Question

Consider the following snapshot of a system running n processes. Process i is holding $x_i$ instances of a resource R, for 1 $\le i\le$n. Courrently, all instances of R are occupied. Further, for all i, process i has placed a request for an additional $y_i$ instances while holding the $x_i$ instances it already has. There are exactly two processes p and q such that $y_p=y_q=0$. Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock?

Answer 1

Total number of processes = n
Process i is holding $x_i$ instances of a resource R for $1\le i\le$n.
Process i holding resource $x_i$ and additional required $y_i$. There are two processes p and q such that $y_p=y_q=0$
For no dead lock can occur
$x_p+x_q\ge (ma{x}_{k\ne p,q}{y}_k$)