Utility-Based Resource Allocation for Mixed Traffic in Wireless Networks

Transcription

1 IEEE IFOCO 2 International Workshop on Future edia etworks and IP-based TV Utility-Based Resource Allocation for ixed Traffic in Wireless etworks Li Chen, Bin Wang, Xiaohang Chen, Xin Zhang, and Dacheng ang Wireless Theories and Technologies (WT&T) Beijing University of Posts and Telecounications (BUPT) Beijing, 876, China (Eail: alibupt@gail.co) Abstract In order to solve the proble that the existing resource allocation strategies cannot give integrative consideration to QoS, spectru efficiency for ixed traffic, this paper proposes a utility-based resource allocation algorith for ixed traffic in wireless networks. The unified utility function for users with different traffics is studied first. After that, the optiization odel for the resource allocation is established based on the unified utility function. A heuristic algorith based on the solution of the odel is proposed in the ixed traffic scenario after analyzing the optiization odel. The algorith which has lower coplexity than the existing work can autoatically guarantee the QoS requireent for the real-tie traffic and ake a tradeoff between throughput and fairness for users with best effort traffic due to the unified utility function. ueric siulation results indicate that the algorith is very applicable for ixed traffic, and the resource requireents for QoS users can be satisfied preferentially in the ixed traffic scenario. I. ITRODUCTIO Since radio resource is liited and scarce in wireless networks, resource allocation between users is a crucial issue. The channel quality of each user ay vary over tie. With the given available resource, there are different criteria or strategies to assign resource to each user, which leads to different benefits, such as syste throughput, user fairness, or the Quality of Service (QoS) of user data flow. When the utility theory in econoics is applied to the resource allocation or the cross-layer design between Physical layer and AC layer, the coplexity of resource allocation algorith can be reduced. oreover, the tradeoff between throughput and fairness can be ade through the crosslayer optiization based on the utility. In this paper, the perforance etric for the resource allocation strategy is the user satisfaction, which is described by the utility function of users. The ore the resource is allocated to the user, the higher the utility function is, so that the user can be better satisfied. As wireless networks evolve, the traffic evolves toward ixed one. Different perforance requireents for various traffics can be et through different utility functions. Various types of traffic in practical systes can be classified into two categories. One is the best effort (BE) traffic that has no QoS requireent, like soe data traffics without delay requireent. The fairness aong users should be guaranteed to the best. The work in this paper is sponsored by China s ajor Projects on Science and Technology for ew-generation Broadband Wireless obile Counications etwork (2ZX3-). The other is the traffic with QoS requireent, which needs certain resource to satisfy this requireent, like interactive edia, streaing, or IP-based TV. The research on resource allocation in wireless networks has obtained a few achieveents, including any strategies based on utility function. Distributed resource allocation was studied in [] under target data rate in ulti-cell networks. [2] analyzed the resource allocation for QoS-aware OFDA. [3, 4] adopted a cross-layer design based on utility function to allocate the resource in OFD. The utility-based resource allocation in the syste with two traffics is studied in [5, 6]. In [7], the utility was assued as the sigoid utility function, and the utility-based resource allocation for soft QoS traffic was studied. The sigoid utility function was discussed for realtie systes in [8]. [9] is one of the first papers introducing a unified utility function (for BE only) into scheduling. Resource anageent based on unified utility function was studied in [, ]. We can see that either the axiu throughput or the iniu power consuption can be used as the objective to explore the resource allocation. We can also establish the odel by axiizing the aggregate utility. In this paper, we study the resource allocation for the ixed traffic scenario. The previous related literatures studied the utility-based resource allocation in certain traffic, or discussed the resource allocation for ultiple traffics separately. The solutions in [6] can be recognized as different resource allocation probles with different utility functions, and resource allocation based on unified utility function for single traffic in [, ]. [2] studied the dynaic resource allocation for applications with real-tie resource requireents according to their utility functions. But hardly any research or siulation of the resource allocation strategy based on unified utility function in the ixed traffic scenario is done. Thus, we focus on studying a unified utility function when the ixed traffic exists in the syste. After that, the resource allocation for ixed traffic is studied based on this utility function, which can satisfy both the requireents of BE traffic and QoS traffic. The rest of this paper is organized as follows: Section II proposes a unified utility function for various traffics. The optial resource allocation odel based on unified utility function and the corresponding solution is analyzed in Section III, and the practical allocation algorith is also studied in this section. Section IV presents the siulation results for the algorith. Finally, conclusions are suarized in section V //$26. 2 IEEE 9

2 II. UTILIT FUCTIO In this section, we ainly discuss the utility function in the ixed traffic scenario. Since the perforance etrics for users with different traffics are different, we study the unified utility function which is fit for the ixed traffic. Types of users are distinguished by the paraeters of the unified utility function. The detailed ethod to explore the utility function is as follows. First, the characteristics for the unified utility function are extracted fro the practical situations and the characteristics of different user traffics. After that, appropriate utility function is constructed based on these characteristics. For the users with BE traffic, the utility function should be onotonically increasing since the syste pursues the axiu aggregate utility. oreover, for the sake of fairness of users, the slope of the utility function, the arginal utility function, should be onotonically decreasing, which prevents assigning too uch resource to the users with good channel condition. In suary, the utility function for BE users should be a convex function with respect to the allocated resource. For the users with QoS traffic, siilarly, the utility function should be a onotonically increasing function. Since the QoS requireent needs to be satisfied, when the resource obtained by the user is less than the critical value for the QoS requireent, the priority of the request for the resource of this user is high, and the arginal utility function is onotonically increasing. When the resource obtained by the user is ore than the critical value for the QoS requireent, the priority of the request for the resource of this user is low, which prevents assigning too uch resource to soe certain users, and the arginal utility function is onotonically decreasing. In suary, the utility function for QoS users should be a sigoid function with respect to the allocated resource. In the following, we study the specific for of the utility function. Assuing the fors of utility functions for all users are unified, denoted by U(r), where r is the resource assigned to the user. The total resource in the syste is R, so the doain of U(r) is [,R]. In order to give integrative consideration to the resource assignent for users with different traffics so that the utility values of users are coparable, we assue the range of the utility function is [, ]. The arginal utility can be expressed as u(r) =U (r). Fro the analysis above, the utility of BE and QoS users are convex and sigoid functions, respectively. In order to unify the utility functions of users with different traffics, without loss of the generality, we assue the for of the unified utility function is a universal sigoid function, which has different characteristics with different paraeters. It can represent the utility functions for both the BE and QoS users. The sigoid function can be expressed as: U(r) = + D () A + Be C(r d) where A, B, C, D, and d are the paraeters to be deterined. Paraeter C affects the slope of the curve. Paraeters A, B and D ainly affect the range of the utility function. Through adjusting A, B and D, the utility values of different traffics are coparable, which is helpful to the ipleentation of the resource allocation in the ixed traffic scenario. d is the inflexion of the utility function, which denotes the resource requireent of users. When the resource allocated to users is saller than d, the utility function is concave, which represents that the user requires the resource of d strongly. While the resource allocated to users is larger than d, the utility function is convex, which represents that the user requires the resource of d not so strongly. The values and the eanings of these paraeters are discussed in the following. For the users with QoS traffic, the resource requireent is r, then we can get the characteristics of the utility function <r<r,u(r) >,u (r) > r r<r,u(r) >,u (2) (r) U(),U(R) (3) where u (r) is the first derivative of u(r). According to the conditions (2)(3), we get the utility function for QoS users U (r) = (4) +e C(r r) where the paraeter is used to adjust the slope of the utility curve around r. It reflects the deand degree of the user for the resource requireent r. The larger is, the higher the slope of the utility curve around r is, so that the user deands the resource r ore strongly, or on the contrary, the deand is weaker. The effect of on the utility curve is reflected by the solid curves in Fig., where r =. Today s wireless networks contain heterogeneous traffic like voice, video, FTP etc. which require different levels of QoS treatent. They can be represented by different values of and r. For the users with BE traffic, the requireent satisfies r =. The utility function has the following characteristics <r<r,u(r) >,u (r) < (5) U() (6) In a siilar way, we can get the utility function for BE users U 2 (r) = + D (7) +Be C2r To ake sure the utility of BE users is lower than that of QoS users when r > r, we assue B =.5. Fro(6), D =.4. In (7), the paraeter C 2 can be used to adjust the slope of the utility curve. It reflects the tradeoff between the spectru efficiency and the user fairness. The larger C 2 is, the faster the curve rises, which indicates that the utility function tends to better fairness. The saller C 2 is, the slower the curve rises, which indicates that the utility function tends to higher throughput. The effect of C 2 on the utility curve is reflected by the dotted curves in Fig.. We call the paraeters and C 2 as utility paraeters. In order to reflect the deand of QoS users on r, should have a relative large value. For achieving the tradeoff between throughput and fairness for BE users, C 2 should be selected by the practical situation. Thus, in the following siulation, we will select the ost appropriate values of and C 2 after studying how they affect the algorith perforance. Fro Fig. 92

3 Utility Value Fig Relationship between utility function and paraeter C =. C =.2 C =.4 C =.8 C = 3.2 C = 2.8 C2 =. C2 =.2 C2 =.4 C2 = Resource The effect of the utility paraeters on unified utility function, we can see that if the rest resource is ore than r, higher utility can be obtained by assigning the resource to the QoS user, and if the rest resource is less than r, higher utility can be obtained by assigning the resource to the BE user. III. UIFIED-UTILIT-BASED RESOURCE ALLOCATIO In this section, we study the resource allocation based on the unified utility function. We first establish the optiization odel, and then analyze the solution of this odel. Finally, the resource allocation algorith is proposed. A. Syste odel and Assuptions The syste being studied consists of one cell and users, including QoS users and 2 BE users. The total resource in the syste is R. r indicates the resource assigned to the user. q eans the channel quality, q. The saller q is, the worse the channel quality is. Thus, the effective resource for the user can be expressed as r q. The utility of the user is U ( ) =U(r q ).In practice, the resource could be tie-slot, frequency, or other radio resource for data transission, which is assigned by the controller located at the base station (BS). The channel quality can be indicated by SIR. The optiization objective of the resource allocation odel is to axiize the aggregate utility of users in the entire network. The resource assigned to the users can be dynaically adjusted to iprove the network perforance, with the total radio resource constraint. Thus, the optiization odel for the resource allocation can be expressed as ax O = s.t. U(r q )= = U (r q )+ 2 2 = U 2(r 2 q 2 ) r R, r,, 2,..., (8) For the QoS users, if the resource is enough, the following constraint should be satisfied, naely the effective resource of the user is no less than the resource requireent: r q r, =, 2,..., (9) B. Solution of the Unified-Utility-Based Resource Allocation The odel in (8) is a constrained non-convex optiization proble. We use Lagrangian ethod to analyze the optial solution first. We construct the Lagrangian function as [ ] O 2 = U(r q ) λ r R. () With the Karush-Kuhn-Tucker (KKT) conditions, we have O 2 r = O 2 λ = U(r q ) r λ = () r R = (2) for =, 2,..., where λ is the assistant constant for the Lagrangian solution and can be obtained fro () and (2). Fro (), for =, 2,..., we have [ ] U(r q ) = u (r )=λ (3) r where the arginal utility function, can be expressed as u (r )= du(r q ) = q U (r ) (4) dr where U (r ) is the first derivative of the utility function. The paraeter λ in (3) should be the sae for all in optial solution. Thus, we can get a necessary condition for the optial resource allocation: Condition I : i, j =, 2,..., u i (r i )=u j (r j ). (5) For users with QoS traffic, to achieve the sae arginal utility, the difference in the effective resource allocated to different users is sall if the exponential coefficient is large. Siilarly, the difference in the effective resource allocated to BE users is big since the exponential coefficient C 2 is sall. This conclusion can be verified by the siulation. ext, we propose the sufficient condition for the optial resource allocation proble through the following theore. Theore: The sufficient conditions for the optial resource allocation R = r,, 2,..., are that every user whose resource r > has an identical arginal utility and the derivative of the arginal utility u (r ) < for all. Proof : Consider any other solution for the resource allocation R = r,, 2,..., where users i and j are allocated an aount of r i r and r j + r, respectively. r is a very sall real nuber. The resource allocated to other users in R are the sae to that in R. Thus, the difference in the total utilities of R and R can be expressed as U(R ) U(R ) =[U(r i)+u(r j)] [U(r i r)+u(r j + r)] =[U(r i) U(r i r)] [U(r j + r) U(r j)] (6) = ri r i r u i(r)dr rj + r r j u j(r)dr. 93

4 If u (r ) < for all, u (r) is decreasing. Thus, (6) iplies U(R ) U(R ) u i(r i) r u j(r j) r. (7) When all users have an identical arginal utility, u i (r i )= u j (r j ), we get U(R ) U(R ) (8) which iplies that R is the optial solution. Hence, every user has an identical arginal utility u (r ) and u (r ) < for all are the sufficient conditions of the optial resource allocation R. The above analysis is based on the assuption that the aount of resource is enough for users. If the available resource is liited, the users especially QoS users would be selected to be served. In the scenario with QoS users only, since the user utility is close to zero when the effective resource is saller than r, soe users cannot be assigned resource in the solution, while other users whose resource r > have an identical arginal utility. However, the derivative of the arginal utility u (r ) for the users with the worst channel condition ay be larger than, which eans their effective resource is saller than r. In the scenario with ixed traffic, if the effective resource for a QoS user is saller than r, the resource would be allocated to BE users for higher aggregate utility since the utility of BE users is higher than that of QoS users when the resource is lower than r. C. Resource Allocation Algorith The previous optiization odel is a non-convex optiization proble. It is hard to get the precise theoretical solution of the odel through analytical ethod. We propose a heuristic algorith based on the theore and analysis in subsection B to solve the resource allocation. First of all, we consider the situation with QoS users only. To ake the algorith converge fast, the axiu nuber of QoS users supported by the liited resource is estiated at the beginning of the algorith, and the resource is initialized aong these users. In the theoretical solution, all users have an identical arginal utility. Thus, the resource of the users who have saller arginal utility and u (r ) < should be allocated to the users who have greater arginal utility or u (r ) >, which eans that the resource of the users with higher effective resource should be allocated to the users with lower effective resource. The algorith is described in the following. Algorith I Resource allocation algorith for QoS users ) Prophase preparation: The BS estiates the axiu nuber of QoS users supported by the syste according to the channel quality of each user { and the aount of i } available resource. =argax r q R i 2) Initialization: Initialize the resource for QoS users, r = R/. Due to the different channel quality of users, the effective resource obtained by each user r q is not equal. 3) Resource allocation: Adjust the initial resource of each user. If the effective resource of the user is ore than the Fig. 2. Prepare: estiate Initialize: r = R / U r q ( ) Sort the effective resource rq in descending order i=, u= -i O i i, u i, 5 r r r r u O U r q i i, j j /, ( ) O i< O O 3/4 is changed? End Flow chart of the resource allocation algorith for QoS users requireent r, the arginal utility function decreases rapidly. Thus, the criterion of the adjustent is to assign the resource of users with ore effective resource to the users with less effective resource. The specific process is: Adjust the resource with the step length β. Ifthe aggregate utility of all users after adjusting can iprove, then execute the adjusting and go on. Otherwise, reduce the step length β to the next attept. 4) Iteration: Assign the resource fro the user with the ost effective resource to the one with the least effective resource, and then go on the next iteration. 5) End: If the aggregate utility cannot be iproved in one iteration, end the iteration. The flow chart of this algorith is shown in Fig. 2. This algorith is fit for the heterogeneous network with different levels of QoS. The ones with strong deand for QoS would be serviced preferentially according to our algorith. ext, we consider the syste with BE users only. The process of the algorith is as follows. It is siilar to that of Algorith I. The flow chart is siilar to Fig. 2. Algorith II Resource allocation algorith for BE users ) Initialization: Initialize the resource allocation for 2 BE users, r = R/ 2. 2) Resource allocation: Adjust the initial resource of each BE user. The process is siilar to that of QoS users. If the syste has the ixed traffic, the iteration algorith is the integration of the previous two algoriths. We first initialize the allocation by assigning the resource to QoS users according to Algorith I, and then adjust the resource of QoS users and allocate to BE users, which should lead to the iproveent of the aggregate utility. The process and the flow chart are siilar to the previous ones. The difference is just that the aggregate utility in the process here is the su of the utility of two kinds of users. Fro the algorith flow in Fig. 2, we can see that every loop in all users has r r 94

5 Effective Resource =. =.2 =.4 =.8 =3.2 = Channel Quality Fig. 3. Resource allocation for QoS users under different values of polynoial coplexity. Thus, the algorith has coplexity of several polynoial ties. The optial solution for QoS users can be obtained at the convex part of the sigoid function since the axiu nuber of QoS users supported by the syste is estiated first. The utility function of BE users is convex, so the optial solution is obtained at the convex part. In suary, the optial solution for single traffic or ixed traffic is obtained at the convex part, and the convex optiization proble with constraint has a unique optial solution. Hence, the solution fro the heuristic algorith here is close to the optial one. IV. UERICAL SIULATIO AD AALSIS In this section, we evaluate the perforance of the resource allocation based on unified utility function through nuerical siulation. We assue all users adopt the utility function proposed above. The channel quality of each user is noralized and generated randoly fro the range of [, ] [5]. We first evaluate the perforance of the resource allocation algorith when the syste contains only QoS users, and vary the slope of utility function by tuning the paraeter so as to observe how the QoS requireent degree affects the results. We assue the total resource R is 8, the user nuber is 6, the requireent r is. Siulation results are plotted in Fig. 3, where the effective resource for QoS users with different channel qualities is shown under different values of. Fro the results, we observe that different values of result in different perforances. The larger is, the faster the arginal utility saturate with the increase of the allocated resource. The syste tends to assigning ore resource to the users with worse channel quality, and the effective resource of each user is uch closer to its requireent, so that better user fairness can be obtained. The saller is, the ore slowly the arginal utility saturate with the increase of the allocated resource. Thus, is set to 2.8 in the following siulation. To achieve the axiu aggregate utility, the syste allocates ore effective resource to the users with better channel quality. When the syste contains BE users only, we vary C 2 to observe the effects on the perforance of the user fairness. We assue the total resource R is 8, the user nuber is 5. The fairness indexes of users, indicated by F, under different values of C 2 are shown in Table I. The fairness index F based on the effective resource is extended fro the fairness index TABLE I FAIRESS IDEX FOR DIFFERET UTILIT PARAETER Utility Paraeter C Fairness Index F based on the throughput in [3]. It can be defined as ( 2 ) 2 2 F = r q / 2 (r q ) 2 (9) The conclusion we can draw fro Table I is the sae as that in the analysis. Larger value of C 2 leads to better user fairness, which eans that BS allocates ore resource to the users with worse channel quality, but at the cost of the syste throughput decrease. Thus, C 2 should be selected to balance the tradeoff between the syste throughput and user fairness according to the actual situation. In the following, C 2 =.2, which can give higher priority to QoS users with =2.8. ext, we evaluate the perforance of the proposed algorith when the syste contains both QoS users and BE users. We vary the proportion of these two categories of users to observe how the algorith perforance varies in the ixed traffic scenario. Total resource R is set to 8, the requireent of QoS users r is. We assue there are 2 users in the syste. The perforance coparison of the resource allocation based on unified utility function under different user proportions is shown in Fig. 4. The last several users (higher user nuber) are BE users in every proportion case. The saller user nuber reflects the worse channel quality. Fro the results, we can see that if the total resource is sufficient, the resource requireent of QoS users can be always satisfied. When both QoS users and BE users exist in the syste, in order to guarantee the aggregate utility of syste, the effective resource allocated to QoS users is a little higher than the requireent r. The reason is that the utility is ost to the syste s profit when the effective resource of QoS users is a little higher than r fro Fig., naely the least resource achieves the ost utility increase. The rest resource is allocated aong BE users. Since the resource is liited, if the QoS users exceed the axiu nuber that the syste can support (e.g. 8QoS : 2BE), the first QoS user with the worst channel quality cannot be serviced. Then two BE users utilize the rest resource to obtain higher aggregate utility. In the following, we evaluate the perforance of the resource allocation strategy by setting different total resource in the ixed traffic scenario. We assue the user proportion is 6QoS : 4BE. The siulation results for the resource allocation under different total resource are shown in Fig. 5. Fro the results, we can see that when there is not so uch resource (R = 6), syste would satisfy the requireent of QoS users with better channel quality preferentially. The rest resource that is not enough for QoS users to reach effective resource of r is allocated to BE users. With the increasing of the total resource, QoS users with worse channel quality are satisfied in turn. When the total resource rises fro 6 to 8, the effective resource for BE users decreases instead. The 95

6 Fig. 5. Effective Resource Fig Effective Resource 5QoS : 5BE 6QoS : 4BE 7QoS : 3BE 8QoS : 2BE :2 User nuber 7:3 6: :5 User proportion Resource allocation under different user proportions 3 2 Total resource is 6 Total resource is 7 Total resource is 8 Total resource is User nuber Total resource Resource allocation in ixed traffic under different total resource Siulation tie (s) Fig User nuber Siulation tie under different user nuber reason is that the increased resource is used for the resource requireent of QoS users, so that the aggregate utility achieves axiu. After all QoS users have enough effective resource (R = 8 or 9), the total resource continues to increase, the effective resource for BE users would upturn. The proposed resource allocation strategy can guarantee the requireent of QoS users preferentially in the ixed traffic scenario (Fig. 5) and the fairness of BE users (Table I). These advantages coe fro the algorith based on the unified utility function. The arginal utility for QoS users is largest at r. When the resource is a little larger than r, the utility of QoS users is twice ore than that of BE users, so that the resource allocation based on this unified utility function can satisfy the resource requireent of QoS users preferentially. oreover, the utility function for BE users is convex, which prevents assigning too uch resource to the users with good channel condition, so that the user fairness can be guaranteed. Finally, we evaluate the coputation coplexity of the proposed algorith by observing the siulation tie under different users. R is set to 8, the user proportion is assued to be 6QoS : 4BE. The siulation tie under different user nubers is shown in Fig. 6. We can see that the siulation tie is nearly linear proportional with the user nuber, which verifies that the coplexity of this algorith is polynoial. V. COCLUSIO The resource allocation in wireless networks is the hotspot of the recent research. We analyze the resource allocation in the ixed traffic scenario under the existing research. We first study the unified utility function for ixed traffic, and then establish the optiization odel for resource allocation based on the unified utility function. The odel is analyzed theoretically. The heuristic algorith ipleentations for the resource allocation strategy under different traffic deployents are proposed subsequently. Finally, the nueric siulation is perfored to evaluate the perforance of the algorith. The results iply that the proposed resource allocation strategy is fit for the heterogeneous networks with different levels of QoS requireent. The results can autoatically satisfy the resource requireent of QoS users preferentially, and the fairness of BE users can be guaranteed autoatically to a certain degree. REFERECES []. Pischella and J.-C. Belfiore, Distributed resource allocation for rateconstrained users in ulti-cell OFDA networks, IEEE Counications Letters, vol. 2, no. 4, pp. 49-5, ay 23. [2]. Pischella and J.-C. Belfiore, Resource allocation for QoS-aware OFDA using distributed network coordination, IEEE Trans. on Vehicular Technology, vol. 58, no. 4, pp , ay 29. [3] G. Song and. Li, Cross-layer optiization for OFD wireless networks-part I: theoretical fraework, IEEE Transactions on Wireless Counications, vol. 4, no. 2, pp , arch 25. [4] G. Song and. Li, Utility-based resource allocation and scheduling in OFD-based wireless broadband networks IEEE Coun. ag., vol. 43, no. 2, pp , Dec. 25. [5] W.-H. Kuo and W. Liao, Utility-Based Resource Allocation in Wireless etworks, IEEE Transactions on Wireless Counications, vol. 6, no., pp , Oct. 27. [6] W.-H. Kuo and W. Liao, Utility-based optial resource allocation in wireless networks, in Proc. IEEE Globeco 25. St. Louis, issouri, pp , Dec. 25. [7] W.-H. Kuo and W. Liao, Utility-based Radio Resource Allocation for QoS Traffic in Wireless etworks, IEEE Trans. on Wireless Coun., vol. 7, no. 7, pp , July 28. [8] A. Sang, X. Wang, and. adihian, Real-Tie QoS in Enhanced 3G Cellular Packet Systes of A Shared Downlink Channel, IEEE Trans. on Wireless Coun., vol. 6, no. 5, pp , ay 27. [9] A. Sang, X. Wang,. adihian, et.al., Downlink Scheduling Schees in Cellular Packet Data Systes of ultiple-input ultiple-output Antennas, in Proc. IEEE GLOBECO 24, Dallas, USA, ov. 24. [] L. Badia, S. erlin, and. Zorzi, Resource anageent in IEEE 82. ultiple Access etworks with Price-based Service Provisioning, IEEE Trans. on Wireless Coun., vol. 7, no., pp , 28. [] S. Pal,. Chatterjee, and SK Das, A Two-level Resource anageent Schee in Wireless etworks Based on User-Satisfaction, AC SIGOBILE C2R, vol. 9, no. 5, pp. 4-4, 25. [2] J. ie, X. Chen, and W. Wang, A Two-level Resource anageent Schee in Wireless etworks Based on User-Satisfaction, in SWCTC 29, Hubei, China, April 29. [3] A. Sang, X. Wang,. adihian, and R.D.Gitlin, A flexible downlink scheduling schee in cellular packet data systes, IEEE Trans. on Wireless Coun., vol. 5, no. 3, pp , arch