Avoiding Register Overflow in the Bakery Algorithm

Computer systems are designed to make resources available to users and users may be interested in some resources more than others, therefore, a coordination scheme is required to satisfy the users’ requirements. This scheme may implement certain policies such as “never allocate more than X units of resource Z”. One policy that is of particular interest is the inability of users to access a single resource at the same time, which is called the problem of mutual exclusion. Resource management concerns the coordination and collaboration of users, and it is usually based on making a decision. In the case of mutual exclusion, that decision is about granting access to a resource. Therefore, mutual exclusion is useful for supporting resource access management. The first true solution to the mutual exclusion problem is known as the Bakery algorithm that does not rely on any lower-lever mutual exclusion. We examine the problem of register overflow in real-world implementations of the Bakery algorithm and present a variant algorithm named Bakery++ that prevents overflows from ever happening. Bakery++ avoids overflows without allowing a process to write into other processes’ memory and without using additional memory or complex arithmetic or redefining the operations and functions used in Bakery. Bakery++ is almost as simple as Bakery and it is straightforward to implement in real systems. With Bakery++, there is no reason to keep implementing Bakery in real computers because Bakery++ eliminates the probability of overflows and hence it is more practical than Bakery. Previous approaches to circumvent the problem of register overflow included introducing new variables or redefining the operations or functions used in the original Bakery algorithm, while Bakery++ avoids overflows by using simple conditional statements. The result is a new mutual exclusion algorithm that is guaranteed never to allow an overflow and it is simple, correct and easy to implement. Bakery++ has the same temporal and spatial complexities as the original Bakery. We have specified Bakery++ in PlusCal and we have used the TLC model checker to assert that Bakery++ maintains the mutual exclusion property and that it never allows an overflow.