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Scheduling task with heavy tail distributions

Scheduling task with heavy tail distributions. Eddie Aronovich. Heavy tail dist. Some properties… . Infinitive variance (for infinitive mean) Tiny fraction (usually < 1%) requests comprise over half of total load !. Some more properties.

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Scheduling task with heavy tail distributions

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  1. Scheduling task with heavy tail distributions Eddie Aronovich

  2. Heavy tail dist.

  3. Some properties… • Infinitive variance (for infinitive mean) • Tiny fraction (usually < 1%) requests comprise over half of total load !

  4. Some more properties • Expectation paradox:E[X|X>k] ~ k(declining hazard rate) • Mass-count disparity (for n>2)

  5. What is it good for ? • Files size (in both – file systems & web) & data files transferred over the net • I/O traces of fs, disk etc. • Process time, Session time • Name servers & popularity of web sites

  6. Why are they difficult to deal with ? • M/G/1 queue length is proportional to second moment of service time. • Have no closed form Laplace transformation => systems must be numerically evaluated

  7. Some implementations… • Scheduling web servers • Routing & Switching • Load sensitive routing

  8. How web server works ? • Name resolution • Session establishments • Request • Reply • End of session The network is the bottleneck !

  9. Some important knowledge • Each computer is identified by address. • Each application is a computer is identified by port number Socket = {ip-addr, port number} Session = source socket : dest socket File descriptor – identifies socket / session

  10. Default Linux model Socket1 {process} Socket2 {process} Socket3 {process} Socket4 {process} fairly feed single priority queue NIC

  11. Shortest Remaining Processing Time (proposed model) Socket1 {process} {1st prio. Que.} Socket2 {process} {2nd prio. Que.} Socket3 {process} Socket4 {process} {3rd prio. Que.} feed first feed second NIC feed third

  12. Size cut-offs The following are rules-of-thumb: • 50% of request <= X1 • 1%-5% of requests > Xn • The middle cut are less important

  13. Evaluated metrics • Mean response time • Mean slowdown (normalized response time) • Mean response time as a function of request size

  14. Some results….

  15. Why does it work ? • We know the file size (reply) a-priory • Short requests should wait short time • Linux is easy to be changed

  16. What is next ? • Distributed processing • Task assigment • TAGS

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