8 problems

Uniform minimization conjecture. For every $q\geq 0$, the coefficient under the uniform policy equals the minimum over all edge-selection probability vectors:

Consider a redundancy system with $N$ parallel servers and jobs replicated to $d$ servers. Assume that the replica sizes are independent and identically distributed, and that the j…

Consider the redundancy-$d$ model with $K$ servers, FCFS scheduling, exponentially distributed service times, and identical copies. Let $\bar\ell$ denote the quantity determining t…

Consider a redundancy-$d$ system with $K$ servers, FCFS scheduling, exponentially distributed service times, and identical copies. Let $\bar\ell$ denote the quantity governing the…

Stability conjecture. For any work-conserving non-preferential scheduling policy, the system is stable if

NWU load conjecture. For NWU distributed speed variations, the loads satisfy

Stochastic-optimality conjecture. This stochastic optimality may hold for all values of $\lambda$.

Let a redundancy-$d$ system use processor sharing (PS), and let job sizes have general distributions. Write $\tilde{\rho}$ for the corresponding system load parameter. Sufficient s…