Chapter 3: Process Deadlocks

Single-Unit Request Model

• process restricted to requesting only one unit of request at a time.
• out degree of nodes in Wait-for-graph (WFG) is at most one.
• if only one unit of every resource in system, deadlock corresponds to a cycle in WFG.

AND Request Model

• a process can simultaneously request multiple resources.
• process blocked until all requests are granted.
• if single copy of every resource in sytem, cycle implies deadlock.
• process may be concurrently involved in multiple deadlocks.
• single-unit request model is a special case of the AND model.

OR Request Model

• process can simultaneously request multiple resources.
• blocked until any one of the requested resources is granted.
• cycle in WFG is not a sufficient condition for deadlock even if only one copy of each resource is present.
• presence of a knot is a sufficient condition for deadlock.

Knot: subgraph such that starting from any node in the subgraph it is impossible to leave the knot following the edges of the graph.

AND-OR Request Model

• generalization of the AND and the OR models.
• knot is a sufficient condition for deadlock.

P-out-of-Q Request model.

Resource Types

Reusable resources: do not vanish after use

• fixed number of units of resource
• neither created, nor destroyed.

Consumable resources: vanish on use

• no fixed number of units of resource
• one or more producers of resource
• producer, if not blocked, can produce any number of units of resource.

General Resource Graph (GRG)

• a bi-partite graph with the following edges:
• request edge: directed from a process P to resource R
• assignment edge: directed from reusable resource R to process P
• producer edge: directed from consumable resource to its producer process.

General Resource Graph (contd.)

For every reusable resource:

• number of assignment edges $\leq$ number of units of the resource.
• available units = total units - assigned units.
• a process can never request more than total units of a resource.

For every consumable resource:

• an edge from R_i to P_j if P_j is a producer of R_i.
• available units $\geq$ 0

Operations on GRG

Request:

draw corresponding number of request edges (e).

Acquisition:

$r_j \geq e$ units of R_j available:

• if reusable resource R_j: replace request edge with assignment edge
• if consumable resource R_j: remove all e request edges.

decrement r_j by e

Release:

performed by process with no outstanding request

• if reusable resource: remove assignment edge(s), increment r_j.
• if consumable resource: r_j can be increased by any number.

GRG Reduction Method

Blocked process: whose requests for any resource exceed the number of available units of that resource.


Graph reduction method: by unblocked process P_i

• for each reusable resource R_j: reduce the request and assignment edges between P_i and R_j
• for each consumable resource R_j:
  • decrement r_j by number of request edges
  • if P_i is producer of R_j: set r_j to $\infty$
  • delete all edges between P_i and R_j

Deadlock Determination by Reduction

• A graph is completely reducible if a sequence of reductions delete all edges in the graph.
• Theorem: Process P_i is not deadlocked if reductions leave it in an unblocked state.
• Corollary: A system is deadlock free if its GRG is completely reducible.

However, lack of reducibility does not necessarily indicate the system is deadlocked.

Deadlock Detection

Expedient state: all processes with outstanding requests are blocked.



Theorem: In a general resource graph:

• a cycle is a necessary condition for deadlock.
• if the graph is expedient, a knot is a sufficient condition for a deadlock.

However, absence of a deadlock does not necessarily imply the absence of deadlock.


Theorem: An expedient GRG with single-unit requests represents a deadlock state if and only if it contains a knot.