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Queuing Theory in Packet Transmission: Key Concepts and Performance Metrics

This lecture focuses on the fundamentals of queuing theory as applied to packet transmission in computer networks. Key topics include the attributes of a queue, arrival and service processes, and performance parameters such as average delay, queue length, and utilization factor. The lecture explores single-server queue models, the impact of interarrival and service times, and provides insights into probability distributions related to queue lengths and wait times. References for further reading are also included to enhance understanding of these critical concepts in computer architecture.

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Queuing Theory in Packet Transmission: Key Concepts and Performance Metrics

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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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