ECEN4533 Data CommunicationsLecture #18 18 February 2013Dr. George Scheets

Problems: 2011 Exam #1Problems: 2011 Exam #1 Corrected Design #1Corrected Design #1

Due 18 February (Live)Due 18 February (Live) 1 week after you get them back (DL)1 week after you get them back (DL)

Exam #1: 22 February (Live), Exam #1: 22 February (Live), << 1 March (DL) 1 March (DL)

ECEN4533 Data CommunicationsLecture #19 20 February 2013Dr. George Scheets

Read 11.1 - 11.3Read 11.1 - 11.3 Problems: 2012 Exam #1Problems: 2012 Exam #1 Exam #1Exam #1

22 February (Live)22 February (Live), , << 1 March (DL) 1 March (DL)

Possible Test Topics

S

Reading HW

Lectures

Anything in the circles is fair game.

Exponentially Distributed Packet Length(Somewhat decent fit to real world traffic)

Bytes

BinCount

Little's Rule

Under steady-state conditionsUnder steady-state conditions

E[K(t)] = E[K(t)] = λλ E[T] E[T]E[Kq(t)] = E[Kq(t)] = λλ E[Tq] E[Tq]E[# in server] = E[# in server] = λλ E[Ts] E[Ts]

regardless of PDF's involved.regardless of PDF's involved.

M/G/1

Exponentially distributed IATExponentially distributed IAT Arbitrary packet size distributionArbitrary packet size distribution Single ServerSingle Server

E[Tq] = E[TsE[Tq] = E[Ts22]/[2(1-]/[2(1-ρρ)])] E[TsE[Ts22] = ] = σσTsTs

22 + E[Ts] + E[Ts]22

M/M/1 Queues Exponentially Distributed IAT'sExponentially Distributed IAT's Exponentially Distributed Packet SizesExponentially Distributed Packet Sizes

E[Ts] = E[Ts] = σσTsTs if Exponential if Exponential Single ServerSingle Server

E[Tq] = E[Tq] = ρρE[Ts]/(1-E[Ts]/(1-ρρ))

Multiple Input, Multiple Output Switch?Multiple Input, Multiple Output Switch? Repeat analysis once per output trunkRepeat analysis once per output trunk Base on input traffic exiting that trunkBase on input traffic exiting that trunk

Classical M/M/1 Queuing Theory

0% 100%Offered Load

AverageQueue

Size

DroppedPacket

Probability

Finite Buffer Queuing Performance

0% 100%Trunk Offered Load

Probability of dropped packets

Average Delay fordelivered packets

M/M/a Queues Exponentially Distributed IAT'sExponentially Distributed IAT's Exponentially Distrubuted PacketsExponentially Distrubuted Packets Multiple Servers (# = a)Multiple Servers (# = a)

Queue servicing "a" output trunksQueue servicing "a" output trunks Trunks have identical loadsTrunks have identical loads

M/M/1 versus equal speed M/M/aM/M/1 versus equal speed M/M/a EX) M/M/1 @ 100 Mbps had E[T] = 172.5 EX) M/M/1 @ 100 Mbps had E[T] = 172.5 μμsec sec

M/M/2 @ 2x50 Mbps had E[T] = 185.4 M/M/2 @ 2x50 Mbps had E[T] = 185.4 μμsec sec Want a big trunk to minimize delay thru switchWant a big trunk to minimize delay thru switch

M/M/1 Queues with Priorities Exponentially Distributed IAT'sExponentially Distributed IAT's Exponentially Distrubuted PacketsExponentially Distrubuted Packets Single ServerSingle Server

Hi priority traffic to head of Hi priority traffic to head of queuequeue Gets output more speedilyGets output more speedily Packet is server is not premptedPacket is server is not prempted

Low priority traffic slower to exitLow priority traffic slower to exit Overall average ≈ same as M/M/1Overall average ≈ same as M/M/1

Queuing with Priorities

0% 100%Offered Load

HighPriority

AverageDelay

M/M/1LowPriority

Overall AverageStays ≈ the Same

M/D/1 Queues Exponentially Distributed IAT'sExponentially Distributed IAT's Fixed Packet Size (i.e. Cells)Fixed Packet Size (i.e. Cells) Single ServerSingle Server

E[Tq] = E[Tq] = ρρ[Ts]/[2(1-[Ts]/[2(1-ρρ)])]

Given equivalent loads and same average Given equivalent loads and same average sizes, fixed size cells are moved faster.sizes, fixed size cells are moved faster.

Classical Queuing Theory

0% 100%Offered Load

M/D/1ρ2/(1-ρ)

M/M/1ρ/(1-ρ)

Average# in

System

Armed with The average service time E[Ts]The average service time E[Ts] An equation for E[Time in Queue] or An equation for E[Time in Queue] or

E[Time in System]E[Time in System] Little's RuleLittle's Rule

Average # packets = E[Time] Average # packets = E[Time] E[Packet Arrival Rate]E[Packet Arrival Rate]where E[Packet Arrival Rate] = where E[Packet Arrival Rate] = λλ packets/second packets/second

You can find a large number of parametersYou can find a large number of parameters E[T], E[Tq], E[K(t)], E[Kq(t)]E[T], E[Tq], E[K(t)], E[Kq(t)]