Question

Prove that the wait-die and wound-wait protocols avoid deadlock and starvation.

Short answer

Wait-die and wound-wait are deadlock prevention methods that ensure older transactions are prioritized and younger transactions either wait or are rolled back to prevent cyclic waits. In case of continuous rollbacks, a transaction cannot be starved of resources because it will eventually become the oldest transaction in the system, and as such, is guaranteed to gain the necessary resources.

Step-by-step solution

Understanding the Wait-Die Protocol

In the wait-die method, if a transaction \(T_i\) requests a resource currently held by \(T_j\), the timestamp of \(T_i\) is checked. If the timestamp of \(T_i\) is older than or equal to \(T_j\) (i.e., \(T_i\) has been waiting for a longer time), \(T_i\) is allowed to wait for \(T_j\) to release the resource. This is because older transactions have higher priority. If \(T_i\) is younger than \(T_j\), \(T_i\) is rolled back or killed. So no younger transaction can wait for an older one, preventing any possibility of cyclic waits and thus, deadlocks.

Understanding Wound-Wait Protocol

The wound-wait strategy is a little different. Here, when a transaction \(T_i\) requests a resource held by \(T_j\), their timestamps are compared. If \(T_i\) is older than \(T_j\), \(T_j\) is rolled back or wounded to permit \(T_i\) to proceed; if \(T_i\) is younger, it's made to wait until the resource is available. This scheme prevents a younger transaction from waiting for an older one, thus preventing deadlocks.

Preventing Starvation

In both the wait-die and wound-wait strategies, an older transaction always has priority over the younger ones. In the case of continuous rollbacks, the rolled-back transactions are restarted with the same timestamp. Therefore, a transaction cannot be starved for resources because after a number of rollbacks, the transaction will become the oldest transaction in the system and will get all the resources it needs. This shows that the protocols prevent both deadlock and starvation.

Key concepts

Wait-Die Protocol

The Wait-Die Protocol is a concurrency control method that ensures older transactions have priority over younger ones, using timestamps as a key mechanism. When a transaction, say \(T_i\), wants a resource currently held by another transaction \(T_j\), their timestamps are compared. If \(T_i\) is older, it waits for \(T_j\) to release the resource. If \(T_i\) is younger, it is rolled back, or "killed."
This strategy effectively prevents deadlock by ensuring that no younger transaction can wait for an older one. Hence, cyclic waiting conditions are avoided. Moreover, since the rolled-back transaction retains its original timestamp, it can eventually become the oldest transaction in the system, gaining priority over others.

Wound-Wait Protocol

The Wound-Wait Protocol is slightly different from the Wait-Die Protocol but still focuses on using transaction timestamps to avoid deadlocks. Here, when a transaction \(T_i\) requests a resource held by a transaction \(T_j\), a comparison is made between their timestamps. If \(T_i\) is older, \(T_j\) must be rolled back or "wounded," hence allowing \(T_i\) to proceed. If \(T_i\) is younger, it is instructed to wait.
This strategy also prevents deadlock. Older transactions have the ability to wound younger ones, hence, stopping any possibility of a younger transaction holding resources needed by an older one for extended periods. Like in the Wait-Die Protocol, this mechanism also helps in cycling transactions through rollbacks without deadlocks.

Deadlock Prevention

Deadlock occurs when a set of transactions is unable to proceed because each is waiting for another transaction in the set to release a resource. Both the Wait-Die and Wound-Wait Protocols are designed to prevent this situation.
These protocols prevent the formation of cycles by ensuring that any waits occur in a unidirectional manner according to timestamps. For example, younger transactions cannot wait for older ones indefinitely, preventing the cycle of waits that constitutes a deadlock condition. This proactive handling of waits is crucial in preserving system functionality and efficiency.

Starvation Prevention

Starvation refers to a situation where a transaction waits indefinitely to obtain all the resources needed to proceed. In both the Wait-Die and Wound-Wait Protocols, starvation prevention is inherently built-in.
Transactions maintain their original timestamps even after being rolled back and restarted. Over time, these repeated rollbacks make a transaction the oldest in the system, granting it priority to access necessary resources. Thus, these protocols ensure that every transaction eventually becomes the most qualified to obtain resources, effectively preventing starvation by cycle-through prioritization.