Queuing Systems: Lecture 4 Amedeo odoni October 22. 2001
Queuing Systems: Lecture 4 Amedeo R. Odoni October 22, 2001
Quiz #1: October 29 Open book, 85 minutes( start 10: 30 Chapter 4 coverage: Sections 4. 1through 4.7(inclusive); Section 4.9 (skim through 4.9.4 Review Problem set 3 Review some old quizzes
Quiz #1: October 29 • Open book, 85 minutes (start 10:30) • Chapter 4 coverage: Sections 4.1through 4.7 (inclusive); Section 4.9 (skim through 4.9.4) • Review Problem Set 3 • Review some old quizzes
A few additional items A simpler(than in the book derivation of the expression for L for M/G/1 systems is rovided in a note on the website: it assumes FiFo service A derivation of expression(4.113)in the book for M/M/1 queuing systems with preemptive priorities and two classes of customers is provided in another note on the website We shall skip Section 4.8 in the book except for a brief discussion at end of this lecture you may wish to skim through the section
A few additional items • A simpler (than in the book) derivation of the expression for L for M/G/1 systems is provided in a note on the website; it assumes FIFO service • A derivation of expression (4.113) in the book for M/M/1 queuing systems with preemptive priorities and two classes of customers is provided in another note on the website • We shall skip Section 4.8 in the book except for a brief discussion at end of this lecture; you may wish to skim through the section
Lecture outline Introduction to systems with priorities Representation of a priority queuing system The M/G/ non-preemptive priority system An important optimization theorem and an important corollary Brief mention of other priority systems Bounds for G/G/1 systems A numerical example
Lecture Outline • Introduction to systems with priorities • Representation of a priority queuing system • The M/G/1 non-preemptive priority system • An important optimization theorem • … and an important corollary • Brief mention of other priority systems • Bounds for G/G/1 systems • A numerical example
Background and observations W, L, Waand la are not affected as long as the queue discipline does not give priority to certain classes of customers WEIFOWSIRO= WLIFo (What about the corresponding variances?) Things may change, however, in systems where customers are assigned to various priority classes, if different classes have different service-time characteristics Preemptive VS non-preemptive priority systems Preemptive-resume Vs. preemptive-repeat
Background and observations • W, L, Wq and Lq are not affected as long as the queue discipline does not give priority to certain classes of customers • WFIFO = WSIRO = WLIFO (what about the corresponding variances?) • Things may change, however, in systems where customers are assigned to various priority classes, if different classes have different service-time characteristics • Preemptive vs. non-preemptive priority systems • Preemptive-resume vs. preemptive-repeat