1. Queueing Systems They’re EVERYWHERE!

2. Basic Concept Service Request... Done Numerous requests made for service Lines back up waiting for service Waiting times increase non-linearly

3. Consider a perfect system Customers arrive in optimal fashion CustomerArrives at Service Required 12341234 0 10 16 24 10 6 8 7 Never any waiting time. Perfect resource utilization.

4. Consider a REALISTIC system Customers arrive in NON-optimal fashion CustomerArrives at Service Required 12341234 Slightly different problem. NOTE: arrival rate results in wait/delay. Start Wait 0 15 21 29 05650565 End 15 21 29 36 0 10 15 24 15 6 8 7

5. Practical comparisons Business waiting lines Homework assignments waiting completion Bills waiting to be paid by your income Fans trying to get into the stadium for seating at a sporting event Need for legislation waiting proper processing required by legislators

6. Characterizing Queueing System load Arrival rates and inter-arrival sequences Waiting line length Waiting time Time to go through the system Resource utilization

7. Basic tradeoff ! Desires –Customer: low waiting time (none if possible) –Resource owner: high utilization Reality –high utilization -> many demands -> waiting lines –low utilization -> low demand -> underutilized resources Tradeoff –high resource utilization –short wait time

8. Non-linear results The tradeoff RATE goes up significantly as demand goes up. 10% increase in load -> more than 75% increase in delay. load Wait time 50%100%

9. How does this relate to Communications? Demand : messages waiting delivery Resource : network capacity Desires: –low waiting time/delay (users don’t like waiting) –high utilization (networks are expensive) Reality: must under-utilize to have reasonable wait time and delay Use previous figure : 70% utilization –10Mbps becomes 7Mbps More Overhead