1. INFOCOM 2013 – Torino, Italy
Content-centric wireless networks with limited buffers: when mobility hurts
Giusi Alfano, Politecnico di Torino, Italy
Michele Garetto, Università di Torino, Italy
Emilio Leonardi, Politecnico di Torino, Italy

2. Outline Motivation Previous work System assumptions Main results
Possible extensions

3. Why another paper on scaling laws of wireless networks?
The way users search and retrieve data is changing:
from host-to-host paradigm
to host-to-content paradigm
Contents are usually replicated to save bandwidth and improve QoS
e.g.: content-delivery networks (CDN)
The dominant traffic is going to be anycast, and not unicast

4. Existing scaling laws for wireless networks
The traditional way to start:
″consider N (unicast) flows randomly established among the nodes…″
e.g.: Gupta-Kumar (1999)
Grossglauser-Tse (2001)
A lot of work also on multicast…
Only few papers on anycast (and associated caching strategy)
all of them assume static nodes

5. Joint replication and delivery problem
Previous work
S. Gitzenis, G.S. Paschos, L. Tassiulas, “Asymptotic laws for content replication and delivery in wireless networks” (INFOCOM ′12)
We cache #123 !
grid
I want content #123 !
Here it is !
Joint replication and delivery problem

6. System assumptions 𝑁 nodes moving in a square (of area 1)
𝑀 contents (𝑀= 𝑁 𝛽 , 0 ≤𝛽≤1)
Zipf-like popularity: 𝑝 𝑖 = 𝐻 𝑖 𝛼 , 𝛼≥0
𝐾 cache size at each node. 𝐾 finite!!
measured in number of equal-size contents
(same scaling laws if bounded ratio maxsize/minsize)

7. Communication model Nodes can either use:
unique transmission range 𝑅
content-dependent transmission range:
𝑅 𝑚 : transmision range of content 𝑚
(with power control to compensate attenuation)
Interference is taken into account by:
Physical model (𝑆𝐼𝑁𝑅> 𝜎) …which is shown to be equivalent to a:
Generalized protocol model (also with variable tx-ranges)

8. Traffic model
Each transmission between two nodes allows to exchange an entire content (same scaling laws if you exchange only a segment of a content, each content split in bounded number of segments – no fluid limit)
Each node cycles these steps:
requests a random content (Zipf law)
waits until content is received
waits an additional idle time (to allow throughput-delay trade-offs)
requests another content…
Which implies: at most one pending content request per node
(same scaling laws if bounded number of parallel requests)

9. Mobility model We first consider for simplicity:
reshuffling mobility model (i.i.d.): (new random topology generated at each time slot)
then we extend the analysis to:
random walk (each node displaced by flight size 𝐹 from slot to slot) (but no communication while moving)
Flight size 𝐹 is varied from 1/ 𝑁 (quasi-static network) to 1 (similar to i.i.d.)

10. Contents’ replication
As in previous work, we assume caches of nodes are pre-populated by the system
As consequence of the fact that we consider static set of contents with constant popularity
No run-time optimizations (cache replacements induced by traffic)
We leave to future work: dynamic set of contents with varying popularity

11. Main results Performance metrics:
𝜆 : per-node throughput (in contents/slot)
𝐷 : average content transfer delay
We are interested in trade-offs between 𝜆 and 𝐷
Things we can play with:
number of replicas for each content
transmission range(s)
idle time between successive content requests
…and of course a communication scheme !…

12. For the reshuffling (i.i.d.) mobility:
Main results
For the reshuffling (i.i.d.) mobility:
Using unique transmission range 𝑅:
𝛼>2 : best possible performance 𝜆=Θ 1 , 𝐷=Θ 1
1<𝛼<2 : 𝐷=Θ 𝜆 𝑀 2−𝛼
𝛼<1: 𝐷=Θ 𝜆 𝑀
Using content-adaptable transmission ranges 𝑅 𝑚 :
𝛼>3/2 : best possible performance 𝜆=Θ 1 , 𝐷=Θ 1
1<𝛼<3/2 : 𝐷=Θ 𝜆 𝑀 3−2𝛼
𝑇ℎ𝑒𝑠𝑒 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑟𝑒𝑠𝑢𝑙𝑡𝑠 𝑎𝑐ℎ𝑖𝑒𝑣𝑎𝑏𝑙𝑒 𝑖𝑛 𝑎 𝑠𝑡𝑎𝑡𝑖𝑐 𝑔𝑟𝑖𝑑 𝑛𝑒𝑡𝑤𝑜𝑟𝑘!

13. Main results (with reshuffling mobility)
Take-away messages :
mobility hurts !
Throughput-delay trade-offs are worse than those achievable in static network (in the case of fixed transmission range 𝑅)
With power control (transmission range adapted to the content, smaller 𝑝 𝑚 -> larger 𝑅 𝑚 ) we recover exactly the trade-offs of a static network !

14. Main facts about optimal strategy (with reshuffling mobility)
One-hop communications are optimal ! i.e.: wait until you meet a node caching the content you want, and get it
Use tx-range(s) such that you compete only with bounded other nodes, and no smaller than this
Optimal number of replicas 𝑋 𝑚 are:
𝑋 𝑚 ∝ 𝑝 𝑚 (constant tx range)
𝑋 𝑚 ∝ 𝑝 𝑚 2/3 (variable tx ranges)

15. The optimal replication (reshuffling mobility)
A constrained optimization problem
…solved using standard methods

16. Main results (with random walk mobility)
For the random walk mobility model:
Multi-hop communications become feasible, provided that flight size F < R (tx-range)
As we vary the flight size, we obtain intermediate trade-offs in between the best ones (quasi-static network, F=Θ 1/ 𝑁 ) and the worst ones (fully mobile network, F=Θ 1 )
Using content-adaptable transmission ranges 𝑅 𝑚 we can always recover the best trade-offs of a quasi-static network

17. Conclusions and future work…with some criticism
We derived scaling laws of mobile wireless networks under content-centric (anycast) traffic in one simple scenario
Many (too many?) possible extensions:
Cache size scaling with 𝑁
Fluid limit (arbitrarily small packets)
Communications while moving
Dynamic contents with varying popularity
But…are these things really interesting?

18. One possible application…
Off-loading of 3G/4G cellular networks by device-to-device opportunistic communications
Do we meet enough people with common interests to make it effective? (𝛼<1)‼
Are we patient enough to wait?
How about energy cost to keep wireless interfaces up?

19. Thanks!