Summary of results

Our analysis of SBCS-ID and SBCS-CQ via DR will lead to the following conclusions:

• Both SBCS-ID and SBCS-CQ can provide an unbounded benefit, over Dedicated, to the short jobs while the long jobs are not penalized much by having their idle cycles stolen. The unbounded benefit is due to the increased stability region: SBCS-ID and SBCS-CQ can provide finite mean response time while Dedicated leads to infinite mean response time.
• SBCS-CQ is a superior policy to SBCS-ID from the perspective of both the short jobs and the long jobs.
• When the ``short'' jobs have shorter expected size than the ``long'' jobs, SBCS-ID and SBCS-CQ typically improves upon Dedicated with respect to the overall mean response time even at low load, $\rho_S$ (with an unbounded benefit at high load). However, when the ``short'' jobs have longer expected size than the ``long'' jobs (pathological case), cycle stealing can worsen the overall mean response time at low load, $\rho_S$ (although they can still provide an unbounded benefit at high load).
• The service demand variability of the long jobs has a surprisingly small effect on the mean response time of the short jobs under SBCS-ID but has a much larger effect under SBCS-CQ. Observe that when the long jobs have more variable sizes, long server provides more irregular help to the short jobs, which we expect worsens the response time of the short jobs.

We first characterize the stability regions under Dedicated, SBCS-ID, and SBCS-CQ in Section 5.4.2. In Section 5.4.3, we study the mean response time under these policies.