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### Call Admission Control Optimization in WiMAX Networks

Bo Rong, University of Puerto Rico at Mayaguez, USA

Yi Qian, National Institute of Standards and Technology, USA

Kejie Lu, University of Puerto Rico at Mayaguez, USA

Hsiao-Hwa Chen, National Cheng Kung University, Taiwan

Mohsen Guizani, Western Michigan University, USA

TRANSACTIONS ON VEHICULAR TECHNOLOGY 2008

Outline

- Introduction
- Decomposition of WiMAX CAC
- CAC Strategies
- CAC Algorithms
- Results
- Conclusion

Call Admission Control

- To handle a multiservice WiMAX network, it is very important to implement the CAC mechanism
- to prevent the system from being overloaded
- to help a WiMAX network provide different classes of traffic loads with different priorities by manipulating their blocking probabilities
- This paper decomposes the 2-D uplink (UL) and downlink (DL) WiMAX CAC problem into two independent 1-D CAC problems
- With respect to 1-D CAC optimization problems, most previous studies were focused only on two approaches
- the optimal revenue strategy
- the minimum weighted sum of blocking strategy

Main Contributions

- The optimal revenue policy only considers the profit of service providers
- In this paper, we will also
- take into account the requirements from WiMAX subscribers and
- develop a policy with a satisfactory tradeoff between service providers and subscribers
- Main contributions
- the development of a framework of CAC for WiMAX networks
- the investigation on various CAC optimization strategies
- the proposal of a series of constrained greedy revenue algorithms for fast calculation

CAC Deployment in WiMAX Networks

- Only discuss the issues related to the WiMAX PMP network, which consists of one base station and N subscribers
- OFDMA with TDD duplexing
- Propose to add a CAC manager to the WiMAX base station

CAC Module

- For investigation simplicity, we decouple the 2-D CAC problem into two independent 1-D CAC problems
- only the connection requests that passes both admission tests can be eventually accepted

Modeling the CAC problem (1)

- Either UL CAC or DL CAC can be modeled as a 1-D CAC problem as follows
- M classes of traffic loads share B units of access bandwidth resource
- With respect to class i traffic, we assume the following
- the requests arrive from a random process with an average rateλi
- the average connection holding time is 1/μis
- the bandwidth requirement of a connection is fixed tobi
- the revenue rate of a connection is reri
- Define the bandwidth requirement vector as b = (b1, b2, . . . , bM) and the system state vector as n = (n1, n2, . . . , nM)
- where niis the number of class-i connections in the system

Modeling the CAC problem (2)

- We can further define ΩCS as the set of all possible system states
- which can be expressed as ΩCS = {n|n ·b ≤ B}
- the subscript CS stands for "complete sharing"
- which means that an incoming connection will be accepted ifsufficient bandwidth resources are available
- We can now define a CAC policy, which is denoted by Ω, as an arbitrary subset of ΩCS
- Given Ω, a connection request will be accepted if and only if the system state vector remains in Ω after the connection is accepted

Bandwidth Capacity (1)

- Notation
- N - number of subscribers;
- J - number of subcarriers;
- SJ - set of all subcarriers, defined as {1, 2, . . . , j, . . . , J};
- Δf - physical bandwidth of each subcarrier;
- Dk - subcarrier set assigned to subscriber k;
- SNRk[j] - the SNR function of subscriber k on the frequency of subcarrier j
- p[j] - transmit power on subcarrier j
- ck[j] - achievable transmission efficiency (data rate per hertz) of subscriber k on the frequency of subcarrier j, assuming that subcarrier j is allocated to subscriber k(j ∈ Dk)

Bandwidth Capacity (2)

- Hk(f) and Nk(f) denote the channel frequency response function and noise power density function of the kth subscriber, respectively
- To assign subcarrier set Dkto subscriber k, we assume that a nonoverlapped partition is used such that
- According to [18]–[20], ck[j] can be expressed as

where β = 1.5/ − ln(5BER) is a constant, and f(.) depends on the adaptation scheme

[18] X. Qiu and K. Chawla, “On the performance of adaptive modulation in cellular systems,” IEEE Trans. Commun. 1999.

[19] G. Song and Y. G. Li, “Cross-layer optimization for OFDM wireless networks—Part I: Theoretical framework,” IEEE Trans. Wireless Commun., Mar. 2005.

[20] G. Song and Y. G. Li, “Cross-layer optimization for OFDM wireless networks—Part II: Algorithm development,” IEEE Trans. Wireless Commun., Mar. 2005.

Optimal Revenue Strategy

- In general, service providers expect a CAC policy that can produce high revenues
- We use rerito denote the revenue rate of a class-i connection
- Long-term average revenue of a CAC

where

- PΩ(n) is the steady-state probability that the system is in state n
- r = (r1, r2, . . . , rM) is the reward vector, and ri= reribi is the average revenue generated by accepting a class-i connection
- we use Ω∗to denote the optimal revenue policy

Minimum Weighted Sum of Blocking Strategy

- Minimum Weighted Sum of Blocking Strategy

where

- Pbistands for the blocking probability of class-i traffic
- wistands for the weight of class-i traffic
- Lemma 1: For any CAC policy that satisfies the coordinate convex condition, the long-term average revenue can always be calculated by
- where is a constant, , and wi= riρi

Utility Requirement

- The optimal revenue strategy highlights only the demand of service providers
- we also need to consider the requirements of subscribers
- Let B denote the physical access bandwidth and SB denote the statistical bandwidth that the subscriber can achieve after the CAC policy takes effect
- The utility function is defined as SB/B
- the utility of policy Ω is given by
- we use Ω+ to denote the optimal utility CAC policy

Fairness Requirement

- When the optimal revenue or optimal utility strategy is employed, there may exist a great bias among the blocking probabilities of different traffic classes
- To achieve absolute fairness (AF), each traffic class is given the same blocking probability, whereas the utility of the CAC policy is maximized
- The blocking probability of each traffic class is given by
- where
- where is the lower bound of PbAF

Constrained Optimal Revenue Strategy

- Usually, a contradiction exists between the expectations of service providers and subscribers
- This leads to a concept of a utility- and fairness-constrained optimal revenue policy
- The fairness constraint requires that the highest blocking probability is lower than the threshold PBth
- we use ΩF∗to represent the fairness-constrained optimal revenue policy
- The utility constraint requires that the utility of a CAC policy must be higher than the threshold Uth
- we use ΩUF∗to represent the utility and fairness constrained optimal revenue policy

CP-Structured Admission Control Policy (1)

- In order to reduce complexity, we develop a series of CP-structured (complete partition) heuristic algorithms
- A CP policy separates the overall bandwidth resource B into M nonoverlapped parts, denoted by B1CP, B2CP, ..., BMCP, where BiCP belongs to class-i traffic
- The ith subpolicy can be modeled by an M/M/N/N queuing system
- in which the number of servers is si= BiCP/bi
- The long-term average revenue obtained from class-i traffic is given by

CP-Structured Admission Control Policy (2)

- The statistical bandwidth of class-i traffic is given by
- According to the Erlang B formula, the blocking probability of class-i traffic is [26]
- It is noted that the Erlang B formula can be calculated by the following recursion [26]

[26] D. Jagerman, “Some properties of the Erlang loss function,” Bell Syst. Tech. J., 53, no. 3, pp. 525–551, Mar. 1974

Fairness-Constrained Greedy Revenue Algorithm for CPF∗ (1)

- Supposing that class-i traffic is assigned j (j = BiCP/bi) servers, from Lemma 1, we can derive the corresponding revenue as
- If the server number is reduced to (j − 1), then
- The revenue brought by the jth server as
- The revenue rate of the jth server is

Traffic Load Configuration for 1-D CAC Optimization

- Total bandwidth capacity B:75 Mb/s
- The revenue rate is priced as
- rerUGS = 5, rerrtPS = 2, rernrtPS = 1 and rerBE = 0.5
- uth = 90%, pbth = 65%
- The revenue and utility are normalized by R(Ω∗) and U(Ω+)

CAC Optimization Policies-varying the arrival rate of class-3 traffic

Traffic Load Configuration for 2-D CAC Optimization

- UL CAC and DL CAC employ the same policy with the same uth and pbth setting
- UL/DL bandwidth capacity in a subscriber's local network is 60/75 Mb/s
- DL traffic load is configured in Table II, except that the arrival rate of class-3 traffic is fixed to be 64 calls/h

Simulation Environment for WiMAX PMP Network Scenario (1)

- We investigate the performance of ΩUF∗ and its approximation-algorithm-based 2-D CAC in a WiMAX PMP network
- OFDMA–TDD mode of 32 subscribers with PUSC on the UL and FUSC on the DL
- amount of available subcarriers: 1024
- each subcarrier occupy 10 kHz of physical bandwidth
- the distances between the subscribers and the base station are randomly chosen from 2 to 10 km
- the acceptable BER is set to be 10−6
- TDD DL proportion factor α% as 60%
- the UL and DL channels are assumed to have a bad-urban delay profile
- suffer from shadowing with 8-dB standard deviation

Simulation Environment for WiMAX PMP Network Scenario (2)

- For the traffic pattern
- UL and DL traffic loads are uniformly distributed in [40 Mb/s, 100 Mb/s] and [60 Mb/s, 140 Mb/s]
- the proportions of UGS, rtPS, nrtPS, and BE traffic, which are denoted by PPUGS, PPrtPS, PPnrtPS, and PPBE, are set to be random variables

Conclusion

- Propose a framework for WiMAX CAC, in which the 2-D CAC problem is decomposed into two independent 1-D CAC problems
- Make the 1-D CAC an optimization problem and evaluate its different strategies
- From the perspective of service providers, optimal revenue is the major concern
- From the perspective of subscribers, optimal utility and fairness are the requirements
- Develop a utility- and fairnessconstrained optimal revenue policy, as well as its approximation algorithm

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