1. 1 Call Admission Control for Multimedia Services in Mobile Cellular Networks : A Markov Decision Approach Jihyuk Choi; Taekyoung Kwon; Yanghee Choi; Naghshineh, M, Computers and Communications, 2000. Proceedings. ISCC 2000. Fifth IEEE Symposium on 3-6 July 2000 Page(s):594 - 599

2. 2 Outline  Introduction  Model Description  SMDP Approach in Our CAC  Numerical Results  Conclusion

3. 3 Introduction  There is a growing interest in deploying multimedia services in mobile cellular networks (MCN)  Call admission control (CAC) is a key factor in quality of service (QoS) provisioning for these services  Connection-level QoS in MCN is expressed in terms of Call blocking probability Call dropping probability : is handoff dropping probability  The goal of this paper is to find out optimal CAC for maximize the revenue semi-Markov decision process is employed to model the cellular system

4. 4 Model Description  We model a one-dimensional cellular network and describe how to find out optimal admission decisions  Suppose that there are K classes of calls in an MCN (mobile cellular networks)  Call requests of class-i (i = 1,2,..., K) in cell-n (n =1,2,..., N) are assumed to form a Poisson process with mean arrival rate λ n,i

5. 5 Model Description (cont ’ d)  The call holding time (CHT) of a class-i call is assumed to follow an exponential distribution with mean l/μ i The rate of class-i calls that depart from a cell due to service completion is denoted by μ i  The number of channels required to accommodate the call, is denoted by b i  The revenue for each on-going class-i call is accrued at rate r i

6. 6 Model Description (cont ’ d)  The following simple model is a mobile terminal (MT) moves through the whole cellular system  The cell residence time (CRT), i.e., the amount of time that an MT stays in a cell before handoff, with mean l/η η represents the handoff rate

7. 7 Model Description (cont ’ d)  In our 1-D cellular network, the probability that an MT will handoff to one of its adjacent cells is 0.5 The rate that a call in a given cell will handoff to one of its adjacent cells is η /2  The total bandwidth in each cell is the same and denoted by C  The rate of class-i calls that handoff to our system from outside is denoted by h n,i (n = 1 or N)

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9. 9 Model Description (cont ’ d)  The current state of our cellular system is represented by the vector: where x n,i denotes the number of class-i calls in cell-n  The set Λ of all possible states is given by

10. 10 SMDP Approach in Our CAC  The original semi-Markov decision process (SMDP) model considers a dynamic system  It is observed and classified into one of several possible states at random points in time  The SMDP state of the system at a decision epoch is given by the vector s = (x, e)

11. 11 SMDP Approach in Our CAC (cont ’ d)  The variable e represents the event type of an arrival and is given by  When i <= K the a n,i (a n,i {0, 1})denotes the origination of a class-i call within the cell-n  When i >=K+1 it denotes the arrival (event) of a class-i call due to handoff from adjacent cells

12. 12 SMDP Approach in Our CAC (cont ’ d)  The action space B can be expressed by  For example, when N = 2, K = 2 and  The action space is actually a state dependent subset of B denoted by e n,i is a vector of zeros, except for an one in the (n*(k-1)+i)-th position

13. 13 SMDP Approach in Our CAC (cont ’ d)  If the system is in state x Λ and the action a B x is chosen  The expected time (sojourn time),  (x, a), until a new state is entered is given by

14. 14 SMDP Approach in Our CAC (cont ’ d)  The transition probability P xay from the state x to any next state y Λ with action a takes one of the expressions in Table 1

15. 15 SMDP Approach in Our CAC (cont ’ d)  Let r(X, a) be the revenue rate when the cell is in state x and action a has been chosen  If r i is the revenue rate of class-i call, then the total revenue rate for the cell is calculated by

16. 16 SMDP Approach in Our CAC (cont ’ d)  The decision variable z xa, represents the system is in state x and action a is taken

17. 17 Numerical Results  For numerical results, we simulated one- cell model (N = 1) and two-cell model (N = 2)  We compare our SMDP CAC with the upper limit (UL) CAC policy that has a threshold t i for a class-i call originating in a cell  The UL policy with threshold (2,l) blocks a new class-1 call originating in a cell if there are already at least two class-1 calls in the cell

18. 18 Numerical Results (cont ’ d)  We let C = 5, K = 2, b 1 = 1, b 2 = 2, D 1 = 0.02 and D 2 =0.04  Simulations are carried out as the Erlang load ( λ n,i / μ i ) of every class increases

19. 19 Numerical Results (cont ’ d)

20. 20 Numerical Results (cont ’ d)

21. 21 Numerical Results (cont ’ d)

22. 22 Numerical Results (cont ’ d)

23. 23 Numerical Results (cont ’ d)

24. 24 Numerical Results (cont ’ d)