Homework Assignment #7

Deadlock

Philosophers P[0], P[1], P[2], P[3], and P[4] sit at a circular table.

For i=1,2,3,4, Philosopher P[i] uses two forks, Fork[i-1] and Fork[i]. Fork[i-1] is to his right and Fork[i] is to his left.

Philosopher P[0] uses fork Fork[4] (to his right) and Fork[0] (to his left).

Each philosopher needs only two of the forks, but must follow this protocol:

Get your "first" fork. (The one that comes earlier in the ordering.)
After obtaining your first fork, get your second fork.
Eat.
Put down your forks.

Philosophers 0 - 3 are told: get your left fork first.

Philospher 4 is told: get your right fork first.

Explain why deadlock cannot occur with this protocol.

Answer:

If resources are "ordered" and processes needing more than one
resource are required to request the resources they need in the order
they occur in this given ordering, then circular wait cannot
occur. Since circular wait is a necessary condition for deadlock, this
means that deadlock cannot occur.

The protocol given results from ordering the forks in this order:

(*)   Fork[3], Fork[2], Fork[1], Fork[0], Fork[4]

For example, P[1] uses Fork[0] (right) and Fork[1] (left). This
ordering requires P[1] to get the right fork, Fork[1], first, since
Fork[1] comes before Fork[0] in the order (*) above.

Similarly P[0] uses Fork[4] (right) and Fork[0] (left). This ordering
requires P[0] to get the left fork, Fork[0], first, since Fork[0]
comes earlier than Fork[4] in the orderint (*).

Consider the following snapshot of a system with five processes, P0, P1, P2, P3, and P4 sharing resources of type A, B, C, and D:

	Allocation	Request			Available
	A  B  C  D	A  B  C  D		A  B  C  D
P0	0  1  1  0	3  1  0  0		2  0  0  0
P1	0  0  0  1	no request	
P2	0  1  0  0	2  0  1  1
P3	0  0  1  0	no request
P4	1  1  0  0	2  1  2  0

Which processes, if any, are deadlocked? Explain.

Answer:

To determine if deadlock has occurred, try to find an
execution sequence that would allow all processes to finish
provided no additional requests are made other than those
already pending. 

Resources Returned    After this process        Available
                           finishes             A B C D
A B C D                                         2 0 0 0
0 0 0 1                       P1                2 0 0 1
0 0 1 0                       P3                2 0 1 1
0 1 0 0                       P2                2 1 1 1

No more processes could execute even with the resources A B C D
that would be available after P1, P3, and P2 were finished.

So deadlock has occurred and the deadlock set is { P0, P4}.

Three processes will be executed concurrently. Each of these processes requires from 0 to 4 units of resource A. (These units are interchangeable, so it doesn't matter which particular units of A each process gets.) If a process requests unit(s) of A, the allocation protocol is
1. Check if the requested units of A plus the units of A already held by the process is greater than 4. If so, the request is denied, otherwise
2. check if the requested units of A are available. If available, then the request is granted, otherwise the process is blocked waiting for the resources to become available.
What is the minimum number of units of A that can be in the system, so that deadlock will never occur for these three processes. Assume that no other processes use the units of A.
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Answer:

The largest number of units in the system for which deadlock could
still occur corresponds to the state that all all the resources
are allocated, but no process has its maximum. That is, available
should be 0 and each process should have exactly 1 less than its maximum.

That is, each of the 3 proccesses would hold (4-1) = 3 units of A for
a total of 9 units. Since this is the largest number of units
of A for which deadlock could occur, the minimum number of
units of A for which deadlock would never occur is just 1 more: 

       10 units of A.
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