For Multiple Instances of Each Resource Type - 4.3.1.2 | Module 4: Deadlocks | Operating Systems
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4.3.1.2 - For Multiple Instances of Each Resource Type

Practice

Introduction & Overview

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Quick Overview

For deadlock detection when **multiple instances of each resource type** exist, a simple cycle in the Resource-Allocation Graph (RAG) is no longer a definitive indicator of deadlock; it only suggests a *possibility*. Instead, the detection algorithm adapts the principles of the **Banker's Safety Algorithm**. It iteratively attempts to find a sequence of non-deadlocked processes whose current resource requests can be satisfied by the available resources plus those held by processes assumed to complete. Any process that cannot be included in such a sequence (meaning its requests cannot be met even if all non-deadlocked processes release their resources) is definitively part of a deadlocked set. Key matrices used are `Available`, `Allocation`, and `Request`.

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Deadlock Detection for Multiple Resource Instances

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2. For Multiple Instances of Each Resource Type: This algorithm is an adaptation of the Banker's Safety Algorithm, but instead of the Max matrix, it uses a Request matrix that represents the current outstanding requests of each process. β—‹ The algorithm initializes a Work vector (equal to Available) and a Finish boolean array (all false). β—‹ It then iteratively searches for a process Pi where Finish[i] is false and its Request[i] can be satisfied by the current Work resources. β—‹ If such a Pi is found, its resources are conceptually released: Work = Work + Allocation[i], and Finish[i] = true. The search continues. β—‹ After iterating, any process Pi for which Finish[i] remains false is involved in a deadlocked state. These processes are permanently blocked because their current requests cannot be satisfied even if all processes not in the deadlock released their resources. The frequency of running the detection algorithm can vary: it might be executed periodically (e.g., every few minutes or when CPU utilization drops), upon resource request failure, or when system performance significantly degrades.

Detailed Explanation

When resource types can have multiple instances (e.g., a system with 3 printers of the same model, or 5 network connections), detecting deadlocks becomes more involved than just looking for cycles in the Resource-Allocation Graph (RAG). A cycle in the RAG, in this case, only indicates a possibility of deadlock, not a certainty. This is because a process waiting for a resource in a cycle might still be able to acquire an instance of that resource from a process outside its immediate circular dependency, or from an unallocated pool.

  * **Algorithm Basis: Adaptation of Banker's Safety Algorithm:** The detection algorithm for multiple instances is fundamentally similar to the Banker's Safety Algorithm we discussed for deadlock avoidance. However, instead of using a `Max` matrix (which represents the *maximum* resources a process *might* need), it uses a `Request` matrix.
      * `Request[i][j]` tells us how many instances of resource type `j` process `i` is *currently* requesting.
  * **Key Data Structures (similar to Banker's):**
      * `Available`: A vector representing the number of currently free instances of each resource type. (This is initialized to the system's `Available` resources).
      * `Allocation`: An `nΓ—m` matrix showing how many instances of each resource type are currently allocated to each process.
      * `Request`: An `nΓ—m` matrix showing how many instances of each resource type each process is *currently requesting*. (This is key to detection, replacing `Need` or `Max` from avoidance).
      * `Work`: A temporary vector, initially equal to `Available`. This represents the resources that are currently available for allocation.
      * `Finish`: A boolean array of size `n` (number of processes), initially set to `false` for all processes. `Finish[i] = true` will mean that process `Pi` has been determined to be able to complete.
  * **The Detection Algorithm Steps:**
    1.  **Initialization:** Set `Work = Available`. Set all `Finish[i]` to `false`.
    2.  **Iterative Search:** The algorithm enters a loop, searching for a process `Pi` that meets two conditions:
          * `Finish[i]` is `false` (meaning we haven't yet determined if `Pi` can complete).
          * `Request[i]` \\<= `Work` (meaning `Pi`'s current outstanding request can be satisfied by the currently available `Work` resources).
    3.  **Process Completion Simulation:** If such a process `Pi` is found:
          * We assume `Pi` runs to completion.
          * Its currently allocated resources are "released" back to the system: `Work = Work + Allocation[i]`.
          * Mark `Pi` as complete: `Finish[i] = true`.
          * The search then **repeats from step 2** (it goes back and tries to find *any* process that can now complete, potentially including ones that couldn't before due to new resources in `Work`).
    4.  **Deadlock Identification:** After the loop (when no more processes can be found that satisfy the conditions in step 2):
          * Any process `Pi` for which `Finish[i]` is still `false` is part of a **deadlocked set**. These processes are permanently blocked because their current requests cannot be satisfied, even if all other processes (those for which `Finish[i]` became `true`) eventually complete and release their resources.
  • Frequency of Running the Detection Algorithm:
    • Periodically: The algorithm can be run at fixed intervals (e.g., every few minutes) or when system performance metrics (like CPU utilization) drop significantly, indicating a potential problem.
    • Upon Resource Request Failure: If a process requests resources and they are not immediately available, it's a good trigger to run the detection algorithm. This is more reactive and avoids unnecessary overhead if deadlocks are rare.
    • Trade-offs: Running it frequently incurs overhead. Running it infrequently means deadlocks might persist longer before being detected, leading to reduced throughput and responsiveness.

Examples & Analogies

No real-life example available.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Cycle β‰  Deadlock: For multiple instance resource types, a cycle in the RAG is only a possibility of deadlock, not a guarantee.

  • Banker's Adaptation: The detection algorithm is an adaptation of the Banker's Safety Algorithm.

  • Request Matrix: Used instead of Max to represent current outstanding requests.

  • Iterative Check: The algorithm simulates processes completing and releasing resources to see if all processes can eventually finish.

  • Finish[i] = false: The definitive indicator that process Pi is part of a deadlocked set.

  • Examples

  • Given State:

  • Available Resources: [1, 2, 0] (e.g., 1 instance of R1, 2 of R2, 0 of R3)

  • Allocation Matrix:

  • Process | R1 | R2 | R3

  • --------|----|----|----

  • P0 | 0 | 1 | 0

  • P1 | 2 | 0 | 0

  • P2 | 3 | 0 | 3

  • P3 | 2 | 1 | 1

  • P4 | 0 | 0 | 2

  • Request Matrix: (What each process is currently waiting for)

  • Process | R1 | R2 | R3

  • --------|----|----|----

  • P0 | 0 | 0 | 0 (P0 is not requesting anything currently)

  • P1 | 2 | 0 | 2

  • P2 | 0 | 0 | 0 (P2 is not requesting anything currently)

  • P3 | 1 | 0 | 0

  • P4 | 0 | 0 | 2

  • Detection Algorithm Steps:

  • Initialization:

  • Work = [1, 2, 0] (copy of Available)

  • Finish = [false, false, false, false, false] (for P0 to P4)

  • Iterative Search:

  • Iteration 1:

  • Can P0 run? Finish[0] is false. Request[0] = [0, 0, 0]. [0, 0, 0] <= [1, 2, 0] (Work). YES.

  • Work = Work + Allocation[0] = [1, 2, 0] + [0, 1, 0] = [1, 3, 0]

  • Finish[0] = true

  • Can P1 run? Finish[1] is false. Request[1] = [2, 0, 2]. [2, 0, 2] <= [1, 3, 0] (Work)? No, R1 and R3 request too high.

  • Can P2 run? Finish[2] is false. Request[2] = [0, 0, 0]. [0, 0, 0] <= [1, 3, 0] (Work). YES.

  • Work = Work + Allocation[2] = [1, 3, 0] + [3, 0, 3] = [4, 3, 3]

  • Finish[2] = true

  • Can P3 run? Finish[3] is false. Request[3] = [1, 0, 0]. [1, 0, 0] <= [4, 3, 3] (Work). YES.

  • Work = Work + Allocation[3] = [4, 3, 3] + [2, 1, 1] = [6, 4, 4]

  • Finish[3] = true

  • Can P4 run? Finish[4] is false. Request[4] = [0, 0, 2]. [0, 0, 2] <= [6, 4, 4] (Work). YES.

  • Work = Work + Allocation[4] = [6, 4, 4] + [0, 0, 2] = [6, 4, 6]

  • Finish[4] = true

  • Iteration 2 (restart search for Finish[i] = false processes):

  • Only P1 remains with Finish[1] = false.

  • Can P1 run? Request[1] = [2, 0, 2]. [2, 0, 2] <= [6, 4, 6] (current Work)? YES\!

  • Work = Work + Allocation[1] = [6, 4, 6] + [2, 0, 0] = [8, 4, 6]

  • Finish[1] = true

  • Final Check: All Finish are now true.

  • Conclusion: In this example, no deadlock exists. All processes can eventually run to completion. If, however, P1's request could not have been satisfied even after all other processes conceptually released their resources, then P1 would have been identified as deadlocked.

  • Flashcards

  • Term: Multiple Instance Resource Type

  • Definition: Resource type with more than one available unit.

  • Term: Request Matrix

  • Definition: Matrix showing resources currently requested by each process.

  • Term: Work Vector (Detection)

  • Definition: Temporary vector representing available resources during detection algorithm, updated by released resources.

  • Term: Finish Array (Detection)

  • Definition: Boolean array; false indicates process is potentially deadlocked, true means it can complete.

  • Term: Deadlocked Process (Multiple Instances)

  • Definition: A process Pi for which Finish[i] remains false after the detection algorithm runs, indicating it's permanently blocked.

  • Memory Aids

  • Analogy: The Bus Depot Manager: Imagine a bus depot with multiple buses (R1, R2, R3) and many drivers (P0-P4). The manager (OS) needs to see if all drivers can eventually complete their routes, given the currently available buses and the drivers' current outstanding requests for specific buses.

  • "Check if Driver Can Go": The manager goes driver by driver. If a driver Pi is not yet on their way (Finish[i] is false) AND they can get the specific buses they currently need (Request[i] <= Work), the manager assumes they leave.

  • "Buses Come Back": When a driver leaves, their currently held buses are returned to the depot (Work = Work + Allocation[i]).

  • "Re-check Others": The manager then re-checks ALL drivers (even those previously passed over) with the newly available buses (Work).

  • "Stuck Drivers": After exhaustively checking everyone, any driver still marked false (Finish[i] is false) is stuck. They can't get the buses they need, even if everyone else who could leave has already left and returned their buses. These are your deadlocked drivers.

  • Key Difference from Banker's Avoidance: Remember, in Avoidance, the Banker's algorithm uses MAX to prevent an unsafe state. In Detection, it uses REQUEST to identify if a deadlock already exists by checking if processes can currently complete their requests.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Given State:

  • Available Resources: [1, 2, 0] (e.g., 1 instance of R1, 2 of R2, 0 of R3)

  • Allocation Matrix:

  • Process | R1 | R2 | R3

  • --------|----|----|----

  • P0 | 0 | 1 | 0

  • P1 | 2 | 0 | 0

  • P2 | 3 | 0 | 3

  • P3 | 2 | 1 | 1

  • P4 | 0 | 0 | 2

  • Request Matrix: (What each process is currently waiting for)

  • Process | R1 | R2 | R3

  • --------|----|----|----

  • P0 | 0 | 0 | 0 (P0 is not requesting anything currently)

  • P1 | 2 | 0 | 2

  • P2 | 0 | 0 | 0 (P2 is not requesting anything currently)

  • P3 | 1 | 0 | 0

  • P4 | 0 | 0 | 2

  • Detection Algorithm Steps:

  • Initialization:

  • Work = [1, 2, 0] (copy of Available)

  • Finish = [false, false, false, false, false] (for P0 to P4)

  • Iterative Search:

  • Iteration 1:

  • Can P0 run? Finish[0] is false. Request[0] = [0, 0, 0]. [0, 0, 0] <= [1, 2, 0] (Work). YES.

  • Work = Work + Allocation[0] = [1, 2, 0] + [0, 1, 0] = [1, 3, 0]

  • Finish[0] = true

  • Can P1 run? Finish[1] is false. Request[1] = [2, 0, 2]. [2, 0, 2] <= [1, 3, 0] (Work)? No, R1 and R3 request too high.

  • Can P2 run? Finish[2] is false. Request[2] = [0, 0, 0]. [0, 0, 0] <= [1, 3, 0] (Work). YES.

  • Work = Work + Allocation[2] = [1, 3, 0] + [3, 0, 3] = [4, 3, 3]

  • Finish[2] = true

  • Can P3 run? Finish[3] is false. Request[3] = [1, 0, 0]. [1, 0, 0] <= [4, 3, 3] (Work). YES.

  • Work = Work + Allocation[3] = [4, 3, 3] + [2, 1, 1] = [6, 4, 4]

  • Finish[3] = true

  • Can P4 run? Finish[4] is false. Request[4] = [0, 0, 2]. [0, 0, 2] <= [6, 4, 4] (Work). YES.

  • Work = Work + Allocation[4] = [6, 4, 4] + [0, 0, 2] = [6, 4, 6]

  • Finish[4] = true

  • Iteration 2 (restart search for Finish[i] = false processes):

  • Only P1 remains with Finish[1] = false.

  • Can P1 run? Request[1] = [2, 0, 2]. [2, 0, 2] <= [6, 4, 6] (current Work)? YES\!

  • Work = Work + Allocation[1] = [6, 4, 6] + [2, 0, 0] = [8, 4, 6]

  • Finish[1] = true

  • Final Check: All Finish are now true.

  • Conclusion: In this example, no deadlock exists. All processes can eventually run to completion. If, however, P1's request could not have been satisfied even after all other processes conceptually released their resources, then P1 would have been identified as deadlocked.

  • Flashcards

  • Term: Multiple Instance Resource Type

  • Definition: Resource type with more than one available unit.

  • Term: Request Matrix

  • Definition: Matrix showing resources currently requested by each process.

  • Term: Work Vector (Detection)

  • Definition: Temporary vector representing available resources during detection algorithm, updated by released resources.

  • Term: Finish Array (Detection)

  • Definition: Boolean array; false indicates process is potentially deadlocked, true means it can complete.

  • Term: Deadlocked Process (Multiple Instances)

  • Definition: A process Pi for which Finish[i] remains false after the detection algorithm runs, indicating it's permanently blocked.

  • Memory Aids

  • Analogy: The Bus Depot Manager: Imagine a bus depot with multiple buses (R1, R2, R3) and many drivers (P0-P4). The manager (OS) needs to see if all drivers can eventually complete their routes, given the currently available buses and the drivers' current outstanding requests for specific buses.

  • "Check if Driver Can Go": The manager goes driver by driver. If a driver Pi is not yet on their way (Finish[i] is false) AND they can get the specific buses they currently need (Request[i] <= Work), the manager assumes they leave.

  • "Buses Come Back": When a driver leaves, their currently held buses are returned to the depot (Work = Work + Allocation[i]).

  • "Re-check Others": The manager then re-checks ALL drivers (even those previously passed over) with the newly available buses (Work).

  • "Stuck Drivers": After exhaustively checking everyone, any driver still marked false (Finish[i] is false) is stuck. They can't get the buses they need, even if everyone else who could leave has already left and returned their buses. These are your deadlocked drivers.

  • Key Difference from Banker's Avoidance: Remember, in Avoidance, the Banker's algorithm uses MAX to prevent an unsafe state. In Detection, it uses REQUEST to identify if a deadlock already exists by checking if processes can currently complete their requests.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎨 Fun Analogies

  • The Bus Depot Manager: Imagine a bus depot with multiple buses (R1, R2, R3) and many drivers (P0-P4). The manager (OS) needs to see if all drivers can eventually complete their routes, given the currently available buses and the drivers' current outstanding requests for specific buses.

      * "Check if Driver Can Go"

🧠 Other Memory Gems

  • When a driver leaves, their currently held buses are returned to the depot (Work = Work + Allocation[i]).
    * "Re-check Others"

🧠 Other Memory Gems

  • After exhaustively checking everyone, any driver still marked false (Finish[i] is false) is stuck. They can't get the buses they need, even if everyone else who could leave has already left and returned their buses. These are your deadlocked drivers.

    • Key Difference from Banker's Avoidance

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: Permanently Blocked

    Definition:

    Processes that cannot complete their execution even if all other (non-deadlocked) processes release their resources, indicating they are part of a deadlocked set.

  • Term: `Finish[i] = false`

    Definition:

    The definitive indicator that process Pi is part of a deadlocked set.

  • Term: Conclusion

    Definition:

    In this example, no deadlock exists. All processes can eventually run to completion. If, however, P1's request could not have been satisfied even after all other processes conceptually released their resources, then P1 would have been identified as deadlocked.

  • Term: Definition

    Definition:

    A process Pi for which Finish[i] remains false after the detection algorithm runs, indicating it's permanently blocked.

  • Term: Key Difference from Banker's Avoidance

    Definition:

    Remember, in Avoidance, the Banker's algorithm uses MAX to prevent an unsafe state. In Detection, it uses REQUEST to identify if a deadlock already exists by checking if processes can currently complete their requests.

Deadlock Detection Algorithms For Multiple Instances of Each Resource Type

This section addresses the more complex scenario of detecting deadlocks in systems where resource types can have multiple instances. Unlike the single-instance case, a cycle in the Resource-Allocation Graph (RAG) in this context does not necessarily imply a deadlock; it only indicates a possibility. A more robust algorithm, adapted from the Banker's Safety Algorithm, is required.