0 4 1 3 2 No deterministic symmetric dining solution [RL81] - - PDF document
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0 4 1 3 2 No deterministic symmetric dining solution [RL81] - - PDF document
Jan 31, 2024 415 likes •627 views
Once up on a time ... [Dij71] 0 4 1 3 2 No deterministic symmetric dining solution [RL81] Probabilistic symmetric solution T raditional non-symmetric: Left-Righ t solution Generalized dining philosophers [Lyn81] . . .
SLIDE 1
1 2 3 4
Once up
n
a time ... [Dij71] T raditional non-symmetric: Left-Righ t solution [RL81] Probabilistic symmetric solution No deterministic symmetric dining solution
SLIDE 2
. . . . . . . . .
Now: following:
Generalized dining philosophers [Lyn81]
Eac
h philosopher has an arbitrary n um b er
f
neigh b
urs
9
ne
fork b et w een ev ery pair
f
neigh b
urs
Eac
h philosopher needs all adjacen t forks to eat
Requiremen
ts: Exclusion: Disallo w neigh b
urs
to eat sim ultaneously + no deadlo c k, no starv ation Conict graph,
=
degree
SLIDE 3
SLIDE 4
. . . . . . . . .
i need these bottles hick!
9
ne
b
ttle
b et w een eac h pair
f
neigh b
urs
Drinking philosophers [CM84]
Eac
h thirst y philosopher needs a (presp ecied) subset
Requiremen
ts: pro vided that they need to drink from dieren t (presp ecied) b
ttles
(ma y dier eac h time)
f
its inciden t b
ttles
to drink Exclusion: Allo w neigh b
urs
to drink sim ultaneously , + no deadlo c k, no starv ation
SLIDE 5
SLIDE 6
Mobile
Philosophers [GPT96] Channel (F requency) Allo cation base station user (philosopher), mobile host
F
requency sp ectrum same in eac h cell
Eac
h philosopher needs some (arbitrary , not presp ecied) subset
f
frequencies to comm unicate
Requiremen
ts: p
ssible
for neigh b
urs
to
p
erate sim ultaneously
Request
satisabilit y (Bandwidth Utilisation) Exclusion: Allo w c hoice
f
frequencies so as to mak e it + no deadlo c k, no starv ation
SLIDE 7General Requiremen ts Dieren t constrain ts and exibilit y for eac h v ersion No deadlo c k Ev aluation Criteria No starv ation Time and comm unication complexit y (to satisfy a request) F ailure lo calit y [CS92] F ault tolerance (units dep end
n
the comm unication system) Exclusion Request Satisabilit y (for mobile philosophers)
SLIDE 8
. . . . . . . . . . . . . . .
then w ait for .... then w ait for .... Generalized Left-Righ t Dining [Lyn81] p iC +1 , eating pic k ed b y p i Idea: Color resources (edge-color conict graph), C colors p i pic ks forks in increasing color
rder
(using m utex for eac h) color
rder
guaran tees no deadlo c k, no starv ation Pro cess w aiting c hains = also failure lo calit y max-length = C w ait for fork color 1 pic k ed b y then w ait for .... w ait for p i(C 1) w ait for fork color C p iC pic k ed b y T ree giv es w
rst
case w aiting exp
nen
tial in C fork color C p i1
SLIDE 9Restricting the w aiting c hain length [SP88] Idea: again pic ks forks in increasing color
rder
(using m utex for eac h) but no w: if p i pic k ed color 1, 2, . . . x=2, . . . need to w ait for color x max-w aiting-c hain-length = log C (= also failure lo calit y) in addition: sync hronization do
rw
a y collect forks w ait for p ermission b y eac h
f
the neigh b
urs
to cross Time, comm unication complexit y = O ( log C ) bac ktrac k (release forks bac k to x=2)
SLIDE 10Wh y pic k forks 1-b y-1? Another approac h [CM84] Idea:
Initial
Acyclic Orien tation
Sink-no
des can eat; then
Rev
erse inciden t-edge-direction (send priviledges) using initial lab eling (e.g. no de coloring) and priviledge tok ens Result: (more
n
acyclic
rien
tations in [AST94], [BG94]) dynamic priorit y resolution sc heme can e.g. resolv e p
ssible
conicts in the drinking solution W aiting c hain length = O(n) (= failure lo calit y also)
SLIDE 11Conict
Precedence
Graph Undirected graph in which edges rep resent sha red resources b et w een p ro cesses w e call this graph conflict graph The algo rithm b y Chandy and Misra resolves conicts b y dening fo r every p
ssible
conict a p recedence relation
When
t w
p
ro cesses comp ete fo r a resource the
ne
with higher p recedence ma y access the resource rst
In
rder
to receive a solution which is fair these p recedences will have to change dynamically
The
directed graph graph that changes dynamically is called p recedence graph F
r
each resource an edge
f
the p recedence graph is directed from p ro cesses with lo w er p recedence to p ro cesses with higher p recedence
T
yp eset b y F
il
T E X
SLIDE 12The p recedences
f
the graph a re chosen such that it is alw a ys p
ssible
to distinguish at least
ne
p ro cess from all
ther
p ro cesses ie this p ro cess can enter its critical section NO DEADLOCK This is ensured b y the existence
f
at least
ne
p ro cess which has higher p recedence fo r all its sha red resources A p ro cess with this p rop ert y is called sink Its existence is gua ranteed when the p recedence graph is alw a ys acyclic By changing directions
f
edges it is p
ssible
to change the p recedences dynamically
This
must happ en in a w a y that the p recedence graph sta ys acyclic so p rogress fairness and mutual exclusion is gua ranteed
T
yp eset b y F
il
T E X
SLIDE 13Sta rting with a D A G
The
graph is initialised acyclic fo r example b y a no de colouring algo rithm
The
graph can remain acyclic if after use
f
the critical section a p ro cess reverse all adjacent p recedences in
ne
step
Need
a mechanism to k eep the sense
f
direction
T
yp eset b y F
il
T E X
SLIDE 14The mechanism F
rks
which have the p rop ert y to b e either clean
r
dirt y
A
fo rk will b e cleanedb efo re it is send to a neighb
ur
p ro cess
A
clean fo rk will b ecome dirt y when the holder
f
the resource enters the critical section
After
use it remains dir ty until it is sent to a neighb
ur
p ro cess
T
yp eset b y F
il
T E X
SLIDE 15The dynamic D A G
The
resp ective p recedence graph H can b e dened in the follo wing w a y
F
r
all pairs
f
p ro cesses p and q which sha re a common resource pq
ne
f
the follo wing statements is true
p
holds the fo rk fo r the resource and the fo rk is clean
q
holds the fo rk fo r the resource and the fo rk is dir ty
the
fo rk fo r the resource is in transit from q to p
T
yp eset b y F
il
T E X
SLIDE 16Requesting F
rks
The request
f
fo rks is realized b y request tok ens F
r
each fo rk there exist
ne
request tok en such that
nly
the holder
f
the request tok en can request a fo rk A hungry p ro cess requests a fo rk b y sending the request token to the
wner
f
the desired fo rk A p ro cess is not interested in accessing its resources when it holds a request token but not a fo rk
T
yp eset b y F
il
T E X
SLIDE 17The algo rithm The algo rithm is initialised b y an acyclic p recedence graph H and all p ro cesses with lo w er p recedence
wn
dirt y fo rks while p ro cesses with higher p recedence
wn
request tok ens All p ro cesses a re thinking ie they a re not interested in their resources A p ro cess which b ecomes hungry will send all its request token to neighb
ur
p ro cesses and w ait until it received all fo rks
A
p ro cess which received all fo rks will change its state to eating
A
p ro cess which leaves the critical section changes the state
f
all its fo rks to dir ty Then fo r all held request token the resp ective fo rk is sent to neighb
ur
p ro cesses The ab
ve
steps assume follo wing rules
T
yp eset b y F
il
T E X
SLIDE 18Receiving a request token fo r fo rk f
If
p ro cesso rs state is dierent from eating and f is dir ty then f will b e sent to the requesting p ro cesso r
If
p ro cesso rs state w as also hungry then the request token will also b e sent back Receiving a fo rk f
The
state
f
f will b e set to clean
T
yp eset b y F
il
T E X
SLIDE 19Co rrectness Mutual Exclusion Pro
f
The p recedence graph H is acyclic
No
Sta rvation Pro
f
Let the depth in H
f
any p ro cess p b e dened as the maximum numb er
f
edges along a path from p to another p ro cess without p redecesso r The p ro
f
will sho w b y induction that a p ro cess
f
depth k will eventually eat if p redecesso rs at depth k can ea t
T
yp eset b y F
il
T E X
SLIDE 20Complexities Communication Complexit y Odegree Pro
