omplexity Aalysis of Optimal Statioary all Admissio Policy ad Fixed Set Partitioig Policy for OVSF-DMA ellular Systems Daiel Lee Muhammad Naeem higyu Hsu
Backgroud Presetatio Outlie System Model all Admissio otrol Schemes omplexity Of Proposed Schemes Numerical Results Summary
Backgroud I Widebad DMA orthogoal variable spreadig factor (OVSF) are codes for providig differet chaels for differet users with differet data rates
[ ] [ ] [ ] [ ] [ ] [ ] 4 [ ] 4 [ ] [ ] 3 4 [ ] 4 4 [ ] [ ] k k k k k k Well kow OVSF code geeratio Nodes with the depth l from the root of the tree have code words of code legth l.
Example 4R R R
M Resource costrait: j 0 j k j k k0 Example of capacity regio max3
System Model Radom arrivals of call requests i each class ca be modeled by a stochastic process (Poisso process). For class j Average arrival rate is λ j Average call duratio μ j. I respose to each arrival of call request the etwork operator must make a call admissio cotrol (A) decisio (whether to accept or reject the call request) ad the decisio should be made based o the resource costrait. The objective ca be to maximize average throughput or miimize blockig probability etc.
System Model We allow code re-assigmet
Mai poit The greedy all Admissio Policy is ot ecessarily optimal.
Optimal policy The system ca be modeled by a Markov decisio process so a optimal policy ca be obtaied by optimizig a Markov Decisio Process. Liear Programmig Policy iteratio etc. { M ( ) } i k0 k k M k i 0 i ki Z
Previous Results: optimal policy A optimal policy ca have sigificatly better performace tha the greedy policy Accordig to small-scale cases Large-scale: large large umber of classes etc. omputatioal complexity of liear programmig (e.g. umber of variables) { M ( ) } i k0 k k M k i 0 i ki Z
Previous results: suboptimal policy Eve a fixed set policy ca have sigificatly better performace tha the greedy policy.
Optimal Fixed Set Partitioig OVSF codes are partitioed ito mutually exclusive groups of codes ad uiquely assigs a group to each service class. G j the umber of codes i the subset assiged with class j where j 0 M. Oce vector G (G 0 G. G M- ) is determied the actual partitio of the set is trivial. The umbers of codes i the subsets G 0 G G M- satisfy M j j 0 Average Through put of this scheme M ( ) ( k )( ) T G R P λ µ G F k 0 k k k j where P k ( λ k µ k) Gk 0( λ k µ k)!!
Optimal Fixed Set Partitioig Greedy withi fixed sets
omplexity Aalysis M j 0 ( G G G ) Size of the feasible set: the umber of vectors that satisfy costrait j G j 0 M
ombiatorial Aalysis ad Recursio G M ca have ay value from 0 / M. if G M is x M. The G M ca be 0 3 (/ M- -x M ) ad so o. The relatio betwee adjacet classes has a recursio Γm ( v) ( ) Let be the umber of o-egative itegral vectors G G G that ca occupy the space take by v codes 0 M of largest codes i.e. satisfyig costrait G v. The ( ) v x 0 ( ) ( v) v ( ) v ( ) Γ v Γ v x Γ i m m i 0 m Γ 0 03... m i m i 0 i
( v) ( v) ( v) Fuctios Γ Γ... Γ ca be evaluated from the recursio. 0 M ( G G G ) The umber of vectors that satisfy costrait 0 M ( ) M j M G j 0 j ΓM is.
Numerical Results
Numerical Results
Optimizatio of Markove Decisio process through LP I the case of LP its complexity is closely related to the size of state space { M ( ) } i k0 k k M k i 0 i ki Z
Let χ m (v) be the umber of o-egative iteger vectors (k 0 k k m ) that satisfy the costrait m i m k 0 i v The umber of vectors (k 0 k k m- ) that satisfy this costrait is χ m- ((v-x m )). Therefore we have the followig recursio: i ( ) ( ) m i m m k i 0 i v xm vx m χ m v ( v) ( i) i χ 0 m
χ m (v) ad Γ m (v) have a idetical recursio The size of the state space {( ) M } i k0 k k M k i 0 i ki Z M ( M) ( M ) M χ Γ
Numerical Results
Fixed Set Partitioig (FSP) omplexity The complexity of FSP operatio is characterized as O() lookups DA-A The complexity of DA-A is also O() I summary i both FSP ad DA the computatioal complexity of olie operatios is O() per call arrival.
Thak You.