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Submitted by: 
Varsha Anandani (13MIT0062)
 
TCP = Transmission Control Protocol 
 Connection-oriented protocol 
 Provides a reliable unicast end-to-end byte 
stream over an unreliable internetwork
TCP 

Motivation for mathematical 
modeling of TCP 
 
 1) The sheer scale of systems in which we find 
TCP operating is tremendous. 
 2) There still remain many unknowns in the 
environment in which TCP is operating. 
 3) TCP was not designed using optimization.
Motivation for TCP Modeling 
 
TCP operating scale is very large 
 Models are required to gain deeper 
understanding of TCP dynamics 
Uncertainties can be modeled as 
stochastic processes 
Drive the design of TCP-friendly 
algorithms for multimedia applications 
Optimize TCP performance
FACTORS THAT AFFECT THROUGHPUT 
 Link speed 
 
 the number of bits per second that can be transmitted. 
 Propagation delay, 
 the time it takes the actual electronic, optical, or other 
signals 
 to travel from one end of the connection to the other. 
 Window size, 
 the amount of unacknowledged data that can be 
outstanding on a 
 TCP connection. 
 Link reliability. 
 Network and intermediate device congestion. 
 Path maximum transmission unit (PMTU).
TCP Modeling 
Essentials 
 
 Mainly Reno flavors are modeled 
 Two main features are modeled 
 Window dynamics 
 Packet loss process
Window Dynamics 
 
 Linear increase and multiplicative decrease is 
modelled. 
 The standard assumption 
 X(t) = W(t)/RTT
Packet Loss Process 
 
 Packet loss triggers window decrease 
 Packet loss is uncertain 
 This uncertainty is typically modeled as a 
stochastic process 
 E.g. probability p of losing a packet
Gallery of TCP Models 
 
 Periodic model 
 Detailed packet loss model 
 Finite state machine 
 Fluid flow model 
 And others…
Periodic Model 
 
 Simplest model for 
TCP 
 No specific 
version 
assumed 
 Assumes a periodic 
pattern of 
congestion window 
 X(p) = 
(1/RTT)*Root(3/2p) 
 P is the packet 
loss probability
TCP Congestion Control: window 
algorithm 
 
Window: can send W packets 
 increase window by one per RTT if no loss, W <- W+1 
each RTT 
 decrease window by half on detection of loss W <- W/2 
receiver 
W 
sender 
1 RTT
TCP throughput/loss relationship 
 
Idealized model: 
 W is maximum supportable 
window size (then loss 
occurs) 
 TCP window starts at w/2 
grows to W, then halves, 
then grows to W, then 
halves… 
 one window worth of packets 
each rtt 
 to find: throughput as 
function of loss, RTT 
W 
TCP 
window 
size 
time (rtt) 
W/2 
loss occurs 
period
period 
# packets sent per “period” 
1 
1 
3 
 W  W  W 
2 2 2 
8 
8 
4
Example 1 - Question 
 
If a TCP connection has an average 
RTT of 200ms, and packet loss 
probability 0.05, what is the average 
throughput?
Tcp periodic modeling

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Tcp periodic modeling

  • 1. Submitted by: Varsha Anandani (13MIT0062)
  • 2.  TCP = Transmission Control Protocol  Connection-oriented protocol  Provides a reliable unicast end-to-end byte stream over an unreliable internetwork
  • 4. Motivation for mathematical modeling of TCP   1) The sheer scale of systems in which we find TCP operating is tremendous.  2) There still remain many unknowns in the environment in which TCP is operating.  3) TCP was not designed using optimization.
  • 5. Motivation for TCP Modeling  TCP operating scale is very large  Models are required to gain deeper understanding of TCP dynamics Uncertainties can be modeled as stochastic processes Drive the design of TCP-friendly algorithms for multimedia applications Optimize TCP performance
  • 6. FACTORS THAT AFFECT THROUGHPUT  Link speed   the number of bits per second that can be transmitted.  Propagation delay,  the time it takes the actual electronic, optical, or other signals  to travel from one end of the connection to the other.  Window size,  the amount of unacknowledged data that can be outstanding on a  TCP connection.  Link reliability.  Network and intermediate device congestion.  Path maximum transmission unit (PMTU).
  • 7. TCP Modeling Essentials   Mainly Reno flavors are modeled  Two main features are modeled  Window dynamics  Packet loss process
  • 8. Window Dynamics   Linear increase and multiplicative decrease is modelled.  The standard assumption  X(t) = W(t)/RTT
  • 9. Packet Loss Process   Packet loss triggers window decrease  Packet loss is uncertain  This uncertainty is typically modeled as a stochastic process  E.g. probability p of losing a packet
  • 10. Gallery of TCP Models   Periodic model  Detailed packet loss model  Finite state machine  Fluid flow model  And others…
  • 11. Periodic Model   Simplest model for TCP  No specific version assumed  Assumes a periodic pattern of congestion window  X(p) = (1/RTT)*Root(3/2p)  P is the packet loss probability
  • 12. TCP Congestion Control: window algorithm  Window: can send W packets  increase window by one per RTT if no loss, W <- W+1 each RTT  decrease window by half on detection of loss W <- W/2 receiver W sender 1 RTT
  • 13. TCP throughput/loss relationship  Idealized model:  W is maximum supportable window size (then loss occurs)  TCP window starts at w/2 grows to W, then halves, then grows to W, then halves…  one window worth of packets each rtt  to find: throughput as function of loss, RTT W TCP window size time (rtt) W/2 loss occurs period
  • 14. period # packets sent per “period” 1 1 3  W  W  W 2 2 2 8 8 4
  • 15. Example 1 - Question  If a TCP connection has an average RTT of 200ms, and packet loss probability 0.05, what is the average throughput?