1. ECEN4533 Data Communications Lecture #1818 February 2013 Dr. George Scheets n Problems: 2011 Exam #1 n Corrected Design #1 u Due 18 February (Live) u 1 week after you get them back (DL) n Exam #1: 22 February (Live), < 1 March (DL)

2. ECEN4533 Data Communications Lecture #1920 February 2013 Dr. George Scheets n Read 11.1 - 11.3 n Problems: 2012 Exam #1 n Exam #1 22 February (Live), < 1 March (DL)

3. Possible Test Topics S Reading HW Lectures Anything in the circles is fair game.

4. Exponentially Distributed Packet Length (Somewhat decent fit to real world traffic) Bytes Bin Count

5. Little's Rule n Under steady-state conditions E[K(t)] = λ E[T] E[Kq(t)] = λ E[Tq] E[# in server] = λ E[Ts] regardless of PDF's involved.

6. M/G/1 n Exponentially distributed IAT n Arbitrary packet size distribution n Single Server n E[Tq] = E[Ts 2 ]/[2(1-ρ)] n E[Ts 2 ] = σ Ts 2 + E[Ts] 2

7. M/M/1 Queues n Exponentially Distributed IAT's n Exponentially Distributed Packet Sizes u E[Ts] = σ Ts if Exponential n Single Server n E[Tq] = ρE[Ts]/(1-ρ) n Multiple Input, Multiple Output Switch? u Repeat analysis once per output trunk u Base on input traffic exiting that trunk

8. Classical M/M/1 Queuing Theory 0% 100% Offered Load Average Queue Size Dropped Packet Probability

9. Finite Buffer Queuing Performance 0% 100% Trunk Offered Load Probability of dropped packets Average Delay for delivered packets

10. M/M/a Queues n Exponentially Distributed IAT's n Exponentially Distrubuted Packets n Multiple Servers (# = a) u Queue servicing "a" output trunks u Trunks have identical loads n M/M/1 versus equal speed M/M/a u EX) M/M/1 @ 100 Mbps had E[T] = 172.5 μsec M/M/2 @ 2x50 Mbps had E[T] = 185.4 μsec u Want a big trunk to minimize delay thru switch

11. M/M/1 Queues with Priorities n Exponentially Distributed IAT's n Exponentially Distrubuted Packets n Single Server n Hi priority traffic to head of queue u Gets output more speedily u Packet is server is not prempted n Low priority traffic slower to exit n Overall average ≈ same as M/M/1

12. Queuing with Priorities 0% 100% Offered Load High Priority Average Delay M/M/1 Low Priority Overall Average Stays ≈ the Same

13. M/D/1 Queues n Exponentially Distributed IAT's n Fixed Packet Size (i.e. Cells) n Single Server n E[Tq] = ρ[Ts]/[2(1-ρ)] n Given equivalent loads and same average sizes, fixed size cells are moved faster.

14. Classical Queuing Theory 0% 100% Offered Load M/D/1 ρ 2 /(1-ρ) M/M/1 ρ/(1-ρ) Average # in System

15. Armed with n The average service time E[Ts] n An equation for E[Time in Queue] or E[Time in System] n Little's Rule u Average # packets = E[Time] E[Packet Arrival Rate] where E[Packet Arrival Rate] = λ packets/second n You can find a large number of parameters u E[T], E[Tq], E[K(t)], E[Kq(t)]