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Finite-Source Multiserver Queue with Preemptive Priorities

Finite-Source Multiserver Queue with Preemptive Priorities. Alexandre Brandwajn School of Engineering University of California, Santa Cruz alexb@cse.ucsc.edu. Plan. Motivation System considered Simple recurrent analysis Alternative method Classes on several priority levels Conclusions.

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Finite-Source Multiserver Queue with Preemptive Priorities

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  1. Finite-Source Multiserver Queue with Preemptive Priorities Alexandre Brandwajn School of Engineering University of California, Santa Cruz alexb@cse.ucsc.edu

  2. Plan • Motivation • System considered • Simple recurrent analysis • Alternative method • Classes on several priority levels • Conclusions

  3. Motivation • Priority service • computer application • Finite number of request sources • Multiple servers • Arbitrary number of classes

  4. System considered

  5. Assumptions • M servers • c classes • exponentially distributed • idle times • service demands • 1 class / priority level

  6. Assumptions • Class i, i = 1,…c • Ni sources • 1/li mean idle time • 1/mi mean service demand • Class 1 highest priority

  7. Simple recurrent analysis

  8. Simple recurrent analysis • One class at a time • state description (ni,li) • ni users of class i • li servers unavailable • servers • vanish ai(ni,li) • reappear bi(ni,li)

  9. Simple recurrent analysis • Approximation • ai(ni,li) ai(li) • bi(ni,li) bi(li) • two-dimensional birth & death • p(ni,li) • starting with class 1

  10. Simple recurrent analysis

  11. Simple recurrent analysis

  12. Results with 3 servers

  13. Results with 2 servers

  14. Parameter sets

  15. Set 5 with 3 servers

  16. Set 6 with 3 servers

  17. Set 7 with 2 servers

  18. Simple recurrent analysis • Generally within confidence intervals • occasionally more significant errors • more likely with longer service at higher priority • not systematic • growth with ratio of service times • peak and vanish

  19. Alternative method

  20. Alternative method

  21. Alternative approach • Pair (i, i+1) • State description (ni,ni+1,li) • ni, ni+1 users of class i and i+1 • li servers unavailable to pair

  22. Alternative approach • Servers • vanish ai(ni,li) • reappear bi(ni,li) • Pair (1,2) keep • other (i,i+1) keep results for i+1

  23. Set 6 with 3 servers

  24. Set 7 with 2 servers

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