1. S. Mandayam/ CompArch2/ECE Dept./Rowan University Computer Architecture II: Specialized 0909.444.01/02 Fall 2001 John L. Schmalzel Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall01/comparch2/ Lecture 5 November 8, 2001

2. S. Mandayam/ CompArch2/ECE Dept./Rowan UniversityPlan Queuing Theory for Packet Transmission Model Attributes Single server queue Arrival Process Service Process Performance Parameters

3. S. Mandayam/ CompArch2/ECE Dept./Rowan University Queuing Theory for Packet Transmission Attributes of a Queue Interarrival-time pdf Service-time pdf Number of servers Queuing discipline Buffer (waiting) space

4. S. Mandayam/ CompArch2/ECE Dept./Rowan University Single Server Queue Mean arrival rate customers/sec Mean service rate  customers/sec Server Queue

5. S. Mandayam/ CompArch2/ECE Dept./Rowan University Queue Performance Probability of m arrivals in time t Probability of occurrence of queue length n Average delay Average queue length Average arrival rate Utilization factor 0 1 2 3 4 5 6 7 t 1 t 2 t 3 t 4 t 5 t 6 t 1 ’ t 2 ’ t 3 ’ t 4 ’ t 5 ’ t 6 ’ Number of customers Time Arrivals Departures (service) Queuing time For 2 nd customer Waiting time For 2 nd customer Service time For 2 nd customer Number joined queue by time t Number served by time t Length of queue between t 4 and t 5 ’

6. S. Mandayam/ CompArch2/ECE Dept./Rowan University The Arrival Process Mean arrival rate customers/sec Queue P j-1 tt PjPj P j+1 tt  t) Markov model Time A AAAA AA A  tt t Random interarrival-times

7. S. Mandayam/ CompArch2/ECE Dept./Rowan UniversitySummary

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