1. Mixed Criteria Packet Scheduling Chad R. Meiners Eric Torng

2. Problem Domain Packet Scheduling with Quality of Service Constraints –Finite Buffer Size –Fixed Ordering (FIFO) –Delivery Deadlines Maximized the criteria –Total value of successfully transmitted packets

3. Observation Single Criteria –Total value of successfully transmitted packets Assumption –All packets can be normalized to a single scale –Assumption validity depends on the nature of the network

4. Example Network (Internet) –File downloads Users care about download times Download has value even if it is delivered late Packet Criteria: Flow time –Real-time packets (Video conferencing) Users care about reliable communication Video frame has no value if delivered late Packet Criteria: Throughput with deadline

5. Two Scenarios Scenario One –Flow job f 1 of size x available at time 0 –Unit deadline jobs d 1 …d y where d i is available at time 0 and has deadline x + i Scenario Two –Jobs in the scenario one –Unit deadline jobs e 1 …e x where e i is available at time i-1 and has deadline i

6. Conflicting Priorities Flow jobs –Scenario 1 is fine –Scenario drops e jobs Deadline jobs –Scenario 1 delays f 1 by y units –Scenario 2 is fine Fixed Priorities lead to non-optimal scenarios f1f1 d 1 …d y f1f1 f1f1 e 1 …e x d 1 …d y f1f1 S1 S2

7. Mixing Criteria Is there anyway to avoid fixed priorities? Yes –Mixed Criteria Scheduling –Each type of packet is scheduled according to its own criteria –Priorities may be assigned when there is a true conflict Allows for scenerio 1 to give priority to flow jobs, while allowing for scenerio 2’s deadline job to take priority.

8. Deadflow Problem One Processor –Preemption allowed for all jobs Two sets of jobs –Flow jobs Release and processing time Total flow time –Deadline jobs Release and processing time Deadlines and weights Total Weighted Throughput –Priority is given to a deadline job if throughput is affected

9. Slacker Intuition –Schedule deadline jobs as late as possible –Fill idle times in the flow job schedule with deadline jobs Effectiveness –Works for scenario 1 and scenario 2 –Works for unit sized jobs –Does not work in general

10. Optimality and NP-Completeness Slacker is optimal when –Both flow jobs and deadline job are unit sized –Flow jobs are unit sized and deadline jobs have uniform weight Deadflow is NP-Complete –NP-Complete with a single deadline job and flow jobs of arbitrary size

11. Online Slacker Domain –Unit sized flow jobs and deadline jobs Idea –As jobs arrive at time t (re)apply Slacker to compute a set of accepted job and their new schedule from [t,  ) Effectiveness –The value of deadline jobs is at least half of optimal. –The total flow time of flow jobs is at most optimal

12. Future Work Determine if Deadflow is strongly NP- complete –Current proof is a reduction from Partition Approximations for Deadflow (offline and online) More analysis for bounded size flow jobs Tradeoff between deadline jobs and flow time.