Operating SystemsNecessary Conditions

Necessary Conditions for Deadlock

LevelIntermediate

Duration90 mins

TopicNecessary Conditions

2 / 5

Hold and Wait

The Second Pillar of Deadlock

Mutual exclusion alone cannot cause deadlock. A process that holds an exclusive resource and needs nothing else will eventually complete and release that resource. Deadlock requires something more: processes must hold resources while simultaneously waiting for additional resources. This second necessary condition—hold and wait—describes the resource accumulation pattern that enables deadlock.

Without hold and wait, no process would ever block while holding resources. Without blocked holders, no chain of waiting could form. Without waiting chains, no cycle could emerge. Hold and wait is the condition that transforms isolated resource holdings into interconnected webs of dependency that can entangle processes in permanent stalemate.

What You Will Learn

By the end of this page, you will deeply understand the hold-and-wait condition: what it means formally, why it arises naturally in concurrent programming, how it interacts with mutual exclusion to enable deadlock, and critically, how it can be prevented through strategic resource acquisition protocols.

The Hold and Wait Condition Defined

Formal Definition:

A process holding at least one resource is waiting to acquire additional resources that are currently held by other processes.

This definition has several critical components:

1. Current Holdings — The process already possesses at least one resource. It is not starting from a resource-free state.

2. Additional Requests — The process needs more resources beyond what it currently holds. Its computation cannot proceed with only its current allocations.

3. Blocking Wait — The additional resources are currently held by other processes, so the requesting process must wait.

4. Retention During Wait — Crucially, the process does not release its currently held resources while waiting. It holds and waits simultaneously.

The Coffman Formulation

Coffman et al. stated this condition as: "A process must be holding resources while waiting to acquire additional resources." The conjunction of holding AND waiting is essential—a process that releases its holdings before waiting, or one that holds without needing more, does not satisfy this condition.

Mathematical Formalization:

Let allocation function H(Pᵢ) denote the set of resources held by process Pᵢ, and W(Pᵢ) denote the set of resources Pᵢ is waiting to acquire.

The hold-and-wait condition is satisfied when:

∃Pᵢ: H(Pᵢ) ≠ ∅ ∧ W(Pᵢ) ≠ ∅

That is, there exists a process that has non-empty holdings AND non-empty wait set. The process simultaneously occupies resources and desires more.

State Characterization:

A process Pᵢ can be in one of four states with respect to hold-and-wait:

Holds Resources	Wants More	Contributes to Hold-and-Wait?
No	No	No — idle or resource-free
No	Yes	No — pure waiter (will block)
Yes	No	No — can proceed or will complete
Yes	Yes	Yes — hold and wait!

Why Hold and Wait Occurs

Hold and wait is not an aberration or poor programming practice—it arises naturally and often necessarily from the requirements of concurrent computation. Understanding why it occurs reveals why eliminating it requires significant effort.

Why Processes Hold While Waiting

•Incremental Resource Acquisition — Programs often cannot know all resources they'll need until runtime. A process parsing a file may discover it needs a database connection only after examining the file's contents.
•Efficiency Concerns — Acquiring and releasing resources has overhead. Holding resources across multiple operations is often more efficient than repeatedly acquiring and releasing them.
•Atomicity Requirements — Many operations require holding multiple resources simultaneously for correctness. Releasing one resource mid-operation would violate transactional semantics.
•Programming Simplicity — Incremental acquisition is natural to programmers. The alternative—determining all resources upfront—is cognitively demanding and sometimes impossible.
•Dynamic Workloads — The resources needed often depend on data discovered during execution. A web server handling a request doesn't know if it needs the cache lock until it finds a cache miss.

The Natural Pattern:

Consider a realistic scenario: a process transferring funds between bank accounts.

1. Acquire lock on source account    → Process now holds 1 resource
2. Verify sufficient balance         → Process still holds 1 resource
3. Acquire lock on destination acc   → Process wants 2nd resource
                                        If held by another: HOLD AND WAIT

This pattern is not a programming mistake—it's how transactions must work. The source account lock cannot be released before the destination is verified, or the transfer could partially complete. The process must hold the source lock while attempting to acquire the destination lock.

Legitimate Hold and Wait

Hold and wait is often semantically necessary. Banking, inventory management, and database transactions all require holding multiple resources atomically. The goal is not to eliminate hold and wait entirely (often impossible), but to manage it carefully or prevent deadlock through other means.

The Cascade Effect: How Hold and Wait Spreads

Hold and wait doesn't just affect the process in that state—it cascades through the system, potentially blocking many other processes and amplifying the deadlock risk.

Cascade Scenario:

Consider four processes and four resources:

Time T0:
  P1: Holds R1, requests R2    → R2 held by P2
  P2: Holds R2, runs (not waiting)
  P3: Runs (no resources)
  P4: Runs (no resources)

Time T1: P2 completes with R2
  P1: Acquires R2 (now holds R1, R2)
  P2: Exits
  P3: Requests R2 → WAIT (R2 held by P1)
  P4: Requests R1 → WAIT (R1 held by P1)

Time T2: P1 requests R3
  P1: Holds R1, R2, requests R3 → WAIT (R3 held by P5)
  P3: Waiting for R2 (held by P1)
  P4: Waiting for R1 (held by P1)
  
Result: P1 in hold-and-wait has blocked P3 and P4

P1's hold-and-wait state has created a chain: P1 → P5, and both P3 and P4 → P1. If P5 happens to wait for a resource held by P3 or P4, a cycle forms instantly.

Hold and Wait Multiplies Risk

Every process in a hold-and-wait state becomes a potential link in a deadlock chain. The more processes holding resources while waiting, the more potential edges exist in the resource allocation graph, and the greater the probability that a cycle will eventually form.

Resource Accumulation:

Processes in hold-and-wait tend to accumulate resources over time:

Start with 0 resources
Acquire R1 (hold 1)
Wait for R2, acquire R2 (hold 2)
Wait for R3, acquire R3 (hold 3) ...

Each acquisition potentially creates wait states for other processes. The longer a process holds resources, the more it blocks other processes, and the greater the cascade effect. This is why long-running transactions are particularly dangerous for deadlock.

Visualizing Hold and Wait

Resource allocation graphs provide a powerful visualization of hold-and-wait relationships. Understanding how to read these graphs is essential for deadlock analysis.

Resource Allocation Graph Notation:

Circles (Pᵢ): Processes
Rectangles (Rⱼ): Resource types
Dots inside rectangles: Resource instances
Arrow Pᵢ → Rⱼ: Request edge — Pᵢ is waiting for an instance of Rⱼ
Arrow Rⱼ → Pᵢ: Assignment edge — an instance of Rⱼ is allocated to Pᵢ

Identifying Hold and Wait:

A process is in hold-and-wait if and only if:

It has at least one incoming assignment edge (holds resource)
It has at least one outgoing request edge (wants resource)

resource_allocation_graph.txt
Resource Allocation Graph Example:
═══════════════════════════════════
 
                    ┌─────┐
                 ┌──│ R1  │──┐
                 │  │  •  │  │
    Request     │  └─────┘  │   Assignment
    ───────►    │           │   ───────►
                │           ▼
           ┌────┴────┐  ┌────────┐
           │   P1    │  │   P2   │
           └────┬────┘  └────┬───┘
                │           │
    Assignment  │           │    Request
    ◄───────    │           │    ◄───────
                │  ┌─────┐  │
                └─►│ R2  │◄─┘
                   │  •  │
                   └─────┘
 
ANALYSIS:
─────────
• P1: Has R2 (incoming assignment), wants R1 (outgoing request)
      → P1 is in HOLD-AND-WAIT state
      
• P2: Has R1 (incoming assignment), wants R2 (outgoing request)
      → P2 is in HOLD-AND-WAIT state
 
• Both processes are in hold-and-wait
• There is a cycle: P1 → R1 → P2 → R2 → P1
• With single-instance resources, this cycle = DEADLOCK

Graph Properties and Hold-and-Wait:

In a resource allocation graph:

Pure holder (no outgoing requests): Process will eventually release resources
Pure waiter (no held resources): Process will eventually acquire or can be considered non-blocking
Hold-and-wait (both edges): Dangerous state — potential deadlock participant

The presence of hold-and-wait states is a prerequisite for deadlock cycles. Without hold-and-wait, either:

All request edges would originate from pure waiters (no cycle possible through them), or
All holders would have no request edges (they complete and release)

Hold-and-wait creates the possibility for request chains to pass through holding processes, enabling cycles.

Real-World Hold and Wait Scenarios

Hold and wait manifests throughout software systems. Understanding common patterns helps recognize and prevent deadlock risks.

Scenario 1: Database Transactions

-- Transaction T1
BEGIN TRANSACTION;
SELECT * FROM accounts WHERE id = 1 FOR UPDATE;  -- Holds row lock on account 1
-- Processing...
SELECT * FROM accounts WHERE id = 2 FOR UPDATE;  -- Requests lock on account 2
                                                  -- If T2 holds it: HOLD AND WAIT

-- Transaction T2  
BEGIN TRANSACTION;
SELECT * FROM accounts WHERE id = 2 FOR UPDATE;  -- Holds row lock on account 2
-- Processing...
SELECT * FROM accounts WHERE id = 1 FOR UPDATE;  -- Requests lock on account 1
                                                  -- If T1 holds it: HOLD AND WAIT

Both transactions are in hold-and-wait. If they proceed concurrently with this ordering, deadlock results.

hold_wait_file_operations.py
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import threading
import time
 
# File locks simulated with Python locks
lock_config = threading.Lock()
lock_data = threading.Lock()
 
def updater_a():
    """Updates data based on configuration"""
    
    # Step 1: Acquire config lock to read configuration
    with lock_config:  # HOLDS lock_config
        print("Updater A: Acquired config lock")
        config = read_config()
        
        time.sleep(0.1)  # Simulate processing
        
        # Step 2: Need data lock to update data
        # HOLD AND WAIT: Holds lock_config, waits for lock_data
        with lock_data:
            print("Updater A: Acquired data lock")
            update_data(config)
 
def updater_b():
    """Updates configuration based on data"""
    
    # Step 1: Acquire data lock to read data
    with lock_data:  # HOLDS lock_data
        print("Updater B: Acquired data lock")
        data = read_data()
        
        time.sleep(0.1)  # Simulate processing
        
        # Step 2: Need config lock to update config
        # HOLD AND WAIT: Holds lock_data, waits for lock_config
        with lock_config:
            print("Updater B: Acquired config lock")
            update_config(data)
 
# If run concurrently, these threads may deadlock
# Thread A: holds config, waits for data
# Thread B: holds data, waits for config
# DEADLOCK!
 
thread_a = threading.Thread(target=updater_a)
thread_b = threading.Thread(target=updater_b)
 
thread_a.start()
thread_b.start()
 
# These joins may never complete
thread_a.join()
thread_b.join()

Scenario 3: Operating System Kernel

The kernel frequently encounters hold-and-wait:

Process: Page fault handler

1. Holds: Address space lock (to prevent concurrent mmap)
2. Needs: Free page from physical memory allocator
3. Allocator locked by memory reclaimer

Reclaimer:
1. Holds: Allocator lock (modifying free page list)
2. Needs: Address space lock (to unmap pages)

→ Potential deadlock if not carefully ordered

Kernel developers must meticulously analyze resource acquisition patterns to prevent such scenarios. Lock ordering rules ("always acquire the address space lock before the allocator lock") are essential in kernel code.

Nested Lock Acquisition

The pattern of acquiring locks while holding other locks—nested or hierarchical lock acquisition—is the quintessential hold-and-wait pattern. Every nested lock acquisition is a potential deadlock setup. Careful lock ordering and design is essential.

Preventing Hold and Wait

Unlike mutual exclusion, hold and wait can often be prevented through careful protocol design. Eliminating this condition is one of the primary strategies for deadlock prevention.

Strategies to Prevent Hold and Wait

•All-at-Once Acquisition — Require processes to request all needed resources before execution begins. If all resources are available, grant them all; otherwise, grant none and make the process wait. This ensures no process ever holds while waiting.
•Release Before Request — Before requesting a new resource, a process must release all currently held resources. It then requests the resources it still needs (including the released ones). This ensures the process is never holding while waiting.
•Two-Phase Protocol — Phase 1 (Growing): Acquire all needed resources without releasing any. Phase 2 (Shrinking): Release resources without acquiring new ones. A process can never be in hold-and-wait because once it starts releasing, it never acquires again.
•Lock Timeout with Retry — If a process cannot acquire a resource within a timeout, it releases all held resources and retries from the beginning. This breaks the static hold-and-wait pattern through dynamic release.

all_at_once_acquisition.c
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#include <pthread.h>
#include <stdbool.h>
 
// Global resource manager
pthread_mutex_t resource_manager_lock = PTHREAD_MUTEX_INITIALIZER;
 
// Resource availability array
bool resources[MAX_RESOURCES];
int num_resources;
 
// Request all resources at once
bool request_all_resources(int process_id, int *needed, int count) {
    pthread_mutex_lock(&resource_manager_lock);
    
    // Check if ALL needed resources are available
    for (int i = 0; i < count; i++) {
        if (!resources[needed[i]]) {
            // At least one resource unavailable - request denied
            pthread_mutex_unlock(&resource_manager_lock);
            return false;  // Process must wait and retry
        }
    }
    
    // All resources available - allocate them all atomically
    for (int i = 0; i < count; i++) {
        resources[needed[i]] = false;  // Mark as allocated
        printf("Process %d: Acquired resource %d\n", process_id, needed[i]);
    }
    
    pthread_mutex_unlock(&resource_manager_lock);
    return true;  // Process received all resources, can proceed
}
 
// Release all resources at once
void release_all_resources(int process_id, int *held, int count) {
    pthread_mutex_lock(&resource_manager_lock);
    
    for (int i = 0; i < count; i++) {
        resources[held[i]] = true;  // Mark as available
        printf("Process %d: Released resource %d\n", process_id, held[i]);
    }
    
    pthread_mutex_unlock(&resource_manager_lock);
    // Signal waiting processes to retry their requests
    broadcast_resource_available();
}
 
// Usage example - no hold-and-wait possible
void process_work(int process_id) {
    int needed[] = {RESOURCE_A, RESOURCE_B, RESOURCE_C};
    int count = 3;
    
    // Keep trying until all resources obtained
    while (!request_all_resources(process_id, needed, count)) {
        // Wait and retry - no resources held during wait
        wait_for_resources();
    }
    
    // Now holds all needed resources - do work
    do_critical_work();
    
    // Release all at once
    release_all_resources(process_id, needed, count);
}

Trade-offs of Preventing Hold and Wait:

Strategy	Advantages	Disadvantages
All-at-Once	Simple; guarantees no hold-and-wait	May not know resources needed upfront; reduces resource utilization; possible starvation
Release Before Request	Flexible; can adapt to runtime needs	Complex rollback; wasted work; possible livelock
Two-Phase Protocol	Clear structure; proven safe	Requires planning phases; not always applicable
Timeout with Retry	Breaks deadlock; self-healing	Wasted computation; complex retry logic; possible livelock

Practical Challenges in Preventing Hold and Wait

While preventing hold and wait is theoretically attractive, practical implementation faces significant challenges that explain why it's not universally applied.

Implementation Challenges

•Unknown Future Needs — Many programs cannot predict their resource requirements until runtime. A compiler doesn't know how many temporary files it needs until it parses the source code.
•Over-Allocation — Requesting all potentially needed resources upfront leads to over-allocation. A process that might need a network connection holds it even if the code path requiring it is never executed.
•Reduced Concurrency — Holding resources longer than strictly necessary (waiting for all to be available) reduces system concurrency and throughput.
•Starvation Risk — If a process needs many resources, it may never find them all simultaneously available, leading to indefinite waiting (starvation).
•Rollback Complexity — Release-before-request strategies require process state to be rolled back, which is complex or impossible for I/O operations.
•Work Loss — Releasing resources and re-acquiring them wastes computation performed while holding the resources.

The All-at-Once Dilemma:

Consider a database query processor:

SELECT * FROM orders o
JOIN customers c ON o.customer_id = c.id
WHERE c.region = 'WEST'

The optimizer determines the execution plan:

Scan customers index for region='WEST'
For each matching customer, probe orders table

What resources are needed?

Lock on customers table? (Maybe partial, depends on data)
Lock on orders table? (Depends on matching customer IDs)
Memory for hash join? (Depends on customer count)
Disk I/O buffers? (Depends on buffer pool state)

The actual resources needed depend on data content, statistics, and runtime conditions. Declaring all resources upfront would require massive over-allocation or special query planning.

Practical Approach

In practice, systems often accept hold-and-wait but prevent deadlock through other means: lock ordering (breaking circular wait), timeout and retry with intelligent backoff, or deadlock detection and recovery. Hold-and-wait prevention is valuable for specific subsystems with predictable resource needs.

Hold and Wait in Distributed Systems

Hold and wait becomes even more challenging in distributed systems, where resources are spread across multiple nodes and network delays complicate coordination.

Distributed Lock Acquisition:

Node A (New York):     Node B (London):      Node C (Tokyo):
─────────────────     ─────────────────     ───────────────
     Lock L1               Lock L2              Lock L3
     
Transaction T1:
1. Acquire L1 (local)     → Holds L1
2. Request L2 on Node B   → Network RTT 70ms
                          → Wait if L2 held
3. Request L3 on Node C   → Network RTT 100ms
                          → Wait if L3 held

During steps 2-3: T1 is in HOLD-AND-WAIT state
Lock L1 is held by T1 for entire duration of network calls

Network latency extends hold-and-wait duration dramatically. A local lock acquisition might take microseconds; a distributed acquisition might take hundreds of milliseconds. Resources are held for much longer, increasing deadlock risk.

Two-Phase Commit and Hold-and-Wait:

The two-phase commit protocol inherently creates extended hold-and-wait:

Phase 1 (Prepare):

Coordinator asks all participants to prepare
Each participant acquires locks and writes to redo log
All participants HOLD resources, waiting for coordinator

Phase 2 (Commit/Abort):

Coordinator decides commit or abort
Participants execute and release locks

Between phases, all participants are in hold-and-wait. If the coordinator fails, participants may hold locks indefinitely (the blocking problem of 2PC). This is a fundamental limitation related to hold-and-wait in distributed transactions.

Distributed Deadlock Detection

In distributed systems, detecting hold-and-wait cycles is complicated by the lack of global state. No single node knows what resources processes on other nodes hold and wait for. Distributed deadlock detection requires collecting information from multiple nodes, which is expensive and can produce false positives due to message delays.

Modern Approaches:

Distributed databases like Google Spanner and CockroachDB use various techniques:

Wound-Wait and Wait-Die: Older transactions wound (abort) younger ones, or younger transactions die (abort themselves). This prevents cycles by ordering transactions.
Heartbeats and Timeouts: If a distributed lock isn't confirmed within timeout, abort and retry. Breaks hold-and-wait at the cost of work loss.
Optimistic Concurrency Control: Don't acquire locks during read phase. Validate at commit time. Reduces hold-and-wait duration significantly.
Centralized Lock Managers: Use a global lock manager to detect and prevent circular waits directly.

Summary: Hold and Wait as Deadlock Condition

We have explored hold and wait—the second necessary condition for deadlock—in comprehensive depth. Let's consolidate the key insights:

Key Takeaways

•Hold and Wait Defined — A process holds at least one resource while waiting to acquire additional resources held by other processes.
•Arises Naturally — Incremental resource acquisition, efficiency concerns, and atomicity requirements make hold-and-wait common in concurrent programs.
•The Cascade Effect — Processes in hold-and-wait block other processes, potentially creating long chains that increase deadlock probability.
•Visualized in Graphs — In resource allocation graphs, hold-and-wait manifests as processes with both incoming assignment edges and outgoing request edges.
•Can Be Prevented — Unlike mutual exclusion, hold-and-wait can often be prevented through all-at-once acquisition, release-before-request, or two-phase protocols.
•Practical Challenges — Prevention is complicated by unknown future needs, over-allocation, reduced concurrency, and rollback complexity.
•Distributed Complexity — Network latency extends hold-and-wait duration; distributed detection requires expensive coordination.

What's Next:

Mutual exclusion and hold-and-wait together still cannot guarantee deadlock—if resources could be forcibly taken from processes, the waiting chains could be broken. The next page examines the no preemption condition: why resources are not forcibly reclaimed, how this interacts with the previous conditions, and when preemption is feasible as a deadlock prevention strategy.

Page Complete

You now possess a thorough understanding of hold and wait as a deadlock condition: its definition, natural occurrence, cascade effects, visualization, prevention strategies, practical challenges, and distributed system implications. Next, we examine the no-preemption condition to complete our analysis of how resource retention enables deadlock.

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Operating SystemsNecessary Conditions

Necessary Conditions for Deadlock

LevelIntermediate

Duration90 mins

TopicNecessary Conditions

2 / 5

Hold and Wait

The Second Pillar of Deadlock

What You Will Learn

The Hold and Wait Condition Defined

Formal Definition:

A process holding at least one resource is waiting to acquire additional resources that are currently held by other processes.

This definition has several critical components:

1. Current Holdings — The process already possesses at least one resource. It is not starting from a resource-free state.

2. Additional Requests — The process needs more resources beyond what it currently holds. Its computation cannot proceed with only its current allocations.

3. Blocking Wait — The additional resources are currently held by other processes, so the requesting process must wait.

4. Retention During Wait — Crucially, the process does not release its currently held resources while waiting. It holds and waits simultaneously.

The Coffman Formulation

Mathematical Formalization:

Let allocation function H(Pᵢ) denote the set of resources held by process Pᵢ, and W(Pᵢ) denote the set of resources Pᵢ is waiting to acquire.

The hold-and-wait condition is satisfied when:

∃Pᵢ: H(Pᵢ) ≠ ∅ ∧ W(Pᵢ) ≠ ∅

That is, there exists a process that has non-empty holdings AND non-empty wait set. The process simultaneously occupies resources and desires more.

State Characterization:

A process Pᵢ can be in one of four states with respect to hold-and-wait:

Holds Resources	Wants More	Contributes to Hold-and-Wait?
No	No	No — idle or resource-free
No	Yes	No — pure waiter (will block)
Yes	No	No — can proceed or will complete
Yes	Yes	Yes — hold and wait!

Why Hold and Wait Occurs

Why Processes Hold While Waiting

•Incremental Resource Acquisition — Programs often cannot know all resources they'll need until runtime. A process parsing a file may discover it needs a database connection only after examining the file's contents.
•Efficiency Concerns — Acquiring and releasing resources has overhead. Holding resources across multiple operations is often more efficient than repeatedly acquiring and releasing them.
•Atomicity Requirements — Many operations require holding multiple resources simultaneously for correctness. Releasing one resource mid-operation would violate transactional semantics.
•Programming Simplicity — Incremental acquisition is natural to programmers. The alternative—determining all resources upfront—is cognitively demanding and sometimes impossible.
•Dynamic Workloads — The resources needed often depend on data discovered during execution. A web server handling a request doesn't know if it needs the cache lock until it finds a cache miss.

The Natural Pattern:

Consider a realistic scenario: a process transferring funds between bank accounts.

1. Acquire lock on source account    → Process now holds 1 resource
2. Verify sufficient balance         → Process still holds 1 resource
3. Acquire lock on destination acc   → Process wants 2nd resource
                                        If held by another: HOLD AND WAIT

Legitimate Hold and Wait

The Cascade Effect: How Hold and Wait Spreads

Hold and wait doesn't just affect the process in that state—it cascades through the system, potentially blocking many other processes and amplifying the deadlock risk.

Cascade Scenario:

Consider four processes and four resources:

Time T0:
  P1: Holds R1, requests R2    → R2 held by P2
  P2: Holds R2, runs (not waiting)
  P3: Runs (no resources)
  P4: Runs (no resources)

Time T1: P2 completes with R2
  P1: Acquires R2 (now holds R1, R2)
  P2: Exits
  P3: Requests R2 → WAIT (R2 held by P1)
  P4: Requests R1 → WAIT (R1 held by P1)

Time T2: P1 requests R3
  P1: Holds R1, R2, requests R3 → WAIT (R3 held by P5)
  P3: Waiting for R2 (held by P1)
  P4: Waiting for R1 (held by P1)
  
Result: P1 in hold-and-wait has blocked P3 and P4

P1's hold-and-wait state has created a chain: P1 → P5, and both P3 and P4 → P1. If P5 happens to wait for a resource held by P3 or P4, a cycle forms instantly.

Hold and Wait Multiplies Risk

Resource Accumulation:

Processes in hold-and-wait tend to accumulate resources over time:

Start with 0 resources
Acquire R1 (hold 1)
Wait for R2, acquire R2 (hold 2)
Wait for R3, acquire R3 (hold 3) ...

Visualizing Hold and Wait

Resource allocation graphs provide a powerful visualization of hold-and-wait relationships. Understanding how to read these graphs is essential for deadlock analysis.

Resource Allocation Graph Notation:

Circles (Pᵢ): Processes
Rectangles (Rⱼ): Resource types
Dots inside rectangles: Resource instances
Arrow Pᵢ → Rⱼ: Request edge — Pᵢ is waiting for an instance of Rⱼ
Arrow Rⱼ → Pᵢ: Assignment edge — an instance of Rⱼ is allocated to Pᵢ

Identifying Hold and Wait:

A process is in hold-and-wait if and only if:

It has at least one incoming assignment edge (holds resource)
It has at least one outgoing request edge (wants resource)

resource_allocation_graph.txt
Resource Allocation Graph Example:
═══════════════════════════════════
 
                    ┌─────┐
                 ┌──│ R1  │──┐
                 │  │  •  │  │
    Request     │  └─────┘  │   Assignment
    ───────►    │           │   ───────►
                │           ▼
           ┌────┴────┐  ┌────────┐
           │   P1    │  │   P2   │
           └────┬────┘  └────┬───┘
                │           │
    Assignment  │           │    Request
    ◄───────    │           │    ◄───────
                │  ┌─────┐  │
                └─►│ R2  │◄─┘
                   │  •  │
                   └─────┘
 
ANALYSIS:
─────────
• P1: Has R2 (incoming assignment), wants R1 (outgoing request)
      → P1 is in HOLD-AND-WAIT state
      
• P2: Has R1 (incoming assignment), wants R2 (outgoing request)
      → P2 is in HOLD-AND-WAIT state
 
• Both processes are in hold-and-wait
• There is a cycle: P1 → R1 → P2 → R2 → P1
• With single-instance resources, this cycle = DEADLOCK

Graph Properties and Hold-and-Wait:

In a resource allocation graph:

Pure holder (no outgoing requests): Process will eventually release resources
Pure waiter (no held resources): Process will eventually acquire or can be considered non-blocking
Hold-and-wait (both edges): Dangerous state — potential deadlock participant

The presence of hold-and-wait states is a prerequisite for deadlock cycles. Without hold-and-wait, either:

All request edges would originate from pure waiters (no cycle possible through them), or
All holders would have no request edges (they complete and release)

Hold-and-wait creates the possibility for request chains to pass through holding processes, enabling cycles.

Real-World Hold and Wait Scenarios

Hold and wait manifests throughout software systems. Understanding common patterns helps recognize and prevent deadlock risks.

Scenario 1: Database Transactions

-- Transaction T1
BEGIN TRANSACTION;
SELECT * FROM accounts WHERE id = 1 FOR UPDATE;  -- Holds row lock on account 1
-- Processing...
SELECT * FROM accounts WHERE id = 2 FOR UPDATE;  -- Requests lock on account 2
                                                  -- If T2 holds it: HOLD AND WAIT

-- Transaction T2  
BEGIN TRANSACTION;
SELECT * FROM accounts WHERE id = 2 FOR UPDATE;  -- Holds row lock on account 2
-- Processing...
SELECT * FROM accounts WHERE id = 1 FOR UPDATE;  -- Requests lock on account 1
                                                  -- If T1 holds it: HOLD AND WAIT

Both transactions are in hold-and-wait. If they proceed concurrently with this ordering, deadlock results.

hold_wait_file_operations.py
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import threading
import time
 
# File locks simulated with Python locks
lock_config = threading.Lock()
lock_data = threading.Lock()
 
def updater_a():
    """Updates data based on configuration"""
    
    # Step 1: Acquire config lock to read configuration
    with lock_config:  # HOLDS lock_config
        print("Updater A: Acquired config lock")
        config = read_config()
        
        time.sleep(0.1)  # Simulate processing
        
        # Step 2: Need data lock to update data
        # HOLD AND WAIT: Holds lock_config, waits for lock_data
        with lock_data:
            print("Updater A: Acquired data lock")
            update_data(config)
 
def updater_b():
    """Updates configuration based on data"""
    
    # Step 1: Acquire data lock to read data
    with lock_data:  # HOLDS lock_data
        print("Updater B: Acquired data lock")
        data = read_data()
        
        time.sleep(0.1)  # Simulate processing
        
        # Step 2: Need config lock to update config
        # HOLD AND WAIT: Holds lock_data, waits for lock_config
        with lock_config:
            print("Updater B: Acquired config lock")
            update_config(data)
 
# If run concurrently, these threads may deadlock
# Thread A: holds config, waits for data
# Thread B: holds data, waits for config
# DEADLOCK!
 
thread_a = threading.Thread(target=updater_a)
thread_b = threading.Thread(target=updater_b)
 
thread_a.start()
thread_b.start()
 
# These joins may never complete
thread_a.join()
thread_b.join()

Scenario 3: Operating System Kernel

The kernel frequently encounters hold-and-wait:

Process: Page fault handler

1. Holds: Address space lock (to prevent concurrent mmap)
2. Needs: Free page from physical memory allocator
3. Allocator locked by memory reclaimer

Reclaimer:
1. Holds: Allocator lock (modifying free page list)
2. Needs: Address space lock (to unmap pages)

→ Potential deadlock if not carefully ordered

Nested Lock Acquisition

Preventing Hold and Wait

Unlike mutual exclusion, hold and wait can often be prevented through careful protocol design. Eliminating this condition is one of the primary strategies for deadlock prevention.

Strategies to Prevent Hold and Wait

•All-at-Once Acquisition — Require processes to request all needed resources before execution begins. If all resources are available, grant them all; otherwise, grant none and make the process wait. This ensures no process ever holds while waiting.
•Release Before Request — Before requesting a new resource, a process must release all currently held resources. It then requests the resources it still needs (including the released ones). This ensures the process is never holding while waiting.
•Two-Phase Protocol — Phase 1 (Growing): Acquire all needed resources without releasing any. Phase 2 (Shrinking): Release resources without acquiring new ones. A process can never be in hold-and-wait because once it starts releasing, it never acquires again.
•Lock Timeout with Retry — If a process cannot acquire a resource within a timeout, it releases all held resources and retries from the beginning. This breaks the static hold-and-wait pattern through dynamic release.

all_at_once_acquisition.c
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#include <pthread.h>
#include <stdbool.h>
 
// Global resource manager
pthread_mutex_t resource_manager_lock = PTHREAD_MUTEX_INITIALIZER;
 
// Resource availability array
bool resources[MAX_RESOURCES];
int num_resources;
 
// Request all resources at once
bool request_all_resources(int process_id, int *needed, int count) {
    pthread_mutex_lock(&resource_manager_lock);
    
    // Check if ALL needed resources are available
    for (int i = 0; i < count; i++) {
        if (!resources[needed[i]]) {
            // At least one resource unavailable - request denied
            pthread_mutex_unlock(&resource_manager_lock);
            return false;  // Process must wait and retry
        }
    }
    
    // All resources available - allocate them all atomically
    for (int i = 0; i < count; i++) {
        resources[needed[i]] = false;  // Mark as allocated
        printf("Process %d: Acquired resource %d\n", process_id, needed[i]);
    }
    
    pthread_mutex_unlock(&resource_manager_lock);
    return true;  // Process received all resources, can proceed
}
 
// Release all resources at once
void release_all_resources(int process_id, int *held, int count) {
    pthread_mutex_lock(&resource_manager_lock);
    
    for (int i = 0; i < count; i++) {
        resources[held[i]] = true;  // Mark as available
        printf("Process %d: Released resource %d\n", process_id, held[i]);
    }
    
    pthread_mutex_unlock(&resource_manager_lock);
    // Signal waiting processes to retry their requests
    broadcast_resource_available();
}
 
// Usage example - no hold-and-wait possible
void process_work(int process_id) {
    int needed[] = {RESOURCE_A, RESOURCE_B, RESOURCE_C};
    int count = 3;
    
    // Keep trying until all resources obtained
    while (!request_all_resources(process_id, needed, count)) {
        // Wait and retry - no resources held during wait
        wait_for_resources();
    }
    
    // Now holds all needed resources - do work
    do_critical_work();
    
    // Release all at once
    release_all_resources(process_id, needed, count);
}

Trade-offs of Preventing Hold and Wait:

Strategy	Advantages	Disadvantages
All-at-Once	Simple; guarantees no hold-and-wait	May not know resources needed upfront; reduces resource utilization; possible starvation
Release Before Request	Flexible; can adapt to runtime needs	Complex rollback; wasted work; possible livelock
Two-Phase Protocol	Clear structure; proven safe	Requires planning phases; not always applicable
Timeout with Retry	Breaks deadlock; self-healing	Wasted computation; complex retry logic; possible livelock

Practical Challenges in Preventing Hold and Wait

While preventing hold and wait is theoretically attractive, practical implementation faces significant challenges that explain why it's not universally applied.

Implementation Challenges

•Unknown Future Needs — Many programs cannot predict their resource requirements until runtime. A compiler doesn't know how many temporary files it needs until it parses the source code.
•Over-Allocation — Requesting all potentially needed resources upfront leads to over-allocation. A process that might need a network connection holds it even if the code path requiring it is never executed.
•Reduced Concurrency — Holding resources longer than strictly necessary (waiting for all to be available) reduces system concurrency and throughput.
•Starvation Risk — If a process needs many resources, it may never find them all simultaneously available, leading to indefinite waiting (starvation).
•Rollback Complexity — Release-before-request strategies require process state to be rolled back, which is complex or impossible for I/O operations.
•Work Loss — Releasing resources and re-acquiring them wastes computation performed while holding the resources.

The All-at-Once Dilemma:

Consider a database query processor:

SELECT * FROM orders o
JOIN customers c ON o.customer_id = c.id
WHERE c.region = 'WEST'

The optimizer determines the execution plan:

Scan customers index for region='WEST'
For each matching customer, probe orders table

What resources are needed?

Lock on customers table? (Maybe partial, depends on data)
Lock on orders table? (Depends on matching customer IDs)
Memory for hash join? (Depends on customer count)
Disk I/O buffers? (Depends on buffer pool state)

The actual resources needed depend on data content, statistics, and runtime conditions. Declaring all resources upfront would require massive over-allocation or special query planning.

Practical Approach

Hold and Wait in Distributed Systems

Hold and wait becomes even more challenging in distributed systems, where resources are spread across multiple nodes and network delays complicate coordination.

Distributed Lock Acquisition:

Node A (New York):     Node B (London):      Node C (Tokyo):
─────────────────     ─────────────────     ───────────────
     Lock L1               Lock L2              Lock L3
     
Transaction T1:
1. Acquire L1 (local)     → Holds L1
2. Request L2 on Node B   → Network RTT 70ms
                          → Wait if L2 held
3. Request L3 on Node C   → Network RTT 100ms
                          → Wait if L3 held

During steps 2-3: T1 is in HOLD-AND-WAIT state
Lock L1 is held by T1 for entire duration of network calls

Two-Phase Commit and Hold-and-Wait:

The two-phase commit protocol inherently creates extended hold-and-wait:

Phase 1 (Prepare):

Coordinator asks all participants to prepare
Each participant acquires locks and writes to redo log
All participants HOLD resources, waiting for coordinator

Phase 2 (Commit/Abort):

Coordinator decides commit or abort
Participants execute and release locks

Distributed Deadlock Detection

Modern Approaches:

Distributed databases like Google Spanner and CockroachDB use various techniques:

Wound-Wait and Wait-Die: Older transactions wound (abort) younger ones, or younger transactions die (abort themselves). This prevents cycles by ordering transactions.
Heartbeats and Timeouts: If a distributed lock isn't confirmed within timeout, abort and retry. Breaks hold-and-wait at the cost of work loss.
Optimistic Concurrency Control: Don't acquire locks during read phase. Validate at commit time. Reduces hold-and-wait duration significantly.
Centralized Lock Managers: Use a global lock manager to detect and prevent circular waits directly.

Summary: Hold and Wait as Deadlock Condition

We have explored hold and wait—the second necessary condition for deadlock—in comprehensive depth. Let's consolidate the key insights:

Key Takeaways

•Hold and Wait Defined — A process holds at least one resource while waiting to acquire additional resources held by other processes.
•Arises Naturally — Incremental resource acquisition, efficiency concerns, and atomicity requirements make hold-and-wait common in concurrent programs.
•The Cascade Effect — Processes in hold-and-wait block other processes, potentially creating long chains that increase deadlock probability.
•Visualized in Graphs — In resource allocation graphs, hold-and-wait manifests as processes with both incoming assignment edges and outgoing request edges.
•Can Be Prevented — Unlike mutual exclusion, hold-and-wait can often be prevented through all-at-once acquisition, release-before-request, or two-phase protocols.
•Practical Challenges — Prevention is complicated by unknown future needs, over-allocation, reduced concurrency, and rollback complexity.
•Distributed Complexity — Network latency extends hold-and-wait duration; distributed detection requires expensive coordination.

What's Next:

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