PPT-Introduction to 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. Louis Queueing Queueing Networks Networks Raj Jain Washington University in Saint Louis Saint Louis MO 63130 Jaincsewustledu AudioVideo recordings of th is lecture are available at httpwwwcsewustledujaincse56708 brPage 2br 322 2008 Raj Jain CSE5 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 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. Internet congestion control. Damon . Wischik. , UCL. Mark Handley, UCL. Gaurav. . Raina. , Cambridge / IIT Madras. A little bit about me. I did a PhD in mathematics at Cambridge and I continued there afterwards as a research fellow. 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?. 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 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 . A Scalable Architecture to Approximate Fair Bandwidth Allocations in High Speed Networks. Ion . Stoica. , Scott . Shenker. , and . Hui. Zhang. SIGCOMM’98, Vancouver, August 1998. subsequently. IEEE/ACM Transactions on Networking 11(1), 2003, pp. 33-46.. (Part 1). Nikhil Bansal (TU Eindhoven). Adam Wierman (Caltech). Scheduling. Competitive Analysis . Queueing. Relative. to best . Absolute. guarantees . Worst case . inputs . of Queues and Networks. Yoni . Nazarathy. Swinburne University of Technology, Melbourne.. Based on collaborations with . . Ahmad Al . Hanbali. , Daryl Daley, . Michel . Mandjes. ,. Gideon Weiss and Ward Whitt. 01623 62929501623 629275COVO-RAIL153Outdoor queuing But the weather hasn146tNational DistributionRapid InstallationBritish Made