Post on 30-Dec-2015
description
Application of QueuingTheory to Data
Communications Systems
Queuing Theory for Data:End-to-End Delays
Three Useful Models of System Delay:
1. Applicable end-to-end queuing delay = Taq or tot. queuing delay experienced by a block
2. Block turnaround time = Tta or tot. turn-around time experienced by a block
3. “Bid-to-start of message” = BST or the totaldelay measured from bid to the SOM.
–Time
T
T
T
T
R
R
R
R
DTE
PS2
PS1
Host
BST
K1
K2
A Time Chart for Modeling Response Time
HTT
Queuing Theory for Data:Nodal Queuing Times
PS Node: E ( Tq ) =E ( Tq1 )+E ( Tq2 )
Input Process 1:(assume M/D/1 queue)
E ( Tq1 ) = [Ts1 (2- /[2 (1-)]
Output Process 2:(assume M/D/1 queue)
E ( Tq2 ) = [Ts2 (2- /[2 (1-)]
where Tqi , Tsi and i represent ith server(i=1, 2) i.e. PS-CPU and a single outputline.
Queuing Theory for DATA:Nodal Queuing Times
Fast Packet Switch (FPS) & Frame-Relay:
E( Tq )= 0 .... pass through packet
E( Tq )=[ s ...local packet
where andare netlink utilizationscaused by pass through and local trafficssuch that + =
FPS
SNA Data Nets: Avg. BTS Delay
BTS=E(D)= (W/2)[1-/N]/(1 -)+Tmm/(1 -)
This is equivalent to Equation 4.21 of TEXTwhere
= Avg. utilization of the shared netlink
= Nm..... is msg. arrival rate/contrllr
Tmm=EMD=exp. msg. duration=m
N=No. of controllers per netlink
W=walk time (Idle poll of N controllers).
SNA Networks: Avg. Walk Time
Avg. Walk Time for SNA with host polling:
W=4N(Tnp) +2N(Tpm)+2N(Tm)+N+1)/2
Avg. Walk Time for SNA with hub polling:
W=4N(Tnp) +2N(Tpm)+2N(Tm)+where Tnp is nodal msg. processing time, Tpm is
poll message transmit time, Tm is modem timeand is propagation time on the entirenetlink consisting of N controllers.
Note: Above 4 Eqtns. are from M. Schwartz’s Text.
Queuing Theory for DATA:Block Turnaround Times
SNA Application: N controllers on netlink.
Tta = 4NTnp+ +2N(Tm+2Tpm)
FPS Application:N FPSs sharing a netlink.
Tta 4Tnp+ + 2N(Tm + 2Tmm)
where Tnp=nodal processing time, Tm ismodem time, is the 2-way propagationtime on the netlink, Tpm is poll messagetransmit time and Tmm is packet/blocktransmit time. FPS uses nodal bypass.
X.25 PS System:Block TA Time
• Tta=4NTnp +N+1)/2 +N(Tm+Tmm)
where
Tta= block turnaround time
Tnp=nodal processing time
Tm=modem time
Tmm=packet/block time
= 2-way propagation time
Note: Tnp includes ACK and NAK times
LANs:Shared Media Utilization
Considering two extreme cases when (A)only one node is active and (B) N nodes areactive, one can compute the maximummean throughput rate in bits per second:
1. Token Ring (TR) LAN as employed inoffice environements:
Rp= Lm /[Tmsg +Tp +N*Tint]bps....Case A
Rp= Lm /[Tmsg +Tint + Tp/N]bps ....Case B
LANs:Shared Media Utilization
Considering two extreme cases when (A)only one node is active and (B) N nodes areactive, one can compute the maximum meanthroughput rate in bits per second:
2. Token Bus LAN as employed inmanufacturing environments:
Rp= Lm /[Tmsg +N*(Tint+Tp]bps....Case A
Rp= Lm /[Tmsg +Tint + Tp]bps ..... Case B
LANs Shared Media Utilization
Considering two extreme cases when (A) onlyone node is active and (B) N nodes areactive, one can compute the maximum meanthroughput rate in bits per second:
3. CSMA/CD LAN as employed in offices:
Rp = Lm /[Tmsg +Tifg] .... Case A
Rp = Lm /[Tmsg +Tifg +(2e-1)( Ts+ Tj)] ..... Case B
where Tifg ,Ts and Tj are interframe gap, slotand jam times respectively
LANs Shared Media Utilization
Assumptions:
1. N =100
2. Only onenode active
3. Packet/Msgsize=2000 bits
10
5
02515 201050
20
25
15
Rp
Media capacity (Mbps)
(Mbps)
TR
TBus
CSMA/CD
LANs Shared Media Utilization
10
5
02515 201050
20
25
15
Rp
Media capacity (Mbps)
(Mbps)
Assumptions:
1. N =100
2. All nodesare active
3. Packet/Msgsize=2000 bits CSMA/CD
TR
TBus
LANs Performance (Contd.)
1. LAN performance for any given operatingenvironment is almost impossible to analyzeusing analytical simulation.
2. Simplified analytical models can be createdand when combined with a spreadsheet canprovide meaningful answers for simple set ofoperating environs.
3. Computer simulation can be employedjudiciously to derive useful analytical modelsaccording to the scheme discussed earlier.
50*Ts
0. 5
25
00 1
Aloha U
AlohaS CSMA/CD
TR X.25
FPS
* X.25 & FPS have 10 link-nodes* TR for*CSMA/CD for = 0.1 and 0.05
= Tp/Ts
where Tp =prop. time
Ts=slot. time
= (Tp+N*Tint)/Ts
Legend:
AlohaU for Unslotted,
AlohaS for Slotted,
TR =Token Ring
FPS =Fast PS
LANs/WANs Performance Vs.
0.1 .05
shared media load
1-way delay
Class Assignments
1. Redraw Figure 4.4 for=0.75
2. Redraw Figure 4.5 for=0.75