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Computer Architecture II: Specialized 0909.444.01/02 Fall 2001

Computer Architecture II: Specialized 0909.444.01/02 Fall 2001. Lecture 5 November 8, 2001. John L. Schmalzel Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall01/comparch2/. Plan. Queuing Theory for Packet Transmission Model Attributes

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Computer Architecture II: Specialized 0909.444.01/02 Fall 2001

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  1. Computer Architecture II: Specialized0909.444.01/02Fall 2001 Lecture 5November 8, 2001 John L. Schmalzel Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall01/comparch2/

  2. Plan • Queuing Theory for Packet Transmission • Model Attributes • Single server queue • Arrival Process • Service Process • Performance Parameters

  3. Queuing Theory for Packet Transmission Attributes of a Queue • Interarrival-time pdf • Service-time pdf • Number of servers • Queuing discipline • Buffer (waiting) space

  4. Queue Server Mean arrival rate l customers/sec Mean service rate m customers/sec Single Server Queue

  5. Probability of m arrivals in time t Probability of occurrence of queue length n Average delay Average queue length Average arrival rate Utilization factor 7 Number joined queue by time t Service time For 2nd customer 6 5 Queuing time For 2nd customer Length of queue between t4 and t5’ 4 Number of customers 3 Number served by time t 2 Waiting time For 2nd customer 1 Time Arrivals Departures (service) 0 t1 t2 t3 t4 t5 t6 t1’ t2’ t3’ t4’ t5’ t6’ Queue Performance

  6. Queue (1-ldt) Mean arrival rate l customers/sec A A A A A A A A Pj Pj+1 Pj-1 ldt ldt Time t t dt The Arrival Process Random interarrival-times Markov model

  7. Summary

  8. References • I. A. Glover and P. M. Grant, Digital Communications, Prentice-Hall, 1998. • Jean Walrand, Communication Networks, 2nd Edition, WCB/McGraw-Hill, 1998.

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