Analysis and Optimization of Caching for Content Delivery in - - PowerPoint PPT Presentation
1896 1920 1987 2006 Analysis and Optimization of Caching for Content Delivery in Wireless Networks Ying Cui Department of Electronic Engineering Shanghai Jiao Tong University, China 1 Outline Introduction Caching at BSs joint
1896 1920 1987 2006
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– reduce delay, backhaul burden and load of wireless links – caching at BSs and caching at end users
– reduce traffic load of wireless links – based on cache content at BSs and end users
– increase transmission rate over wireless links – based on cache content at BSs
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enabled wireless networks," IEEE Trans. Wireless Commun., vol. 15, no. 7, pp. 5101-5112, 2016. (IEEE GLOBECOM, 2015)
heterogeneous wireless networks," IEEE Trans. Wireless Commun., vol. 16, no. 1, pp. 250-264, 2017. (IEEE GLOBECOM, 2016)
heterogeneous wireless networks," IEEE GLOBECOM 2016.
Multi-Tier Wireless Multicasting Networks,” major revision, IEEE Trans. Commun., 2017. (IEEE GLOBECOM, 2017)
heterogeneous wireless networks,” major revision, IEEE Trans. Commun., 2017. (IEEE ICC, 2017)
minor revision, IEEE Trans. Wireless Commun., 2017. (IEEE ICC, 2017)
multicasting networks with asynchronous content requests," submitted to IEEE Trans. Wireless Commun.,
good performance in finite file size regime," submitted to IEEE Trans. Information Theory, 2016. (IEEE GLOBECOM, 2016)
coded delivery," submitted to IEEE Trans. Information Theory, 2017.
wireless networks," submitted to IEEE Trans. Commun., 2017. (IEEE GLOBECOM, 2017)
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Caching at BSs Caching at users
– Giuseppe Caire, Technical University of Berlin, Germany – Vincent Lau, Hong Kong University of Science and Technology, Hong Kong – Stephen Hanly and Philip Whiting, Macquarie University, Australia – Hui Liu, Shanghai Jiao Tong University, China – Shi Jin and Fuchun Zheng, Southeast University, China
– Dongdong Jiang, Yaping Sun, Jifang Xing, Sian Jin, Zitian Wang, Zhehan Cao and Fan Lai, Shanghai Jiao Tong University, China – Wanli Wen, Southeast University, China
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in large-scale cache-enabled wireless networks,” IEEE Trans. Wireless Commun., vol. 15, no. 7,
wireless multicasting networks with asynchronous content requests," submitted to IEEE Trans. Wireless Commun., 2017.
large-scale multi-tier wireless multicasting networks," submitted to IEEE Trans. Commun., 2017.
networks," submitted to IEEE Trans. Wireless Commun., 2017
transmission in heterogeneous wireless networks," submitted to IEEE Trans. Wireless Commun., 2017.
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single-tier network partition-based caching & non-orthogonal transmission
[Jiang17]
caching & cooperation two-tier HetNet random caching & non-coherent joint transmission
[Wen17]
caching & multicasting single-tier network random caching & multicasting
[Cui16]
random caching & aggregation-based multicasting [Xing17] joint/competitive random caching & multicasting
[Wang17]
two-tier HetNet
– locations of BSs in tier j: PPP with density 𝜇j – locations of MSs: PPP with density 𝜇u
– each BS one transmit antenna – each BS in tier j transmit power Pj, bandwidth W – each MS one receive antenna
– pathloss D-α : D-distance, α-pathloss exponent – small scale fading CN(0,1)
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independent
𝑘 different files
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K N
j
N I K
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parameter-based caching, multicasting and cooperation
parameters: caching dist., file partition, etc. performance metric: successful transmission probability (STP)
STP analysis
(for given parameters)
STP maximization
(optimize parameters) tractable expression non-convex prob.
[Cui16], [Xing17], [Wang17]
locally opt. solution
general region
stochastic geometry
mixed disc.-cont. prob. (MDCP)
[Wen17]
multiple choice knapsack prob. (MCKP) [Jinag17] near opt. solution closed-form expression convex prob. [Cui16], [Xing17] closed-form
non-convex prob. [Wang17] MDCP [Wen17] discrete prob. [Jinag17] locally opt. solution
(e.g., SNR, user density, file size, target rate)
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[Cui16] Ying Cui, D. Jiang and Y. Wu, "Analysis and optimization of caching and multicasting in cache-enabled wireless networks," IEEE Trans. Wireless Commun.,
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– each BS stores comb. 𝑗 wp. – each BS stores file n wp.
– user requesting file n connects to nearest BS storing – serving BS may not be nearest BS
– BS j receiving Kj different file requests from its users multicasts each of these files at rate τ over bandwidth W/Kj
– Kn,0: file load of serving BS of a typical user requesting file n
[0,1], , 1
i i i
p i p
,
n
n i n i n
T p n T K
，
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joint dist. marginal dist.
, , 2 ,0 ,0
( ) ( ), ( ) Pr log 1 SINR
K n K n K n n n n
W q a q q K
p p p
file diversity
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number of files N=3 (red, yellow, blue) circle-MS, square-BS cache size K=2
K=2, one BS-2 Voronoi cells
Kj=2 Kj=1 Kj=1 benefit of multicasting
for each file (same color) determined by locations
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KKT conditions linear prog. cvx prob. non-cvx prob.
simplex method
reverse water-filling structure variables caching prob.
caching constr. variables caching prob.
near opt.
solution set substituting T* cvx prob. variables equivalent
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λu=0.1 nodes/m2
K=30
proposed proposed
[Xing17] J. Xing, Ying Cui and V. Lau, "Temporal-spatial aggregation for cache-enabled wireless multicasting networks with asynchronous content requests," submitted to IEEE Trans. Wireless Commun., 2017. (IEEE GLOBECOM, 2017)
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interference reduction and energy reduction
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constraints relaxation
near opt. solution with performance guarantee
KKT conditions
𝑂2+𝑂 2
+ 1 varibles joint caching prob.
general region
𝑂 varibles
caching prob.
joint caching prob.
MDCP
exhaustive search, grad. proj., graph method
cvx prob.
approximated solution closed-form solution
𝑂 𝐿 + 1 varibles
MDCP delay constr. caching constr. reverse water-filling structure
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large user density region small user density region
most popular uniform comb. dist. i.i.d. file popularity most popular uniform comb. dist. i.i.d. file popularity
proposed proposed
Scheme without spatial aggr. increases slowly due to temporal aggr. for fewer file requests
[Wang17] Z. Wang, Z. Cao, Ying Cui and Y. Yang, “Joint and Competitive Caching Designs in Large-Scale Multi-Tier Wireless Multicasting Networks,” major revision, IEEE Trans. Commun., 2017. (IEEE GLOBECOM, 2017)
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Random caching at each tier
transmission powers of all BSs storing this file
BS BS
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noncvx prob. caching constr.
stationary point
cvx prob. converge slowly difficult to select step size
block successive upper- bound minimization
Proposed iterative algorithm
update 𝐔1 and 𝐔2 alternately at iteration 𝑢
closed-form solution 𝑈
𝑘(𝑢 + 1)
KKT conditions concave function
linearization
guarantee convergence preserve partial concavity for faster convergence yield closed-form opt. solution at each iteration
approx.
nonconcave function
no change
linear function converge faster no step size concave function concave function is tight lower bound of and have same first order behavior
q q
approx. properties approx. benefits
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noncvx prob. caching constr. cvx prob. update 𝐔1 and 𝐔2 alternately
at iteration 𝑢 KKT conditions
converge if unique Nash Equilibrium Proposed iterative algorithm closed-form solution 𝑈
𝑘(𝑢 + 1)
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grad. grad. joint comp.
proposed ones proposed ones
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[Jiang17] D. Jiang and Ying Cui, "Partition-based caching in large-scale SIC-enabled wireless networks,” minor revision, IEEE Trans. Wireless Commun., 2017. (IEEE ICC, 2017)
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– : storage at each BS allocated to file n – : file n is not stored at any BS – : file n is stored at each BS – : file n is partitioned into subfiles, and each BS forms a random linear comb. of subfiles of file n using RLNC, and stores it in its cache
– SIC capability M: decoding and cancelation at most M times
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3 nearest BSs transmit stored coded subfile of file 2 to u0 number of files N=4 cache size K=2 SIC capability M=3 entire file 1 is stored at each BS files 2, 3 and 4 are partitioned into 3 subfiles u0 requests file 2
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decreases exponentially to 0, as increases linearly to , as decreases with S
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NP-hard file-partition constr.
near opt. solution ½ approximation guarantee and polynomial complexity
greedy method MCKP NP-hard equivalent
general file size region
Discrete prob.
Closed-form opt. solution and opt. value
allocate storage of each BS equally to KM most popular files increases with KM
analysis
Closed-form opt. solution and opt. value
store K most popular (entire) files at each BS increases with K and is not affected by M
analysis
small file size region large file size region
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significant performance gains Performance of proposed near optimal caching design increases much faster with K and M not depend on M proposed proposed K most popular entire files 300 most popular files
[Wen17] W. Wen, Ying Cui, F. Zheng and S. Jin, "Random caching based cooperative transmission in heterogeneous wireless networks,” under revision, IEEE Trans. Commun., 2017. (IEEE ICC, 2017)
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– each SBS stores file n wp.
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( )
n n
T T
n
T
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number of files N=3 (green, yellow, blue) cache size M=2 number of cooperative SBSs K=3
49 Problem 1 (STP Max.) Problem 2 (Equivalent STP Max.) Problem 3 (Master problem-# files stored in SBS) Problem 4 (Subproblem-caching dist. in SBS )
complexity: O(N) decomposition subproblem exhaustive search
KKT conditions
noncvx prob. MDCP disc. part cont. part
near opt. solution locally opt. solution closed-form opt. solution threshold based structure
and larger K, more files can be stored at SBSs
increase storage efficiency general region
(low target bit rate) general region (noncvx) # of files stored in SBS
50 Successful Transmission Probability Number of Cooperative SBS Successful Transmission Probability Cache Size
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uncoded placement optimization for coded delivery," submitted to IEEE
bandwidth utilization maximization in wireless networks," submitted to IEEE Trans. Commun., 2017. (IEEE GLOBECOM, 2017)
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– through an error-free link – set of user indices
– set of file indices – each file has indivisible data units
– cache memory of data units,
K
N
1,
,
N
W W
F
{1,2, , } N
{1,2, } K MF [0, ] M N
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Size M N files
1,
,
K K
D D D
File library
Caches Server Shared link
[Jin17] S. Jin, Y. Cui, H. Liu, and G. Caire, “Structural properties of uncoded placement
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[Ali17] [Ali14, Ali15]
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n
W
2K
, ,
( )
n n
x
x
,
( : )
n
W
,
( : , , )
k n
Z W n k
, { },
,| |
k
k D k
W s
k
potential performance improvement
p
, ,
( : \{ }),( : , ) ( )
k k k
D D D
W W k W k recovered from coded multicast msg cached at user k
Characteristics:
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* avg , { } | |>0 1 , , , 1 : \
min max . . 1, , 1, ,
k k K
K d d k k k n n N n n k
R p x s t x n x n x M k
x d ：
Problem 1 (File partition parameter optimization) Problem 2 (Equivalent simplified optimization)
increase coded- multicast opportunities
increase storage efficiency
Arbitrary file popularity
* avg , 1 1 1 1 , , , 1 1
min . . 1, {0,1, , }, 1, , 1 1
s s K N N N n n n s s n n n n n n s K n s s N K n s n s
K R p p y s s t y s K n K y n s K y M s
y
2K N variables
( 1) N K
variables
increase coded- multicast opportunities
* avg
ˆ min 1 . . 1, {0,1, , }, 1
K s s s K s s K s s
K K s R z s s s t z s K K z s K KM sz s N
z
1 K variables CVX problem linear problem linear problem
*
1 , / 0, {0,1, , } { },
s
KM s K N z KM N KM s K N ＼
* avg
(1 / ) ˆ 1 / K M N R KM N Closed-form optimal solution and optimal value Problem 3 (Equivalent simplified optimization)
solution
value
Uniform file popularity
KKT conditions file partition constr. cache constr. worst-cast load in [Ali14] centralized coded caching design in [Ali14]
– optimized scheme
schemes
– as increases, gaps between
baseline schemes increase
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Zipf Exponent
[Sun17] Y. Sun, Y. Cui, and H. Liu, “Joint pushing and caching for bandwidth utilization maximization in wireless networks,” submitted to IEEE, Trans. Commun., 2017. (GLOBECOM 2017).
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bandwidth at low traffic time
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– request state : first-order Markov chain – cache state : ,
– transmission action:
– caching action ,
– per-stage cost
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cache state update increasing convex function to smooth traffic
𝑞𝑙
∗ ≜ arg 𝑛𝑗𝑜𝑞𝑙 𝜚( 𝑔
𝑆𝑔 + 𝑞𝑙) + 𝑋
𝑙(𝑌𝑙, 𝑺 + 𝒛(𝑞𝑙))
multicast at BS: 𝑆𝑔 + max
𝑙
𝑄
𝑙,𝑔 ∗
per-user caching: Δෘ 𝑻𝑙 = 𝑏𝑠 𝑛𝑗𝑜ΔS𝑙 σ𝑔∈𝑇𝑙
′ σ𝐵𝑙 ′ ∈𝐺 𝑟𝐵𝑙,𝐵𝑙 ′
𝑙
ෘ 𝑊
𝑙 1(𝑌𝑙 1)
Problem (Joint pushing and caching optimization) Centralized optimal policy
Bellman equation
per-user per-file value func. Online decentralized algorithm Low complexity decentralized policy
Q-learning
complexity:
( 1) 2
K N
N N O N K M M
complexity:
2 3 log
O K F F ഥ ϕ∗ ≜ min
𝜈 lim sup 𝑈→ ∞
1 𝑈
𝑢=0 𝑈−1
𝐹 𝜚
𝑔∈𝐺
𝑆𝑔 𝑢 + 𝑄
𝑔 𝑢
𝑡. 𝑢. 𝜈 𝒀 ∈ 𝑉 𝒀 a small one reflects a small peak-to-average ratio of bandwidth requirement per-user pushing action:
infinite horizon average cost MDP
value function approximation problem relaxation
7.
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63 Number of users Cache Size Time Slot
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Theory, May 2014.
memory-rate tradeoff,” IEEE/ACM Trans. Netw., Aug. 2015.
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