Summary of results

Our analysis yields many interesting results concerning cycle stealing. While cycle stealing obviously benefits the beneficiary jobs and hurts the donor jobs, we find that when $\rho_B \geq 1$, cycle stealing is profitable overall even under significant switching times, as it may ensure stability of the beneficiary queue. For $\rho_B < 1$, we define load-regions under which cycle stealing pays. We find that in general the switching time is only prohibitive when it is large compared with $\mbox{{\bf\sf E}}\left[ X_D \right]$. Under zero switching times, cycle stealing always pays.

Two counterintuitive results are that when $\rho_B < 1$, the mean response time of the beneficiary jobs is surprisingly insensitive to the switching time, and also insensitive to the variability of the donor job size distribution. Even when the variability of the donor job sizes is very high, and donor help thus is very bursty, the beneficiary jobs still enjoy significant benefits.

Our analysis also allows us to investigate characteristics of the beneficiary and donor side thresholds, $N_B^{th}$ and $N_D^{th}$, both with respect to their impact on stability and their impact on mean response time. With respect to beneficiary stability, we find that $N_B^{th}$ has no effect, while increasing $N_D^{th}$ increases the stability region. Donor stability is not affected by either threshold. With respect to overall mean response time, we find that mean response time is far more sensitive to changes in $N_D^{th}$ than to changes in $N_B^{th}$. We find the optimal value of $N_B^{th}$ tends to be well above 1. The reason is that increasing $N_B^{th}$ does not appreciably diminish beneficiary gain, but it does alleviate donor pain. We find that the optimal setting of $N_B^{th}$ is an increasing function of $\rho _B$, $\rho_D$, and switching times. By contrast, we find that the optimal value of $N_D^{th}$ is often close to 1, provided $\rho_B < 1$. Increasing $N_D^{th}$ significantly hurts the donor, although it may provide significant help to the beneficiary if $\rho _B$ is high. We find that the optimal $N_D^{th}$ is not a monotonic function of $\rho_D$, but is an increasing function of $\rho _B$ and switching times.