem using the Maing Strategy 2. This network toology is the toology discussed in Section with a relocation of the logical servers in the 5 hysical nodes. The assumtions and given information remain the same as rovided in Section Clearly only Grous #1 and #2 can be otimized. Figure 8: An Examle of Formulating Network Cost Otimization roblem, with Flows Involved, for Customized Maing Strategy 2 The objective function can be written as: Minimize F1 10 Minimize F Subject to - Demand Constraints: w w h 400 (44) 5c1,1 c1,2 (42) 2 10c2,3 5c2,4 (43) 11,1,1 11,1,2 11 w 11,2,3 w11,2,4 h (45) w 15,2,3 w15,2,4 h (46) w 16,2,3 w16,2,4 h (47) - Caacity Constraints: 2 2w c 11,1,1 1,1 (48) 2 2w11,1,2 c1,2 (49) 11,2,3 5w11,2,3 w15,2,3 5w16,2,3 2,3 (50) 11,2,4 5w11,2,4 w15,2,4 5w16,2,4 2,4 (51) 2w c 2w c - Constraints on variables: w 0, w 0, w w 11,1,1 15,2,3 0, w 0, w 0, 11,1,2 11,2,3 11,2,4 (52) 15,2,4 0, w16,2,3 0, w16,2,4 0 15,2,3 0 15,2, 4 w 16,2,3 0, w16,2, 4 0 (54) w, w 0 (53) 3. CONCLUSION There are three otential maing strategies introduced in this aer. One of them is the Generic Maing Strategy that includes all the ossible maing ways. Network roviders can decide the tye and the number of logical servers hosted in the hysical nodes according to their needs. Therefore, once the hysical network toology is given by the network rovider, cost otimization roblem can be formulated. Since a hysical node can host one or more logical servers, the comlexity of the otimization formulation increases quickly due to the dramatic increase of otential candidate aths. However, when new constraints are introduced into the formulation, the comutation time can be reduced significantly. This has been shown in the two customized maing strategies. The Customized Maing Strategy 1 only allows a hysical node host one logical server. The overall otimization roblem can then be decomosed into the otimization roblem for each logical server. The comlexity only deends on the number of hysical nodes that suort the secific logical server. This maing strategy can be alied to networks owned by large carriers. The Customized Maing Strategy 2 is, on the other hand, designed for small carriers. In this strategy, hysical nodes are divided into grous. Its comlexity then deends on the number of hysical nodes in a grou. While the otimization comlexity is reduced, it also allows multile logical servers maed to the same hysical node. This will also make server utilization more efficient. Last but not the least, the formulations of the maing strategies roosed in this aer are all based on the novel flow concet we roosed in [8]. Without the flow concet, it s not ossible to formulate the roblems in a scalable way. REFERENCES [1] G. Camarillo and M. A. Garcia-Martin, The 3G IP Multimedia Subsystem (IMS): Merging the Internet and the Cellular worlds, Second Edition, Wiley, [2] J. C. Chen and T. Zhang, IP-based Next-Generation Wireless Network, Wiley, [3] G. T. Digital Cellular Telecommunications System (Phase 2+); Universal Mobile Telecommunications System (UMTS); IP Multimedia Subsystem (IMS); Stage 2, version 7.5.0, ETSI TS123228, [4] S. Pandey, V. Jain, D. Das, V. Planat and R. Periannan, Performance Study of IMS Signaling Plane, Proceeding of International Conference on IP Multimedia Subsystem Architecture and Alications,.1-5, December [5] V. Koukoulidis and M. Shah, The IP Multimedia Domain in Wireless Networks: Concets, Architecture, Protocols and Alications, Proceeding of IEEE 6 th International Symosium on Multimedia Software Engineering, , Miami, December [6] M. Handley, H. Schulzrinne, E. Schooler and J. D. Rosenberg, SIP: Session Initiation Protocol, IETF RFC 2543, March [7] J. Rosenberg, H. Schulzrinne, G. Camarillo, A. Johnson, J. Peterson, R. Sar M. Handley and E. Schooler, The session initiation rotocol (SIP), IETF RFC 3261, [8] J. Xiao, C. Huang and J. Yan, A Flow-based Traffic Model for SIP Messages in IMS, IEEE GLOBECOM, Hawaii USA, November [9] A. A Kist, E. A. Kist and R. J. Harris, ''SIP Signaling Delay in 3GPP, Proceeding of the 6 th International Symosium on Communications Interworking of IFIP interworking 2002, , Fremantle, October [10] J. Hwang, N. Kim, S. Kang and J. Koh, A Framework for IMS Interworking Networks with Quality of Service Guarantee, Proceeding of the 7 th International Conference on Networking, , Cancun, Aril 2008.