Queueing Systems They’re EVERYWHERE!

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

Consider a perfect system Customers arrive in optimal fashion CustomerArrives at Service Required Never any waiting time. Perfect resource utilization.

Consider a REALISTIC system Customers arrive in NON-optimal fashion CustomerArrives at Service Required Slightly different problem. NOTE: arrival rate results in wait/delay. Start Wait End

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

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

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

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%

Ideal results With perfect scheduling, the delay is ZERO until saturation load Wait time 50%100% A steady-state solution reveals infinite wait. If 1 minute behind after one day, 2 minutes after 2 days, minutes after 100 days, only stops at infinity (after saturation)

Difference is customer arrival load Wait time 50%100%

Different Typical View Offered load Throughput 50%100% 50% 100% 150% ideal realistic

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

Reasonable Response Another requirement which costs us bandwidth. Typical in most computing systems. Another example: disk space –high utilization creates long access/response times –takes longer to insert a file (defragging helps)

Be Able To: Identify the fundamental components in an everyday example –resource : your time –demand : homework assignments –arrival rate : order in which assignments given –utilization : how much of your time is busy doing school work –delay : how long to complete assignments

Results Remember that results are statistical average(mean) and standard deviation are both important