Resource Allocation
▸Distributed mutual exclusion
▹Permission-based (Ricart & Agrawala)
▹Quorum-based (Maekawa)
▹Token-based (Raymond)
▸Deadlocks
▹Deadlock properties (Holt)
▹Distributed deadlock detection (Singhal)
Resource Allocation
1
Distributed Mutual Exclusion
▸Mutual Exclusion:
▹a resource granted to a process must be released
before it can be granted to another process
▸Conditions for Distributed Mutual Exclusion:
1. Requests for a resource should be granted in the
order in which they were made
2. Every granted resource will eventually be released,
to ensure every request will eventually be granted
Resource Allocation > Distributed Mutual Exclusion
2
Permission-Based Algorithms
▸Algorithms that ensure mutual exclusion by
obtaining permission from every process in the
system
▸Whenever a process requests a resource, it must
request permission from every other process in
the system
▸Two algorithms:
▹Lamport (1978)
▹Ricart & Agrawala (1981)
Resource Allocation > Distributed Mutual Exclusion > Permission-Based
3
Complexity of Lamport Algorithm
▸ Parameters:
▹N: number of processes in the system
▹T: message transmission time
▹E: critical section execution time
▸ Message complexity: 3(N – 1)
▹N – 1 request messages
▹N – 1 acknowledgement messages
▹N – 1 release messages
▸ Response time (under light competition): 2T + E
▹Transmission time for request messages
▹Transmission time for acknowledgement messages
▹Execution time of current critical section
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Lamport
4
Ricart & Agrawala Algorithm
▸Assumptions:
▹Every message is eventually received but not necessarily
in order sent (i.e., lossless network)
▹Processes do not fail
▹Every request is sequenced based on the highest
sequence number seen before by that process
▹Every process is numbered to determine priority in the
event of equivalent sequence numbers
(lower the number, higher the priority)
▹Each rule is implemented in a separate thread with a
shared semaphore
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
5
Ricart & Agrawala Algorithm
▸Rule 1: Mutual Exclusion Invocation
requesting_critical_section = true;
sequence_no = highest_sequence_no + 1;
outstanding_replies = N – 1;
for(i = 0; i < N; i++) {
if(i != me) send(REQUEST(sequence_no, me), i);
}
while(outstanding_replies > 0) { }
critical_section();
requesting_critical_section = false;
for(i = 0; i < N; i++) {
if(reply_deferred[i]) {
reply_deferred[i] = false;
send(REPLY, i);
}
}
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
6
Ricart & Agrawala Algorithm
▸Rule 2: Receiving Requests(j, k)
highest_sequence_no = max(highest_sequence_no, j);
defer = requesting_critical_section &&
((j > sequence_no) ||(j == sequence_no && k >
me));
if(defer) {
reply_deferred[k] = true;
}
else {
send(REPLY, k);
}
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
7
Ricart & Agrawala Algorithm
▸Rule 3: Receiving Replies
outstanding_replies--;
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
8
Complexity of Ricart & Agrawala
▸Message complexity: 2(N – 1)
▹N – 1 request messages
▹N – 1 reply messages
▸Response time (under light competition): 2T + E
▹Transmission time for request messages
▹Transmission time for reply messages
▹Execution time of current critical section
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
9
Deadlock and Starvation
▸Deadlock:
▹Occurs when no process in the system is in its critical
section and no requesting process can ever proceed to
its own critical section
▸Starvation:
▹Occurs when one process must wait indefinitely to
enter its critical section even though other nodes are
entering and exiting their own critical sections
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
10
Ricart & Agrawala Exercise
▸Assuming P = 0, Q = 1, and R = 2, draw a diagram
showing R and Q invoking mutual exclusion, but
R being granted its critical section first
P
reply
req(2,1)
Q
R
reply
reply req(2,1)
req(1,2)
reply
Resource Allocation > Distributed Mutual Exclusion > Permission-Based > Ricart & Agrawala
11
Resource Allocation
▸Distributed mutual exclusion
▹Permission-based (Ricart & Agrawala)
▹Quorum-based (Maekawa)
▹Token-based (Raymond)
▸Deadlocks
▹Deadlock properties (Holt)
▹Distributed deadlock detection (Singhal)
Resource Allocation
12
Distributed Mutual Exclusion:
Quorum-based Algorithms
CS/CE/TE 6378
Advanced Operating Systems
Quorum-Based Algorithms
▸Algorithms that ensure mutual exclusion by
obtaining permission from every member of a
minimum set of processes (i.e., a quorum)
▸Whenever a process requests a resource, it must
request permission from every process in its
quorum
▸To avoid violation of mutual exclusion, quorums
must adhere to the non-null intersection
property
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
14
Non-Null Intersection Property
▸For any combination of i and j, 1 ≤ i, j ≤ N,
Si ∩ Sj ≠ Ø
▸For any pair of processes, their quorums must
share at least one member
▸Two creation methods on order of √N
▹Projective planes
▹Square grid
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
15
Quiz Question
▸ Which of the following quorum assignments violates the
non-null intersection property?
▹S1 = {1, 2}
S2 = {2, 3}
S3 = {3}
▹S1 = {1, 2}
S2 = {2, 3}
S3 = {1, 3}
▹S1 = {2, 3}
S2 = {1, 3}
S3 = {1, 2}
▹S1 = {1, 2, 3}
S2 = {1, 2, 3}
S3 = {1, 2, 3}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
16
Projective Plane Quorums
▸Based on the mathematical concept of finite
projective planes, in which parallel lines
eventually intersect at points near infinity
▸Size of each quorum is K, where N ≤ K(K – 1) + 1
▹K = 2 for 1 ≤ N ≤ 3
▹K = 3 for 4 ≤ N ≤ 7
▹K = 4 for 8 ≤ N ≤ 13
▹K = 5 for 14 ≤ N ≤ 21
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
17
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
4
5
6
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
18
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
4
5
6
▸First, every process should be a member of its
own quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
19
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
2
3
4
5
6
X
X
X
4
5
6
X
X
X
▸First, every process should be a member of its
own quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
20
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
2
3
4
5
6
X
X
X
4
5
6
X
X
X
▸Select enough processes to complete K for one
process (node #1)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
21
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
1
2
3
X
X
X
4
5
6
X
X
4
5
6
X
X
X
▸Select enough processes to complete K for one
process (node #1)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
22
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
1
2
3
X
X
X
4
5
6
X
X
4
5
6
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #1)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
23
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
X
X
X
4
5
6
X
OR
X
OR
OR
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #1)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
24
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
X
X
X
4
5
6
X
OR
X
OR
OR
X
X
X
▸Select enough processes to complete K for one
process (node #6) not in the latest quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
25
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
X
X
X
4
5
6
X
OR
X
X
OR
X
X
X
X
▸Select enough processes to complete K for one
process (node #6) not in the latest quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
26
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
X
X
X
4
5
6
X
OR
X
X
OR
X
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #6)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
27
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
X
X
X
4
5
OR
X
OR
6
X
OR
X
OR
X
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #6)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
28
Projective Plane Example
▸N = 6, hence K = 3
1
2
3
4
5
6
1
2
3
X
X
X
4
5
OR
X
OR
6
X
OR
X
OR
X
X
X
X
▸Select enough processes to complete K for one
process (node #4) not in the latest quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
29
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
5
6
5
6
OR
X
3
4
4
X
X
X
OR
X
X
X
X
X
▸Select enough processes to complete K for one
process (node #4) not in the latest quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
30
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
5
6
5
6
OR
X
3
4
4
X
X
X
OR
X
X
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #4)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
31
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
4
5
6
X
X
5
6
OR
X
3
4
OR
OR
X
OR
OR
X
X
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #4)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
32
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
4
5
6
X
X
5
6
OR
X
3
4
OR
OR
X
OR
OR
X
X
X
X
X
▸Select enough processes to complete K for one
process (node #2) not in the latest quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
33
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
X
3
4
5
6
X
X
4
OR
5
6
X
X
X
OR
OR
X
X
X
X
X
▸Select enough processes to complete K for one
process (node #2) not in the latest quorum
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
34
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
X
3
4
5
6
X
X
4
OR
5
6
X
X
X
OR
OR
X
X
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #2)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
35
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
X
3
X
4
5
6
X
X
4
OR
5
6
X
X
X
OR
OR
X
X
X
X
X
▸Ensure every other process shares at least one
process with the latest quorum (node #2)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
36
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
X
3
X
4
5
6
X
X
4
OR
5
6
X
X
X
OR
OR
X
X
X
X
X
▸Follow through other requirements to ensure
there’s no conflicts
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
37
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
X
3
X
4
X
5
X
6
X
4
OR
5
6
X
X
X
X
X
X
X
X
▸Follow through other requirements to ensure
there’s no conflicts
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
38
Projective Plane Example
▸N = 6, hence K = 3
1
1
2
3
X
X
X
2
X
3
X
X
4
X
X
5
X
X
X
6
X
X
X
4
6
5
X
X
X
X
▸Follow through other requirements to ensure
there’s no conflicts
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
39
Projective Plane Example
▸N = 6, hence K = 3
▸S1 = {1, 2, 3}
▸S2 = {2, 5, 6}
▸S3 = {2, 3, 4}
▸S4 = {1, 4, 6}
▸S5 = {1, 4, 5}
▸S6 = {3, 5, 6}
1
1
2
3
X
X
X
2
X
3
X
X
4
X
X
5
X
X
X
6
X
X
X
4
6
5
X
X
X
X
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
40
Square Grid Quorums
▸Based on a K x K grid, where N ≤ K2
▹K = 2 for 1 ≤ N ≤ 4
▹K = 3 for 5 ≤ N ≤ 9
▹K = 4 for 10 ≤ N ≤ 16
▹K = 5 for 17 ≤ N ≤ 25
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
41
Square Grid Example
▸N = 6, hence K = 3
1
4
2
5
3
6
▸Quorum members come from same row and same
column in grid
▹S1 = {1, 2, 3, 4}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
42
Square Grid Example
▸N = 6, hence K = 3
▸S1 = {1, 2, 3, 4}
▸S2 = {1, 2, 3, 5}
▸S3 = {1, 2, 3, 6}
▸S4 = {1, 4, 5, 6}
▸S5 = {2, 4, 5, 6}
▸S6 = {3, 4, 5, 6}
1
4
2
5
3
6
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
43
Maekawa Algorithm
▸Assumptions
▹Channels causally order messages (FIFO)
▹Every message is eventually delivered
(i.e., lossless network)
▹Node failure can be detected and failed nodes
removed
▹A REQUEST(Ti, i) precedes another REQUEST(Tj, j),
if (Ti < Tj), or (Ti = Tj and i < j)
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
44
Maekawa Algorithm
▸Rule 1
When process i invokes mutual exclusion, it sends
a REQUEST(TS, i) message to all processes in its
quorum Si, where Ts is greater than any
timestamp received by process i.
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
45
Maekawa Example
▸N = 4, hence K = 2
▸SC = {C, D, E}
▸SD = {C, D, F}
▸SE = {C, E, F}
▸SF = {D, E, F}
C
E
D
F
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based
46
Maekawa Example
▸E invokes mutual exclusion, locks itself, and sends
REQUEST(1,2) messages to SE (C and F)
C
RQC = { }
D
RQD = { }
E
req(1,2)
RQE = {(1,2)} req(1,2)
F
RQF = { }
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
47
Maekawa Example
▸D invokes mutual exclusion, locks itself, and
sends REQUEST(1,1) messages to SD (C and F)
C
RQC = { }
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
F
RQF = { }
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
48
Maekawa Algorithm
▸Rule 2
Upon receiving a REQUEST(TS, i) message, the
receiving process j will queue the request and:
▹Send a LOCKED message to process i, if j is not
currently locked by another request
▹Send a FAILED message to process i, if any other
queued requests precede the new request
▹Send an INQUIRY message to process k, if the new
request precedes the locked request from k
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
49
Maekawa Example
C
RQC = { }
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
F
RQF = { }
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
50
Maekawa Example
▸F queues E’s request, locks itself, and sends a
LOCKED message back to E
C
RQC = { }
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked
F
RQF = {(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
51
Maekawa Example
▸C queues D’s request, locks itself, and sends a
LOCKED message back to D
C
RQC = {(1,1)}
locked
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked
F
RQF = {(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
52
Maekawa Example
▸F queues D’s request and sends an INQUIRE
message to E, since (1,1) < (1,2)
C
RQC = {(1,1)}
locked
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
53
Maekawa Example
▸C queues E’s request and sends a FAILED message
back to E, since (1,1) < (1,2)
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
54
Maekawa Algorithm
▸Rule 3
Upon receiving an INQUIRE message, the
receiving process i will return a RELINQUISH
message if it has received or will ever receive a
FAILED message.
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
55
Maekawa Example
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
56
Maekawa Example
▸E receives F’ inquiry and sends a RELINQUISH
message back after receiving C’s FAILED message
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
relinquish
F
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
57
Maekawa Algorithm
▸Rule 4
Upon receiving a RELINQUISH message, the
receiving process j will lock itself for the most
preceding request in its queue and will send a
LOCKED message to the sender of that request.
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
58
Maekawa Example
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
relinquish
F
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
59
Maekawa Example
▸F receives E’ RELINQUISH message, locks itself
for D, and sends a LOCKED message to D
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
60
Maekawa Algorithm
▸Rule 5
Upon receiving a LOCKED message from every
member of Si, process i enters its critical section.
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
61
Maekawa Example
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
62
Maekawa Example
▸D has received a LOCKED message from every
member of SD and enters its critical section
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
63
Maekawa Algorithm
▸Rule 6
When process i exits its critical section, it sends a
RELEASE message to all processes in Si., after
deleting its own request from its own queue.
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
64
Maekawa Example
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = {(1,1)}
E
req(1,1)
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
65
Maekawa Example
▸D exits its critical section, deletes its own request,
and sends RELEASE messages to SD (C and F)
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = { }
E
release
req(1,1)
release
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
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Maekawa Algorithm
▸Rule 7
Upon receiving a RELEASE message from process i,
process j deletes i’s request from its queue. If
there are remaining requests, j locks itself for the
most preceding request and sends a LOCKED
message to process k, the request’s originator. If
there are no remaining requests, j unlocks itself.
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Maekawa Example
C
RQC = {(1,1),(1,2)}
locked failed
req(1,1)
D
RQD = { }
E
release
req(1,1)
release
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
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Maekawa Example
▸C receives D’s RELEASE message, deletes (1,1)
from its queue, and sends a LOCKED message to E
C
RQC = {(1,2)}
D
RQD = { }
E
locked
locked failed
req(1,1)
release
req(1,1)
release
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
relinquish
locked
RQF = {(1,1),(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
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Maekawa Example
▸F receives D’s RELEASE message, deletes (1,1)
from its queue, and sends a LOCKED message to E
C
RQC = {(1,2)}
D
RQD = { }
E
req(1,1)
release
req(1,1)
release
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
locked
locked failed
relinquish
locked
locked
RQF = {(1,2)}
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Maekawa Example
▸E has received a LOCKED message from every
member of SE and enters its critical section
C
RQC = {(1,2)}
D
RQD = { }
E
req(1,1)
release
req(1,1)
release
req(1,2)
RQE = {(1,2)} req(1,2)
locked inquire
F
locked
locked failed
relinquish
locked
locked
RQF = {(1,2)}
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
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Quiz Question
▸Consider the following system of quorums:
SP = {P, Q, R}
SQ = {P, Q, S}
SR = {P, R, S}
SS = {Q, R, S}
If process Q invokes mutual exclusion, how many
REQUEST messages does it send?
▹1
▹2
▹3
▹4
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Quiz Question
▸ Assume nodes are numbered alphabetically (e.g., Q < R).
If process P has already been locked by process Q’s
REQUEST with timestamp 3, what will happen when
process P receives process R’s REQUEST with
timestamp 2?
▹P will send a FAILED message to R.
▹P will send an INQUIRE message to Q.
▹P will send a LOCKED message to R.
▹P will send a RELINQUISH message to Q.
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Quiz Question
▸ Assume nodes are numbered alphabetically (e.g., Q < R).
If process P has already been locked by process Q’s
REQUEST with timestamp 3, what will happen when
process P receives process R’s REQUEST with
timestamp 4?
▹P will send a FAILED message to R.
▹P will send an INQUIRE message to Q.
▹P will send a LOCKED message to R.
▹P will send a RELINQUISH message to Q.
Resource Allocation > Distributed Mutual Exclusion > Quorum-Based > Maekawa
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Quiz Question
▸ Assume nodes are numbered alphabetically (e.g., Q < R).
If process P has already been locked by process Q’s
REQUEST with timestamp 3, what will happen when
process P receives process R’s REQUEST with
timestamp 3?
▹P will send a FAILED message to R.
▹P will send an INQUIRE message to Q.
▹P will send a LOCKED message to R.
▹P will send a RELINQUISH message to Q.
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Complexity of Maekawa Algorithm
▸ Parameters:
▹ K: size of quorums
▹ T: message transmission time
▹ E: critical section execution time
▸ Message complexity (best case): 3(K – 1)
▹ K – 1 request messages
▹ K – 1 locked messages
▹ K – 1 release messages
▸ Response time (under light competition): 3T + E
▹ Transmission time for request messages
▹ Execution time of current critical section
▹ Transmission time for release messages
▹ Transmission time for locked messages
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