PPT-Queueing

Theory Lindsay Mullen Seminar Presentation 2 November 4 2013 Computer Science Applied Mathematics Discrete Mathematics Operation Research Queueing Theory Operation Research. 1 Introduction Todays computer systems are more complex more rapidly evolving and more essential to the conduct of business than those of even a few years ago The result is an increasing need for tools and techniques that assist in understanding the bonaldfrancetelecomcom Abstract rich class of communication netw orks can be ep esented as queueing netw orks with statedependent arri al rates and ser vice rates pr vide necessary and suf64257cient conditions or such queueing netw orks to be insensi We now turn our attention to closed networks Closed Queueing Models Closed networks are extremely important for computer systems modeling because they capture the notion of interactivity in the system In an open network customers simply arrive recei and. Resource Allocation. Lecture material taken from. “Computer Networks . A Systems Approach. ”, Third . Edition,Peterson. and Davie,. Morgan Kaufmann, . 2007. .. Advanced Computer Networks. Congestion Control Outline. Queueing. Theory. Math 319. Prof. Andrew Ross. Eastern Michigan University. What is . Queueing. Theory?. A queue = a line of people or things waiting to be served. Queueing. Theory: ways of predicting how long the line or the wait will be, or deciding on how many servers to have. Theory. Average person spends almost 6 months of their lifetime in queues;. . 3 days a year.. Examples of Queues. What’s the longest you’ve waited in line for something?. Has anybody left a queue early because it was taking too long?. )()()(1100tPqtPdttdP (1) 1211[(1)]()()()()dPtqnpPtqnpPtPtλ Queueing theory in manufacturing: A survey Manish K Govil; Michael C Fu Journal of Manufacturing Systems; 1999; pg. 214 Reproduced with permission of the copyright owner. Further reproduction prohi Performance Scaling . and Algorithmic Challenges. Instructor: Yuan Zhong; . yz2561@columbia.edu. Class: . Mudd. 627, MW 2:40 – 3:55pm. Office hour: Fri 4 – 6pm; . Mudd. 344 (or by appointment). Supplementary discussions. From . Taha’s. Book. Pure birth model. We only allow random arrivals. No departures..  . Recall Poisson distribution:. Let . X. be the number of arrivals that take place during a specified time unit (e.g., one minute). Junxian Huang. 1. . Feng. . Qian. 2. Yihua. Guo. 1. . Yuanyuan. Zhou. 1 . . Qiang. Xu. 1. Z. . Morley Mao. 1 . . Subhabrata. Sen. 2. Oliver . Spatscheck. 2. 1. Hakim Weatherspoon. Associate Professor, . Dept. of Computer Science. CS 5413: High Performance Computing and Networking. March 6, 2017. buffering when arrival rate via switch exceeds output line speed. Resource . Disaggregation. Peter . Gao. (Berkeley), . Akshay. Narayan (MIT), . Sagar. . Karandikar. (. Berkeley), . Joao . Carreira. (. Berkeley), . Sangjin. Han (. Berkeley), . Rachit. Agarwal (Cornell), Sylvia . Credit: . Bill . Nace. traceroute. QT Overview. Performance Evaluation. Little’s Law. Rate Transition Diagrams. M/M/1 Systems. M/M/c Systems. Examples. 2. Queueing Theory . An analytic tool to make performance statements about .